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+++ b/docs/cancer.html
@@ -4,18 +4,18 @@
 
   <meta charset="utf-8" />
   <meta http-equiv="X-UA-Compatible" content="IE=edge" />
-  <title>Chapter 7 Cancer genomics and epidemiology | Biomedical Data Science - introduction with case studies</title>
+  <title>Chapter 6 Cancer genomics and epidemiology | Biomedical Data Science - introduction with case studies</title>
   <meta name="description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
   <meta name="generator" content="bookdown 0.35 and GitBook 2.6.7" />
 
-  <meta property="og:title" content="Chapter 7 Cancer genomics and epidemiology | Biomedical Data Science - introduction with case studies" />
+  <meta property="og:title" content="Chapter 6 Cancer genomics and epidemiology | Biomedical Data Science - introduction with case studies" />
   <meta property="og:type" content="book" />
   
   <meta property="og:description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
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   <meta name="twitter:card" content="summary" />
-  <meta name="twitter:title" content="Chapter 7 Cancer genomics and epidemiology | Biomedical Data Science - introduction with case studies" />
+  <meta name="twitter:title" content="Chapter 6 Cancer genomics and epidemiology | Biomedical Data Science - introduction with case studies" />
   
   <meta name="twitter:description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
   
@@ -23,14 +23,14 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
   <meta name="apple-mobile-web-app-status-bar-style" content="black" />
   
   
-<link rel="prev" href="infectious-dis.html"/>
+<link rel="prev" href="image-digital.html"/>
 <link rel="next" href="pop-genetics.html"/>
 <script src="libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
 <script src="https://cdn.jsdelivr.net/npm/fuse.js@6.4.6/dist/fuse.min.js"></script>
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
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 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -359,10 +360,10 @@ <h1>
           <div class="page-inner">
 
             <section class="normal" id="section-">
-<div id="cancer" class="section level1 hasAnchor" number="7">
-<h1><span class="header-section-number">Chapter 7</span> Cancer genomics and epidemiology<a href="cancer.html#cancer" class="anchor-section" aria-label="Anchor link to header"></a></h1>
-<div id="cancer-case1" class="section level2 hasAnchor" number="7.1">
-<h2><span class="header-section-number">7.1</span> Case study 1: analysis of cBioportal mutation data<a href="cancer.html#cancer-case1" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="cancer" class="section level1 hasAnchor" number="6">
+<h1><span class="header-section-number">Chapter 6</span> Cancer genomics and epidemiology<a href="cancer.html#cancer" class="anchor-section" aria-label="Anchor link to header"></a></h1>
+<div id="cancer-case1" class="section level2 hasAnchor" number="6.1">
+<h2><span class="header-section-number">6.1</span> Case study 1: analysis of cBioportal mutation data<a href="cancer.html#cancer-case1" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p>Non-small cell lung cancer is a deadly disease, and we would like to identify
 mutations in genes that drive its formation and progression.
 George et al. (2015) has sequenced 120 small cell lung cancer samples and this
@@ -374,8 +375,8 @@ <h2><span class="header-section-number">7.1</span> Case study 1: analysis of cBi
 frequently mutated in non-small cell lung cancer samples.
 We will implement a simple method for identifying candidate tumour suppressors
 based on loss-of-function mutations.</p>
-<div id="exploratory-analysis" class="section level3 hasAnchor" number="7.1.1">
-<h3><span class="header-section-number">7.1.1</span> Exploratory analysis<a href="cancer.html#exploratory-analysis" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="exploratory-analysis" class="section level3 hasAnchor" number="6.1.1">
+<h3><span class="header-section-number">6.1.1</span> Exploratory analysis<a href="cancer.html#exploratory-analysis" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p><strong>Q1</strong>. Load the data named <code>mutations_sclc_ucologne_2015.rds</code> into R.
 Examine it using <code>head</code>.
 In this <code>data.frame</code>, each row is a mutation detected in a particular gene
@@ -433,8 +434,8 @@ <h3><span class="header-section-number">7.1.1</span> Exploratory analysis<a href
 <div class="sourceCode" id="cb142"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb142-1"><a href="cancer.html#cb142-1" tabindex="-1"></a><span class="co"># gene.counts &lt;- table(???, ???);</span></span>
 <span id="cb142-2"><a href="cancer.html#cb142-2" tabindex="-1"></a><span class="co"># gene.counts[???, ]</span></span></code></pre></div>
 </div>
-<div id="statistical-analysis" class="section level3 hasAnchor" number="7.1.2">
-<h3><span class="header-section-number">7.1.2</span> Statistical analysis<a href="cancer.html#statistical-analysis" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="statistical-analysis" class="section level3 hasAnchor" number="6.1.2">
+<h3><span class="header-section-number">6.1.2</span> Statistical analysis<a href="cancer.html#statistical-analysis" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>Here, we implemented a simple statistical test for assessing whether a
 gene is significantly frequently targeted by loss-of-function mutations,
 based on the Fisher’s exact test.</p>
@@ -493,8 +494,8 @@ <h3><span class="header-section-number">7.1.2</span> Statistical analysis<a href
 false discovery rate of 5% (i.e. q-value threshold of 0.05).</p>
 <p><strong>Q17</strong>. Look up the significant genes in the <code>gene.counts</code> matrix.</p>
 </div>
-<div id="literature-search" class="section level3 hasAnchor" number="7.1.3">
-<h3><span class="header-section-number">7.1.3</span> Literature search<a href="cancer.html#literature-search" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="literature-search" class="section level3 hasAnchor" number="6.1.3">
+<h3><span class="header-section-number">6.1.3</span> Literature search<a href="cancer.html#literature-search" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p><strong>Q18</strong>. Do the significant genes appear to be involved in cancer?
 What general roles do they play?</p>
 <p><strong>Q19</strong>. How do these genes contribute specifically to the formation
@@ -503,14 +504,14 @@ <h3><span class="header-section-number">7.1.3</span> Literature search<a href="c
 by mutations or other genomic alterations?</p>
 </div>
 </div>
-<div id="cancer-case2" class="section level2 hasAnchor" number="7.2">
-<h2><span class="header-section-number">7.2</span> Case study 2: Cancer Epidemiology<a href="cancer.html#cancer-case2" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="cancer-case2" class="section level2 hasAnchor" number="6.2">
+<h2><span class="header-section-number">6.2</span> Case study 2: Cancer Epidemiology<a href="cancer.html#cancer-case2" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p><em>by Dr Jason Wong</em></p>
 <p><em>Date: 6-11-2023</em></p>
 <p><a href="https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/M5-epidemiology.Rmd">The RMarkdown notebook to run your own code can be downloaded here</a></p>
 </div>
-<div id="scenario" class="section level2 hasAnchor" number="7.3">
-<h2><span class="header-section-number">7.3</span> 1. Scenario<a href="cancer.html#scenario" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="scenario" class="section level2 hasAnchor" number="6.3">
+<h2><span class="header-section-number">6.3</span> 1. Scenario<a href="cancer.html#scenario" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p>You are a grants officer working for the Hong Kong Health Bureau. The HK government has recently announced new special funding in cancer research to be administered by the Bureau. You are tasked with coming up with a proposal for distribution of funding to specific cancer types that are in most need of research.</p>
 <p><u>Discussion points:</u></p>
 <ul>
@@ -518,8 +519,8 @@ <h2><span class="header-section-number">7.3</span> 1. Scenario<a href="cancer.ht
 <li><p>What type of data is required?</p></li>
 </ul>
 </div>
-<div id="hong-kong-population" class="section level2 hasAnchor" number="7.4">
-<h2><span class="header-section-number">7.4</span> 2. Hong Kong population<a href="cancer.html#hong-kong-population" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="hong-kong-population" class="section level2 hasAnchor" number="6.4">
+<h2><span class="header-section-number">6.4</span> 2. Hong Kong population<a href="cancer.html#hong-kong-population" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p>You are aware that generally cancer is disease that affects the elderly more than the young. You decide to first take a closer look at the structure of the population of Hong Kong.</p>
 <p><a href="https://www.censtatd.gov.hk/en/web_table.html?id=1A">Historic population of Hong Kong</a> can be obtained from the Census and Statistics Department.</p>
 <p>An abridged version of the full historic population of Hong Kong is provided here containing the population of Hong Kong from 1965, 1975, 1985, 1995, 2005, 2015 and 2022 categorised by sex and age (0-19, 20-44, 45-64, 65+).</p>
@@ -528,8 +529,8 @@ <h2><span class="header-section-number">7.4</span> 2. Hong Kong population<a hre
 <li><p>What is the trend in Hong Kong’s population over the past ~60 years?</p></li>
 <li><p>What is the best way to visualise this data?</p></li>
 </ul>
-<div id="download-population-data" class="section level3 hasAnchor" number="7.4.1">
-<h3><span class="header-section-number">7.4.1</span> Download population data<a href="cancer.html#download-population-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="download-population-data" class="section level3 hasAnchor" number="6.4.1">
+<h3><span class="header-section-number">6.4.1</span> Download population data<a href="cancer.html#download-population-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <div class="sourceCode" id="cb150"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb150-1"><a href="cancer.html#cb150-1" tabindex="-1"></a>HKPop<span class="ot">&lt;-</span> <span class="fu">read.table</span>(<span class="st">&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HK_population_1965-2022.txt&quot;</span>, </span>
 <span id="cb150-2"><a href="cancer.html#cb150-2" tabindex="-1"></a>    <span class="at">sep =</span> <span class="st">&quot;</span><span class="sc">\t</span><span class="st">&quot;</span>, <span class="at">header =</span> <span class="cn">TRUE</span>, <span class="at">stringsAsFactor=</span><span class="cn">FALSE</span>, <span class="at">check.names =</span> <span class="cn">FALSE</span>)</span>
 <span id="cb150-3"><a href="cancer.html#cb150-3" tabindex="-1"></a>HKPop</span>
@@ -543,8 +544,8 @@ <h3><span class="header-section-number">7.4.1</span> Download population data<a
 <span id="cb150-11"><a href="cancer.html#cb150-11" tabindex="-1"></a><span class="co">#&gt; 7 female 45-64 286.3 400.7  470.7  535.0  884.7 1224.3 1314.7</span></span>
 <span id="cb150-12"><a href="cancer.html#cb150-12" tabindex="-1"></a><span class="co">#&gt; 8 female   65+  88.7 152.3  235.9  332.5  450.0  594.6  806.5</span></span></code></pre></div>
 </div>
-<div id="format-data-for-plotting" class="section level3 hasAnchor" number="7.4.2">
-<h3><span class="header-section-number">7.4.2</span> Format data for plotting<a href="cancer.html#format-data-for-plotting" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="format-data-for-plotting" class="section level3 hasAnchor" number="6.4.2">
+<h3><span class="header-section-number">6.4.2</span> Format data for plotting<a href="cancer.html#format-data-for-plotting" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>Here we convert the original dataframe into simplified format for ggplot2.</p>
 <div class="sourceCode" id="cb151"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb151-1"><a href="cancer.html#cb151-1" tabindex="-1"></a></span>
 <span id="cb151-2"><a href="cancer.html#cb151-2" tabindex="-1"></a>male<span class="ot">&lt;-</span><span class="fu">data.frame</span>(<span class="at">year =</span> <span class="fu">as.numeric</span>(<span class="fu">colnames</span>(HKPop[<span class="dv">1</span>,<span class="dv">3</span><span class="sc">:</span><span class="dv">9</span>])),</span>
@@ -597,8 +598,8 @@ <h3><span class="header-section-number">7.4.2</span> Format data for plotting<a
 <span id="cb151-49"><a href="cancer.html#cb151-49" tabindex="-1"></a><span class="co">#&gt; 10  1985 20-44                1094.</span></span>
 <span id="cb151-50"><a href="cancer.html#cb151-50" tabindex="-1"></a><span class="co">#&gt; # ℹ 18 more rows</span></span></code></pre></div>
 </div>
-<div id="plotting-population-data" class="section level3 hasAnchor" number="7.4.3">
-<h3><span class="header-section-number">7.4.3</span> Plotting population data<a href="cancer.html#plotting-population-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="plotting-population-data" class="section level3 hasAnchor" number="6.4.3">
+<h3><span class="header-section-number">6.4.3</span> Plotting population data<a href="cancer.html#plotting-population-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>Uses ggplot2 and gridExtra to make line plot of male and female population data side-by-side.</p>
 <div class="sourceCode" id="cb152"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb152-1"><a href="cancer.html#cb152-1" tabindex="-1"></a></span>
 <span id="cb152-2"><a href="cancer.html#cb152-2" tabindex="-1"></a><span class="cf">if</span> (<span class="sc">!</span><span class="fu">require</span>(<span class="st">&quot;ggplot2&quot;</span>)) <span class="fu">install.packages</span>(<span class="st">&quot;gglot2&quot;</span>)</span>
@@ -628,8 +629,8 @@ <h3><span class="header-section-number">7.4.3</span> Plotting population data<a
 <p><img src="BMDatSci_files/figure-html/plot%20data-1.png" width="672" /></p>
 </div>
 </div>
-<div id="cancer-registry-data" class="section level2 hasAnchor" number="7.5">
-<h2><span class="header-section-number">7.5</span> 3. Cancer registry data<a href="cancer.html#cancer-registry-data" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="cancer-registry-data" class="section level2 hasAnchor" number="6.5">
+<h2><span class="header-section-number">6.5</span> 3. Cancer registry data<a href="cancer.html#cancer-registry-data" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p>It is clear that Hong Kong has an aging population, thus cancer incidence would also likely increase. To examine cancer incidence and mortality in Hong Kong you obtain data from the <a href="https://www3.ha.org.hk/cancereg/">Hong Kong Cancer Registry</a>, which is maintained by the Hospital Authority.</p>
 <p>Cancer incidence data was summarised for the last three decades (1990-1999, 2000-2009 and 2010-2019).</p>
 <p><u>Discussion points:</u></p>
@@ -639,8 +640,8 @@ <h2><span class="header-section-number">7.5</span> 3. Cancer registry data<a hre
 <li><p>Has the incidence-to-mortality ratio been decreasing generally? Is it statistically significant?</p></li>
 <li><p>Which cancer type has the highest incidence in children (0-19) when compared with the elderly (65+). Is this statistically significantly different to incidence of children versus elderly cancers in general?</p></li>
 </ul>
-<div id="download-cancer-registry-data" class="section level3 hasAnchor" number="7.5.1">
-<h3><span class="header-section-number">7.5.1</span> Download cancer registry data<a href="cancer.html#download-cancer-registry-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="download-cancer-registry-data" class="section level3 hasAnchor" number="6.5.1">
+<h3><span class="header-section-number">6.5.1</span> Download cancer registry data<a href="cancer.html#download-cancer-registry-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <div class="sourceCode" id="cb153"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb153-1"><a href="cancer.html#cb153-1" tabindex="-1"></a>HKCancer<span class="ot">&lt;-</span> <span class="fu">read.table</span>(<span class="st">&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HK_cancer_incidence_mortality_1990-2020.txt&quot;</span>,</span>
 <span id="cb153-2"><a href="cancer.html#cb153-2" tabindex="-1"></a>                      <span class="at">sep =</span> <span class="st">&quot;</span><span class="sc">\t</span><span class="st">&quot;</span>, <span class="at">header =</span> <span class="cn">TRUE</span>, <span class="at">stringsAsFactor=</span><span class="cn">FALSE</span>)</span>
 <span id="cb153-3"><a href="cancer.html#cb153-3" tabindex="-1"></a>HKCancer</span>
@@ -802,8 +803,8 @@ <h3><span class="header-section-number">7.5.1</span> Download cancer registry da
 <span id="cb153-159"><a href="cancer.html#cb153-159" tabindex="-1"></a><span class="co">#&gt; 25      0     0</span></span>
 <span id="cb153-160"><a href="cancer.html#cb153-160" tabindex="-1"></a><span class="co">#&gt;  [ reached &#39;max&#39; / getOption(&quot;max.print&quot;) -- omitted 23 rows ]</span></span></code></pre></div>
 </div>
-<div id="a.-visualise-changes-in-incidence-and-mortality" class="section level3 hasAnchor" number="7.5.2">
-<h3><span class="header-section-number">7.5.2</span> 3a. Visualise changes in incidence and mortality<a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="a.-visualise-changes-in-incidence-and-mortality" class="section level3 hasAnchor" number="6.5.2">
+<h3><span class="header-section-number">6.5.2</span> 3a. Visualise changes in incidence and mortality<a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <div class="sourceCode" id="cb154"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb154-1"><a href="cancer.html#cb154-1" tabindex="-1"></a><span class="co"># first plot incidence for each cancer type</span></span>
 <span id="cb154-2"><a href="cancer.html#cb154-2" tabindex="-1"></a></span>
 <span id="cb154-3"><a href="cancer.html#cb154-3" tabindex="-1"></a><span class="co">#Import the necessary packages and libraries</span></span>
@@ -863,8 +864,8 @@ <h3><span class="header-section-number">7.5.2</span> 3a. Visualise changes in in
 <span id="cb155-29"><a href="cancer.html#cb155-29" tabindex="-1"></a><span class="fu">do.call</span>(<span class="st">&#39;grid.arrange&#39;</span>,<span class="fu">c</span>(p,<span class="at">ncol=</span><span class="dv">3</span>,<span class="at">nrow=</span><span class="dv">12</span>))</span></code></pre></div>
 <p><img src="BMDatSci_files/figure-html/mortality-1.png" width="1344" /></p>
 </div>
-<div id="b.-calculate-cancer-risk-and-mortality-rate" class="section level3 hasAnchor" number="7.5.3">
-<h3><span class="header-section-number">7.5.3</span> 3b. Calculate cancer risk and mortality rate<a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="b.-calculate-cancer-risk-and-mortality-rate" class="section level3 hasAnchor" number="6.5.3">
+<h3><span class="header-section-number">6.5.3</span> 3b. Calculate cancer risk and mortality rate<a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>To calculate disease risk we need to calculated the number of new cases over the number of persons at risk over a specific time period. We have the incidence for each decade and can estimate the number of persons at risk based on the population in 1995, 2005 and 2015.</p>
 <div class="sourceCode" id="cb156"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb156-1"><a href="cancer.html#cb156-1" tabindex="-1"></a><span class="co"># cancer risk calculation</span></span>
 <span id="cb156-2"><a href="cancer.html#cb156-2" tabindex="-1"></a></span>
@@ -937,8 +938,8 @@ <h3><span class="header-section-number">7.5.3</span> 3b. Calculate cancer risk a
 <span id="cb159-16"><a href="cancer.html#cb159-16" tabindex="-1"></a><span class="fu">do.call</span>(<span class="st">&#39;grid.arrange&#39;</span>,<span class="fu">c</span>(p,<span class="at">ncol=</span><span class="dv">3</span>,<span class="at">nrow=</span><span class="dv">12</span>))</span></code></pre></div>
 <p><img src="BMDatSci_files/figure-html/mortality%20rate%20visulisation-1.png" width="1344" /></p>
 </div>
-<div id="c.-mortality-incidence-ratio" class="section level3 hasAnchor" number="7.5.4">
-<h3><span class="header-section-number">7.5.4</span> 3c. Mortality-incidence ratio<a href="cancer.html#c.-mortality-incidence-ratio" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="c.-mortality-incidence-ratio" class="section level3 hasAnchor" number="6.5.4">
+<h3><span class="header-section-number">6.5.4</span> 3c. Mortality-incidence ratio<a href="cancer.html#c.-mortality-incidence-ratio" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>Cancer research can be focused on improving cancer outcomes in a number of ways. For example cancer prevention research that seeks to reduce cancer incidence which would also ultimately reduce cancer mortality. Another area is cancer therapy which would not affect incidence but seeks to reduce mortality, or at least prolong survival. We don’t go into survival analysis in this tutorial, but a way to get an idea whether treatment is improving by looking at the mortality-incidence ratio.</p>
 <div class="sourceCode" id="cb160"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb160-1"><a href="cancer.html#cb160-1" tabindex="-1"></a></span>
 <span id="cb160-2"><a href="cancer.html#cb160-2" tabindex="-1"></a>HKCancer_inc <span class="ot">&lt;-</span> HKCancer[HKCancer<span class="sc">$</span>Type<span class="sc">==</span><span class="st">&#39;incidence&#39;</span>,]</span>
@@ -971,8 +972,8 @@ <h3><span class="header-section-number">7.5.4</span> 3c. Mortality-incidence rat
 <span id="cb161-16"><a href="cancer.html#cb161-16" tabindex="-1"></a><span class="fu">do.call</span>(<span class="st">&#39;grid.arrange&#39;</span>,<span class="fu">c</span>(p,<span class="at">ncol=</span><span class="dv">3</span>,<span class="at">nrow=</span><span class="dv">12</span>))</span></code></pre></div>
 <p><img src="BMDatSci_files/figure-html/mortality%20incidence%20ratio%20visulisation-1.png" width="1344" /></p>
 </div>
-<div id="d.-paired-t-test-on-mortality-incidence-ratio-change" class="section level3 hasAnchor" number="7.5.5">
-<h3><span class="header-section-number">7.5.5</span> 3d. Paired t-test on mortality-incidence ratio change<a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="d.-paired-t-test-on-mortality-incidence-ratio-change" class="section level3 hasAnchor" number="6.5.5">
+<h3><span class="header-section-number">6.5.5</span> 3d. Paired t-test on mortality-incidence ratio change<a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>In general, across the different cancer types is cancer treatment improving? We can use a paired t-test comparing the mortality-incidence ratio of cancers from the 1990-1999 period with the 2010-2019 period.</p>
 <div class="sourceCode" id="cb162"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb162-1"><a href="cancer.html#cb162-1" tabindex="-1"></a></span>
 <span id="cb162-2"><a href="cancer.html#cb162-2" tabindex="-1"></a><span class="co">#First sum up all incidence and mortality data for each cancer type across age and sex</span></span>
@@ -1057,8 +1058,8 @@ <h3><span class="header-section-number">7.5.5</span> 3d. Paired t-test on mortal
 <span id="cb163-45"><a href="cancer.html#cb163-45" tabindex="-1"></a><span class="co">#&gt; mean difference </span></span>
 <span id="cb163-46"><a href="cancer.html#cb163-46" tabindex="-1"></a><span class="co">#&gt;        0.017148</span></span></code></pre></div>
 </div>
-<div id="e.-childhood-versus-elderly-cancers" class="section level3 hasAnchor" number="7.5.6">
-<h3><span class="header-section-number">7.5.6</span> 3e. Childhood versus elderly cancers<a href="cancer.html#e.-childhood-versus-elderly-cancers" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="e.-childhood-versus-elderly-cancers" class="section level3 hasAnchor" number="6.5.6">
+<h3><span class="header-section-number">6.5.6</span> 3e. Childhood versus elderly cancers<a href="cancer.html#e.-childhood-versus-elderly-cancers" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p>Although it is clear that the incidence of cancer is typically higher in the elderly, some cancers affect children as well. What cancer types disproportionate affect children? For each cancer type, compare the proportion of 0-19 versus 65+ incidence against the 0-19 versus 65+ incidence for all other cancer types.</p>
 <div class="sourceCode" id="cb164"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb164-1"><a href="cancer.html#cb164-1" tabindex="-1"></a><span class="co"># Examine the proportion of childhood </span></span>
 <span id="cb164-2"><a href="cancer.html#cb164-2" tabindex="-1"></a></span>
@@ -1132,8 +1133,8 @@ <h3><span class="header-section-number">7.5.6</span> 3e. Childhood versus elderl
 <span id="cb165-39"><a href="cancer.html#cb165-39" tabindex="-1"></a><span class="co">#&gt; 37                Total             1   -4.121323</span></span></code></pre></div>
 </div>
 </div>
-<div id="existing-cancer-funding-and-publication-data" class="section level2 hasAnchor" number="7.6">
-<h2><span class="header-section-number">7.6</span> 4. Existing cancer funding and publication data<a href="cancer.html#existing-cancer-funding-and-publication-data" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="existing-cancer-funding-and-publication-data" class="section level2 hasAnchor" number="6.6">
+<h2><span class="header-section-number">6.6</span> 4. Existing cancer funding and publication data<a href="cancer.html#existing-cancer-funding-and-publication-data" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p>The Hong Kong government established in Health and Medical Research Fund (HMRF) in 2011 to specifically provide research funding for health and medical research in Hong Kong. Since 2016 over 370 projects in the category of Cancer has been funded for a total of ~$400 M dollars. A list of all funded projects can be found on the Health Bureau <a href="https://rfs1.healthbureau.gov.hk/search/#/fundedsearch/basicsearch?lang=en">webpage</a>. You would like to use this data to see if there is any association between previous project funding and the epidemiology of cancers in Hong Kong.</p>
 <p>We can also do a similar thing with publications and ask if the research publications in Hong Kong have been aligned with the incidence and mortality. We can obtain this data from PubMed using the following terms: <a href="https://pubmed.ncbi.nlm.nih.gov/?term=%28%22Hong+Kong%22%5BAffiliation%5D%29+AND+%28neoplasms%5BMeSH+Terms%5D%29">(“Hong Kong”[Affiliation]) AND (neoplasms[MeSH Terms])</a></p>
 <p>The data has been predownloaded as the Pubmed API via R is a bit slow.</p>
@@ -1143,8 +1144,8 @@ <h2><span class="header-section-number">7.6</span> 4. Existing cancer funding an
 <li>What are the main cancer types being researched in Hong Kong?</li>
 <li>Is there any correlation between funding and cancer incidence and mortality?</li>
 </ul>
-<div id="download-hmrf-grants-and-pubmed-data" class="section level3 hasAnchor" number="7.6.1">
-<h3><span class="header-section-number">7.6.1</span> Download HMRF grants and Pubmed data<a href="cancer.html#download-hmrf-grants-and-pubmed-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="download-hmrf-grants-and-pubmed-data" class="section level3 hasAnchor" number="6.6.1">
+<h3><span class="header-section-number">6.6.1</span> Download HMRF grants and Pubmed data<a href="cancer.html#download-hmrf-grants-and-pubmed-data" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <div class="sourceCode" id="cb166"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb166-1"><a href="cancer.html#cb166-1" tabindex="-1"></a></span>
 <span id="cb166-2"><a href="cancer.html#cb166-2" tabindex="-1"></a>HMRF<span class="ot">&lt;-</span> <span class="fu">read.delim</span>(<span class="st">&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HMRF_cancer_grants.txt&quot;</span>, <span class="at">sep =</span> <span class="st">&quot;</span><span class="sc">\t</span><span class="st">&quot;</span>, <span class="at">header =</span> <span class="cn">TRUE</span>, <span class="at">stringsAsFactor=</span><span class="cn">FALSE</span>, <span class="at">check.names =</span> <span class="cn">TRUE</span>)</span>
 <span id="cb166-3"><a href="cancer.html#cb166-3" tabindex="-1"></a><span class="co">#HMRF</span></span>
@@ -1154,7 +1155,9 @@ <h3><span class="header-section-number">7.6.1</span> Download HMRF grants and Pu
 <span id="cb166-7"><a href="cancer.html#cb166-7" tabindex="-1"></a></span>
 <span id="cb166-8"><a href="cancer.html#cb166-8" tabindex="-1"></a><span class="fu">hist</span>(pubmed<span class="sc">$</span>Publication.Year)</span></code></pre></div>
 <p><img src="BMDatSci_files/figure-html/load%20HMRF-1.png" width="672" /></p>
-<!-- ### Make word cloud for grants -->
+</div>
+<div id="make-word-cloud-for-grants" class="section level3 hasAnchor" number="6.6.2">
+<h3><span class="header-section-number">6.6.2</span> Make word cloud for grants<a href="cancer.html#make-word-cloud-for-grants" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <!-- ```{r wordcloud grants, fig.height=8, fig.width=10} -->
 <!-- if (!require("ggwordcloud")) install.packages("ggwordcloud") -->
 <!-- if (!require("tm")) install.packages("tm") -->
@@ -1198,8 +1201,8 @@ <h3><span class="header-section-number">7.6.1</span> Download HMRF grants and Pu
 <!-- grid.arrange(arrangeGrob(pm, top = 'Pubmed'),arrangeGrob(gp, top = 'Grants'),nrow=2,heights=c(6,6)) -->
 <!-- ``` -->
 </div>
-<div id="make-compare-grant-funding-with-incidence-and-mortality" class="section level3 hasAnchor" number="7.6.2">
-<h3><span class="header-section-number">7.6.2</span> Make compare grant funding with incidence and mortality<a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="make-compare-grant-funding-with-incidence-and-mortality" class="section level3 hasAnchor" number="6.6.3">
+<h3><span class="header-section-number">6.6.3</span> Make compare grant funding with incidence and mortality<a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <div class="sourceCode" id="cb167"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb167-1"><a href="cancer.html#cb167-1" tabindex="-1"></a></span>
 <span id="cb167-2"><a href="cancer.html#cb167-2" tabindex="-1"></a><span class="cf">if</span> (<span class="sc">!</span><span class="fu">require</span>(<span class="st">&quot;ggrepel&quot;</span>)) <span class="fu">install.packages</span>(<span class="st">&quot;ggrepel&quot;</span>)</span>
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@@ -1272,8 +1275,8 @@ <h3><span class="header-section-number">7.6.2</span> Make compare grant funding
 <p><img src="BMDatSci_files/figure-html/grants%20versus%20incidence%20and%20mortality-1.png" width="960" /></p>
 </div>
 </div>
-<div id="open-disucssion" class="section level2 hasAnchor" number="7.7">
-<h2><span class="header-section-number">7.7</span> 5. Open disucssion<a href="cancer.html#open-disucssion" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="open-disucssion" class="section level2 hasAnchor" number="6.7">
+<h2><span class="header-section-number">6.7</span> 5. Open disucssion<a href="cancer.html#open-disucssion" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <p>As a group discuss what cancer type would be most worthy of funding in Hong Kong. Statistics and figures should be used to support your decision. If possible also discuss other data/analyses that can be performed and/or other diseases that are also in need of funding in Hong Kong.</p>
 </div>
 </div>
@@ -1282,7 +1285,7 @@ <h2><span class="header-section-number">7.7</span> 5. Open disucssion<a href="ca
           </div>
         </div>
       </div>
-<a href="infectious-dis.html" class="navigation navigation-prev " aria-label="Previous page"><i class="fa fa-angle-left"></i></a>
+<a href="image-digital.html" class="navigation navigation-prev " aria-label="Previous page"><i class="fa fa-angle-left"></i></a>
 <a href="pop-genetics.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
     </div>
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diff --git a/docs/image-digital.html b/docs/image-digital.html
index 0cdd0e9..df0ab36 100644
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+++ b/docs/image-digital.html
@@ -23,7 +23,7 @@
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-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
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@@ -31,7 +31,7 @@
   
   
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-<link rel="next" href="infectious-dis.html"/>
+<link rel="next" href="cancer.html"/>
 <script src="libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
 <script src="https://cdn.jsdelivr.net/npm/fuse.js@6.4.6/dist/fuse.min.js"></script>
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@@ -56,7 +56,7 @@
 
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 pre > code.sourceCode { white-space: pre; position: relative; }
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+pre > code.sourceCode > span { line-height: 1.25; }
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@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -363,6 +364,11 @@ <h1>
 <h1><span class="header-section-number">Chapter 5</span> Medical Image and Digital Health<a href="image-digital.html#image-digital" class="anchor-section" aria-label="Anchor link to header"></a></h1>
 <!-- # Medical Image and Digital Health {#image-digital} -->
 <p>Contents to be added.</p>
+<!-- # ```{r child="notebooks/module3-infectious/M3-infectious-dis.Rmd", echo=TRUE} -->
+<!-- # ``` -->
+<!-- # Personalised Genomic Medicine {#genomics} -->
+<!-- ```{r child="notebooks/module1-genomics/M1-genomics-01.Rmd", echo=TRUE} -->
+<!-- ``` -->
 </div>
             </section>
 
@@ -370,7 +376,7 @@ <h1><span class="header-section-number">Chapter 5</span> Medical Image and Digit
         </div>
       </div>
 <a href="introClassifier.html" class="navigation navigation-prev " aria-label="Previous page"><i class="fa fa-angle-left"></i></a>
-<a href="infectious-dis.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
+<a href="cancer.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
     </div>
   </div>
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diff --git a/docs/index.html b/docs/index.html
index ca91f14..71bc443 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
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@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -362,7 +363,7 @@ <h1>
 <div id="header">
 <h1 class="title">Biomedical Data Science - introduction with case studies</h1>
 <p class="author"><em>BIOF1001 teaching team</em></p>
-<p class="date"><em>2023-11-06</em></p>
+<p class="date"><em>2024-08-29</em></p>
 </div>
 <div id="welcome" class="section level1 unnumbered hasAnchor">
 <h1>Welcome<a href="index.html#welcome" class="anchor-section" aria-label="Anchor link to header"></a></h1>
diff --git a/docs/infectious-dis.html b/docs/infectious-dis.html
index 9b383d7..bbd2244 100644
--- a/docs/infectious-dis.html
+++ b/docs/infectious-dis.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-24" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
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 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -307,7 +307,8 @@
 <li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
 <li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>7.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="7.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
 <li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
 </ul></li>
@@ -317,6 +318,7 @@
 <ul>
 <li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
 <li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="8.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>8.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
@@ -338,7 +340,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
diff --git a/docs/install.html b/docs/install.html
index e69a56a..f0bd1ef 100644
--- a/docs/install.html
+++ b/docs/install.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -31,7 +31,7 @@
   
   
 <link rel="prev" href="pop-genetics.html"/>
-<link rel="next" href="references.html"/>
+<link rel="next" href="references-1.html"/>
 <script src="libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
 <script src="https://cdn.jsdelivr.net/npm/fuse.js@6.4.6/dist/fuse.min.js"></script>
 <link href="libs/gitbook-2.6.7/css/style.css" rel="stylesheet" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -377,17 +378,17 @@ <h1>Appendix A: Install R &amp; RStudio<a href="install.html#install" class="anc
 This manual is adapted and updated from the
 <a href="https://holab-hku.github.io/R-workshop/prerequisite.html">materials</a> produced
 by Xiunan Fang and other team members in Dr Joshua Ho’s lab.</p>
-<div id="a.1-install-r" class="section level2 unnumbered hasAnchor">
-<h2>A.1 Install R<a href="install.html#a.1-install-r" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="a.1-install-r-4.3.1" class="section level2 unnumbered hasAnchor">
+<h2>A.1 Install R (&gt;=4.3.1)<a href="install.html#a.1-install-r-4.3.1" class="anchor-section" aria-label="Anchor link to header"></a></h2>
 <div id="r-on-windows" class="section level3 unnumbered hasAnchor">
 <h3>R on Windows<a href="install.html#r-on-windows" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <ul>
 <li>Open an internet browser and go to <a href="https://cran.r-project.org/" class="uri">https://cran.r-project.org/</a>.</li>
 <li>Click on the <code>Download R for Windows</code> link at the top of the page.</li>
-<li>Choose the <code>base</code> and then Click on the <code>Download R 4.3.1 for Windows</code>
+<li>Choose the <code>base</code> and then Click on the <code>Download R 4.4.1 for Windows</code>
 link at the top of the page (or a new version if this manual is outdated).</li>
 <li>Once the download is finished, you will obtain a file named
-<code>R-4.3.1-win.exe</code> or similar depending on the version that you download.</li>
+<code>R-4.4.1-win.exe</code> or similar depending on the version that you download.</li>
 <li>Most of the time, you will likely want to go with the defaults, so click the
 button <code>Next</code> until the process is complete.</li>
 </ul>
@@ -399,7 +400,7 @@ <h3>R on macOS<a href="install.html#r-on-macos" class="anchor-section" aria-labe
 <li>Click on the <code>Download R for macOS</code> link at the top of the page.</li>
 <li>Click on the file containing the latest version of R under the
 <strong>Latest release</strong>.</li>
-<li>Save the <code>R-4.3.1-**.pkg</code> file, double-click it to open, and follow the installation
+<li>Save the <code>R-4.4.1-**.pkg</code> file, double-click it to open, and follow the installation
 instructions.</li>
 </ul>
 <blockquote>
@@ -486,12 +487,12 @@ <h3>Some general knowledge<a href="install.html#some-general-knowledge" class="a
    actual function codes
 }</code></pre>
 <p>For example:</p>
-<div class="sourceCode" id="cb180"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb180-1"><a href="install.html#cb180-1" tabindex="-1"></a>my_average <span class="ot">&lt;-</span> <span class="cf">function</span>(x){</span>
-<span id="cb180-2"><a href="install.html#cb180-2" tabindex="-1"></a>  <span class="fu">sum</span>(x)<span class="sc">/</span><span class="fu">length</span>(x)</span>
-<span id="cb180-3"><a href="install.html#cb180-3" tabindex="-1"></a>}</span>
-<span id="cb180-4"><a href="install.html#cb180-4" tabindex="-1"></a></span>
-<span id="cb180-5"><a href="install.html#cb180-5" tabindex="-1"></a><span class="fu">my_average</span>(<span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">4</span>, <span class="dv">5</span>, <span class="dv">7</span>))</span>
-<span id="cb180-6"><a href="install.html#cb180-6" tabindex="-1"></a><span class="co">#&gt; [1] 4.25</span></span></code></pre></div>
+<div class="sourceCode" id="cb183"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb183-1"><a href="install.html#cb183-1" tabindex="-1"></a>my_average <span class="ot">&lt;-</span> <span class="cf">function</span>(x){</span>
+<span id="cb183-2"><a href="install.html#cb183-2" tabindex="-1"></a>  <span class="fu">sum</span>(x)<span class="sc">/</span><span class="fu">length</span>(x)</span>
+<span id="cb183-3"><a href="install.html#cb183-3" tabindex="-1"></a>}</span>
+<span id="cb183-4"><a href="install.html#cb183-4" tabindex="-1"></a></span>
+<span id="cb183-5"><a href="install.html#cb183-5" tabindex="-1"></a><span class="fu">my_average</span>(<span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">4</span>, <span class="dv">5</span>, <span class="dv">7</span>))</span>
+<span id="cb183-6"><a href="install.html#cb183-6" tabindex="-1"></a><span class="co">#&gt; [1] 4.25</span></span></code></pre></div>
 <p>R contains a lot of built-in functions, you can use <code>?</code> or <code>help()</code> to see the
 documentation of a function, there are also a lot of external libraries with
 specific functions. To use a library, we do:</p>
@@ -521,7 +522,7 @@ <h2>A4. Cloud computing<a href="install.html#a4.-cloud-computing" class="anchor-
         </div>
       </div>
 <a href="pop-genetics.html" class="navigation navigation-prev " aria-label="Previous page"><i class="fa fa-angle-left"></i></a>
-<a href="references.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
+<a href="references-1.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
     </div>
   </div>
 <script src="libs/gitbook-2.6.7/js/app.min.js"></script>
diff --git a/docs/introClassifier.html b/docs/introClassifier.html
index 7a85c39..e2c6c29 100644
--- a/docs/introClassifier.html
+++ b/docs/introClassifier.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -678,36 +679,35 @@ <h2><span class="header-section-number">4.3</span> Cross-validation<a href="intr
 <span id="cb125-3"><a href="introClassifier.html#cb125-3" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">&quot;caret&quot;</span>)</span>
 <span id="cb125-4"><a href="introClassifier.html#cb125-4" tabindex="-1"></a>}</span>
 <span id="cb125-5"><a href="introClassifier.html#cb125-5" tabindex="-1"></a><span class="fu">library</span>(caret)</span>
-<span id="cb125-6"><a href="introClassifier.html#cb125-6" tabindex="-1"></a><span class="co">#&gt; Loading required package: lattice</span></span>
-<span id="cb125-7"><a href="introClassifier.html#cb125-7" tabindex="-1"></a></span>
-<span id="cb125-8"><a href="introClassifier.html#cb125-8" tabindex="-1"></a><span class="co"># Define training control</span></span>
-<span id="cb125-9"><a href="introClassifier.html#cb125-9" tabindex="-1"></a><span class="co"># We also want to have savePredictions=TRUE &amp; classProbs=TRUE</span></span>
-<span id="cb125-10"><a href="introClassifier.html#cb125-10" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">0</span>) </span>
-<span id="cb125-11"><a href="introClassifier.html#cb125-11" tabindex="-1"></a>my_trControl <span class="ot">&lt;-</span> <span class="fu">trainControl</span>(<span class="at">method =</span> <span class="st">&quot;cv&quot;</span>, <span class="at">number =</span> <span class="dv">5</span>, </span>
-<span id="cb125-12"><a href="introClassifier.html#cb125-12" tabindex="-1"></a>                             <span class="at">classProbs =</span> <span class="cn">TRUE</span>,</span>
-<span id="cb125-13"><a href="introClassifier.html#cb125-13" tabindex="-1"></a>                             <span class="at">savePredictions =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb125-14"><a href="introClassifier.html#cb125-14" tabindex="-1"></a></span>
-<span id="cb125-15"><a href="introClassifier.html#cb125-15" tabindex="-1"></a><span class="co"># Train the model</span></span>
-<span id="cb125-16"><a href="introClassifier.html#cb125-16" tabindex="-1"></a>cv_model <span class="ot">&lt;-</span> <span class="fu">train</span>(diabetes <span class="sc">~</span> ., <span class="at">data =</span> PimaIndiansDiabetes, </span>
-<span id="cb125-17"><a href="introClassifier.html#cb125-17" tabindex="-1"></a>                  <span class="at">method =</span> <span class="st">&quot;glm&quot;</span>,</span>
-<span id="cb125-18"><a href="introClassifier.html#cb125-18" tabindex="-1"></a>                  <span class="at">family=</span><span class="fu">binomial</span>(),</span>
-<span id="cb125-19"><a href="introClassifier.html#cb125-19" tabindex="-1"></a>                  <span class="at">trControl =</span> my_trControl)</span>
-<span id="cb125-20"><a href="introClassifier.html#cb125-20" tabindex="-1"></a></span>
-<span id="cb125-21"><a href="introClassifier.html#cb125-21" tabindex="-1"></a><span class="co"># Summarize the results</span></span>
-<span id="cb125-22"><a href="introClassifier.html#cb125-22" tabindex="-1"></a><span class="fu">print</span>(cv_model)</span>
-<span id="cb125-23"><a href="introClassifier.html#cb125-23" tabindex="-1"></a><span class="co">#&gt; Generalized Linear Model </span></span>
-<span id="cb125-24"><a href="introClassifier.html#cb125-24" tabindex="-1"></a><span class="co">#&gt; </span></span>
-<span id="cb125-25"><a href="introClassifier.html#cb125-25" tabindex="-1"></a><span class="co">#&gt; 768 samples</span></span>
-<span id="cb125-26"><a href="introClassifier.html#cb125-26" tabindex="-1"></a><span class="co">#&gt;   8 predictor</span></span>
-<span id="cb125-27"><a href="introClassifier.html#cb125-27" tabindex="-1"></a><span class="co">#&gt;   2 classes: &#39;neg&#39;, &#39;pos&#39; </span></span>
-<span id="cb125-28"><a href="introClassifier.html#cb125-28" tabindex="-1"></a><span class="co">#&gt; </span></span>
-<span id="cb125-29"><a href="introClassifier.html#cb125-29" tabindex="-1"></a><span class="co">#&gt; No pre-processing</span></span>
-<span id="cb125-30"><a href="introClassifier.html#cb125-30" tabindex="-1"></a><span class="co">#&gt; Resampling: Cross-Validated (5 fold) </span></span>
-<span id="cb125-31"><a href="introClassifier.html#cb125-31" tabindex="-1"></a><span class="co">#&gt; Summary of sample sizes: 615, 614, 615, 614, 614 </span></span>
-<span id="cb125-32"><a href="introClassifier.html#cb125-32" tabindex="-1"></a><span class="co">#&gt; Resampling results:</span></span>
-<span id="cb125-33"><a href="introClassifier.html#cb125-33" tabindex="-1"></a><span class="co">#&gt; </span></span>
-<span id="cb125-34"><a href="introClassifier.html#cb125-34" tabindex="-1"></a><span class="co">#&gt;   Accuracy   Kappa    </span></span>
-<span id="cb125-35"><a href="introClassifier.html#cb125-35" tabindex="-1"></a><span class="co">#&gt;   0.7708344  0.4695353</span></span></code></pre></div>
+<span id="cb125-6"><a href="introClassifier.html#cb125-6" tabindex="-1"></a></span>
+<span id="cb125-7"><a href="introClassifier.html#cb125-7" tabindex="-1"></a><span class="co"># Define training control</span></span>
+<span id="cb125-8"><a href="introClassifier.html#cb125-8" tabindex="-1"></a><span class="co"># We also want to have savePredictions=TRUE &amp; classProbs=TRUE</span></span>
+<span id="cb125-9"><a href="introClassifier.html#cb125-9" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">0</span>) </span>
+<span id="cb125-10"><a href="introClassifier.html#cb125-10" tabindex="-1"></a>my_trControl <span class="ot">&lt;-</span> <span class="fu">trainControl</span>(<span class="at">method =</span> <span class="st">&quot;cv&quot;</span>, <span class="at">number =</span> <span class="dv">5</span>, </span>
+<span id="cb125-11"><a href="introClassifier.html#cb125-11" tabindex="-1"></a>                             <span class="at">classProbs =</span> <span class="cn">TRUE</span>,</span>
+<span id="cb125-12"><a href="introClassifier.html#cb125-12" tabindex="-1"></a>                             <span class="at">savePredictions =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb125-13"><a href="introClassifier.html#cb125-13" tabindex="-1"></a></span>
+<span id="cb125-14"><a href="introClassifier.html#cb125-14" tabindex="-1"></a><span class="co"># Train the model</span></span>
+<span id="cb125-15"><a href="introClassifier.html#cb125-15" tabindex="-1"></a>cv_model <span class="ot">&lt;-</span> <span class="fu">train</span>(diabetes <span class="sc">~</span> ., <span class="at">data =</span> PimaIndiansDiabetes, </span>
+<span id="cb125-16"><a href="introClassifier.html#cb125-16" tabindex="-1"></a>                  <span class="at">method =</span> <span class="st">&quot;glm&quot;</span>,</span>
+<span id="cb125-17"><a href="introClassifier.html#cb125-17" tabindex="-1"></a>                  <span class="at">family=</span><span class="fu">binomial</span>(),</span>
+<span id="cb125-18"><a href="introClassifier.html#cb125-18" tabindex="-1"></a>                  <span class="at">trControl =</span> my_trControl)</span>
+<span id="cb125-19"><a href="introClassifier.html#cb125-19" tabindex="-1"></a></span>
+<span id="cb125-20"><a href="introClassifier.html#cb125-20" tabindex="-1"></a><span class="co"># Summarize the results</span></span>
+<span id="cb125-21"><a href="introClassifier.html#cb125-21" tabindex="-1"></a><span class="fu">print</span>(cv_model)</span>
+<span id="cb125-22"><a href="introClassifier.html#cb125-22" tabindex="-1"></a><span class="co">#&gt; Generalized Linear Model </span></span>
+<span id="cb125-23"><a href="introClassifier.html#cb125-23" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb125-24"><a href="introClassifier.html#cb125-24" tabindex="-1"></a><span class="co">#&gt; 768 samples</span></span>
+<span id="cb125-25"><a href="introClassifier.html#cb125-25" tabindex="-1"></a><span class="co">#&gt;   8 predictor</span></span>
+<span id="cb125-26"><a href="introClassifier.html#cb125-26" tabindex="-1"></a><span class="co">#&gt;   2 classes: &#39;neg&#39;, &#39;pos&#39; </span></span>
+<span id="cb125-27"><a href="introClassifier.html#cb125-27" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb125-28"><a href="introClassifier.html#cb125-28" tabindex="-1"></a><span class="co">#&gt; No pre-processing</span></span>
+<span id="cb125-29"><a href="introClassifier.html#cb125-29" tabindex="-1"></a><span class="co">#&gt; Resampling: Cross-Validated (5 fold) </span></span>
+<span id="cb125-30"><a href="introClassifier.html#cb125-30" tabindex="-1"></a><span class="co">#&gt; Summary of sample sizes: 615, 614, 615, 614, 614 </span></span>
+<span id="cb125-31"><a href="introClassifier.html#cb125-31" tabindex="-1"></a><span class="co">#&gt; Resampling results:</span></span>
+<span id="cb125-32"><a href="introClassifier.html#cb125-32" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb125-33"><a href="introClassifier.html#cb125-33" tabindex="-1"></a><span class="co">#&gt;   Accuracy   Kappa    </span></span>
+<span id="cb125-34"><a href="introClassifier.html#cb125-34" tabindex="-1"></a><span class="co">#&gt;   0.7708344  0.4695353</span></span></code></pre></div>
 <p>We can also access to detailed prediction results after concatenating the K
 folds:</p>
 <div class="sourceCode" id="cb126"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb126-1"><a href="introClassifier.html#cb126-1" tabindex="-1"></a><span class="fu">head</span>(cv_model<span class="sc">$</span>pred)</span>
diff --git a/docs/introHypoTest.html b/docs/introHypoTest.html
index 0f5faa7..137cb64 100644
--- a/docs/introHypoTest.html
+++ b/docs/introHypoTest.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
diff --git a/docs/introLinearReg.html b/docs/introLinearReg.html
index 46fc3a3..f00e7d3 100644
--- a/docs/introLinearReg.html
+++ b/docs/introLinearReg.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -836,7 +837,7 @@ <h2><span class="header-section-number">3.5</span> Multiple Regression with <cod
     \end{array}
 \]</span>
 For each sample <span class="math inline">\(i\)</span>, the predicted value by the model is:<br />
-<span class="math inline">\(\qquad Y_{i,e} = \alpha + \beta_1*X_1^{(i)} + \beta_2*X_2^{(i)} + \dots + \beta_p*X_p^{(i)}\)</span></p>
+<span class="math inline">\(\qquad Y_{i,e} = \alpha + \beta_1*X_1^{(i)}  + \beta_2*X_2^{(i)} + \dots  + \beta_p*X_p^{(i)}\)</span></p>
 <p>Define the sum of squares
 <span class="math display">\[   S(\alpha,\beta_1,\ldots,\beta_p) = \sum_{i=1}^n
 \left\{     Y_i -Y_{i,e}\right\}^2  =\sum_{i=1}^n \left\{
@@ -859,7 +860,7 @@ <h2><span class="header-section-number">3.5</span> Multiple Regression with <cod
 <p>Consider two regression models</p>
 <ol style="list-style-type: upper-roman">
 <li><p><span class="math inline">\(\quad ~ Y_e = \alpha + \beta_1*X_1\)</span></p></li>
-<li><p><span class="math inline">\(\quad \tilde Y_e = \alpha + \beta_1*X_1 + \beta_2*X_2\)</span></p></li>
+<li><p><span class="math inline">\(\quad  \tilde Y_e = \alpha + \beta_1*X_1  + \beta_2*X_2\)</span></p></li>
 </ol>
 <p>The model (II) has one more input variable <span class="math inline">\(X_2\)</span>.</p>
 <p>The <span class="math inline">\(SSE_I\)</span> of Model (I) is the minimum of</p>
diff --git a/docs/introR.html b/docs/introR.html
index 28f30ad..f4c2ced 100644
--- a/docs/introR.html
+++ b/docs/introR.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -1061,9 +1062,7 @@ <h4><span class="header-section-number">1.6.3.1</span> Install and load package<
 <div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb44-1"><a href="introR.html#cb44-1" tabindex="-1"></a><span class="cf">if</span> (<span class="sc">!</span><span class="fu">requireNamespace</span>(<span class="st">&quot;ggplot2&quot;</span>, <span class="at">quietly =</span> <span class="cn">TRUE</span>))</span>
 <span id="cb44-2"><a href="introR.html#cb44-2" tabindex="-1"></a>    <span class="fu">install.packages</span>(<span class="st">&quot;ggplot2&quot;</span>)</span>
 <span id="cb44-3"><a href="introR.html#cb44-3" tabindex="-1"></a></span>
-<span id="cb44-4"><a href="introR.html#cb44-4" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
-<span id="cb44-5"><a href="introR.html#cb44-5" tabindex="-1"></a><span class="co">#&gt; RStudio Community is a great place to get help:</span></span>
-<span id="cb44-6"><a href="introR.html#cb44-6" tabindex="-1"></a><span class="co">#&gt; https://community.rstudio.com/c/tidyverse</span></span></code></pre></div>
+<span id="cb44-4"><a href="introR.html#cb44-4" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span></code></pre></div>
 </div>
 <div id="histogram-1" class="section level4 hasAnchor" number="1.6.3.2">
 <h4><span class="header-section-number">1.6.3.2</span> Histogram<a href="introR.html#histogram-1" class="anchor-section" aria-label="Anchor link to header"></a></h4>
diff --git a/docs/pop-genetics.html b/docs/pop-genetics.html
index 741b679..89cf4cf 100644
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+++ b/docs/pop-genetics.html
@@ -4,18 +4,18 @@
 
   <meta charset="utf-8" />
   <meta http-equiv="X-UA-Compatible" content="IE=edge" />
-  <title>Chapter 8 Population Genetics and Diseases | Biomedical Data Science - introduction with case studies</title>
+  <title>Chapter 7 Population Genetics and Diseases | Biomedical Data Science - introduction with case studies</title>
   <meta name="description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
-  <meta name="generator" content="bookdown 0.36 and GitBook 2.6.7" />
+  <meta name="generator" content="bookdown 0.35 and GitBook 2.6.7" />
 
-  <meta property="og:title" content="Chapter 8 Population Genetics and Diseases | Biomedical Data Science - introduction with case studies" />
+  <meta property="og:title" content="Chapter 7 Population Genetics and Diseases | Biomedical Data Science - introduction with case studies" />
   <meta property="og:type" content="book" />
   
   <meta property="og:description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
   <meta name="github-repo" content="rstudio/bookdown-demo" />
 
   <meta name="twitter:card" content="summary" />
-  <meta name="twitter:title" content="Chapter 8 Population Genetics and Diseases | Biomedical Data Science - introduction with case studies" />
+  <meta name="twitter:title" content="Chapter 7 Population Genetics and Diseases | Biomedical Data Science - introduction with case studies" />
   
   <meta name="twitter:description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
   
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-24" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -278,53 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>7.6.2</b> Make word cloud for grants</a></li>
-<li class="chapter" data-level="7.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.3</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
-<li class="chapter" data-level="8.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>8.1.3</b> References</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -361,15 +360,15 @@ <h1>
           <div class="page-inner">
 
             <section class="normal" id="section-">
-<div id="pop-genetics" class="section level1 hasAnchor" number="8">
-<h1><span class="header-section-number">Chapter 8</span> Population Genetics and Diseases<a href="pop-genetics.html#pop-genetics" class="anchor-section" aria-label="Anchor link to header"></a></h1>
-<div id="case-study-1-heritability-and-human-traits" class="section level2 hasAnchor" number="8.1">
-<h2><span class="header-section-number">8.1</span> Case study 1: Heritability and human traits<a href="pop-genetics.html#case-study-1-heritability-and-human-traits" class="anchor-section" aria-label="Anchor link to header"></a></h2>
-<div id="part-1" class="section level3 hasAnchor" number="8.1.1">
-<h3><span class="header-section-number">8.1.1</span> Part 1<a href="pop-genetics.html#part-1" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="pop-genetics" class="section level1 hasAnchor" number="7">
+<h1><span class="header-section-number">Chapter 7</span> Population Genetics and Diseases<a href="pop-genetics.html#pop-genetics" class="anchor-section" aria-label="Anchor link to header"></a></h1>
+<div id="case-study-1-heritability-and-human-traits" class="section level2 hasAnchor" number="7.1">
+<h2><span class="header-section-number">7.1</span> Case study 1: Heritability and human traits<a href="pop-genetics.html#case-study-1-heritability-and-human-traits" class="anchor-section" aria-label="Anchor link to header"></a></h2>
+<div id="part-1" class="section level3 hasAnchor" number="7.1.1">
+<h3><span class="header-section-number">7.1.1</span> Part 1<a href="pop-genetics.html#part-1" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p><strong>Scenario:</strong> You are a researcher working on a twin study on cardiovascular traits to assess the genetic and environmental contribution relevant to metabolism and cardiovascular disease risk. You have recruited a cohort of volunteer adult twins of the same ancestry. The volunteers have undergone a series of baseline clinical evaluations and performed genotyping on a panel of single nucleotide polymorphisms that may be associated with the traits.</p>
-<div id="questions-for-discussion" class="section level4 hasAnchor" number="8.1.1.1">
-<h4><span class="header-section-number">8.1.1.1</span> Questions for Discussion<a href="pop-genetics.html#questions-for-discussion" class="anchor-section" aria-label="Anchor link to header"></a></h4>
+<div id="questions-for-discussion" class="section level4 hasAnchor" number="7.1.1.1">
+<h4><span class="header-section-number">7.1.1.1</span> Questions for Discussion<a href="pop-genetics.html#questions-for-discussion" class="anchor-section" aria-label="Anchor link to header"></a></h4>
 <strong>Q1.</strong> Besides the clinical measurements, what data do you need to collect from the subjects?
 <details>
 <summary>
@@ -407,8 +406,8 @@ <h4><span class="header-section-number">8.1.1.1</span> Questions for Discussion<
 </ul>
 </details>
 </div>
-<div id="hands-on-exercise-association-test" class="section level4 hasAnchor" number="8.1.1.2">
-<h4><span class="header-section-number">8.1.1.2</span> Hands-on exercise : Association test<a href="pop-genetics.html#hands-on-exercise-association-test" class="anchor-section" aria-label="Anchor link to header"></a></h4>
+<div id="hands-on-exercise-association-test" class="section level4 hasAnchor" number="7.1.1.2">
+<h4><span class="header-section-number">7.1.1.2</span> Hands-on exercise : Association test<a href="pop-genetics.html#hands-on-exercise-association-test" class="anchor-section" aria-label="Anchor link to header"></a></h4>
 <p>Now, you are given a dataset of age- and sex-matched twin cohort with two cardiovascular phenotypes and 5 quantitative trait loci (QTL). Data set and template notebook are available on Moodle (recommended) and also on this
 <a href="https://github.com/StatBiomed/BMDS-book/blob/main/notebooks/module4-genetics/dataTwin2023.dat">GitHub Repo</a>.</p>
 <p><strong>The information for columns:</strong></p>
@@ -717,8 +716,8 @@ <h4><span class="header-section-number">8.1.1.2</span> Hands-on exercise : Assoc
 <span id="cb173-10"><a href="pop-genetics.html#cb173-10" tabindex="-1"></a><span class="co">#&gt; [1] 7.030723</span></span></code></pre></div>
 </div>
 </div>
-<div id="part-2" class="section level3 hasAnchor" number="8.1.2">
-<h3><span class="header-section-number">8.1.2</span> Part 2<a href="pop-genetics.html#part-2" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="part-2" class="section level3 hasAnchor" number="7.1.2">
+<h3><span class="header-section-number">7.1.2</span> Part 2<a href="pop-genetics.html#part-2" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <p><strong>Scenario:</strong> You are asked to estimate the additive genetic variance, dominance genetic variance and/or shared environmental variance using regression-based method and a classical twin design.</p>
 <p><span class="math display">\[\begin{align*}
 
@@ -768,8 +767,8 @@ <h3><span class="header-section-number">8.1.2</span> Part 2<a href="pop-genetics
 \sigma^{2}_{E} &amp; = 1 - \sigma^{2}_{A} - \sigma^{2}_{C} = 1 - rMZ
 
 \end{align*}\]</span></p>
-<div id="questions-for-discussions" class="section level4 hasAnchor" number="8.1.2.1">
-<h4><span class="header-section-number">8.1.2.1</span> Questions for discussions :<a href="pop-genetics.html#questions-for-discussions" class="anchor-section" aria-label="Anchor link to header"></a></h4>
+<div id="questions-for-discussions" class="section level4 hasAnchor" number="7.1.2.1">
+<h4><span class="header-section-number">7.1.2.1</span> Questions for discussions :<a href="pop-genetics.html#questions-for-discussions" class="anchor-section" aria-label="Anchor link to header"></a></h4>
 <strong>Q1.</strong> What is missing heritability of common traits in the era of genome-wide association analysis (GWAS)?
 <details>
 <summary>
@@ -799,8 +798,8 @@ <h4><span class="header-section-number">8.1.2.1</span> Questions for discussions
 </ul></li>
 </ul>
 </div>
-<div id="hands-on-exercise-variance-explained-using-regression-based-method" class="section level4 hasAnchor" number="8.1.2.2">
-<h4><span class="header-section-number">8.1.2.2</span> Hands-on exercise : variance explained using regression-based method<a href="pop-genetics.html#hands-on-exercise-variance-explained-using-regression-based-method" class="anchor-section" aria-label="Anchor link to header"></a></h4>
+<div id="hands-on-exercise-variance-explained-using-regression-based-method" class="section level4 hasAnchor" number="7.1.2.2">
+<h4><span class="header-section-number">7.1.2.2</span> Hands-on exercise : variance explained using regression-based method<a href="pop-genetics.html#hands-on-exercise-variance-explained-using-regression-based-method" class="anchor-section" aria-label="Anchor link to header"></a></h4>
 <p><strong>Q1.</strong> What is the variance of the phenotype?</p>
 <p><strong>Q2.</strong> Compute the explained variance attributable to the additive genetic component of the QTL with strongest association in Part 1.</p>
 <p><strong>Q3.</strong> Compute the explained variance attributable to the dominance genetic component of the QTL with strongest association in Part 1.</p>
@@ -857,8 +856,8 @@ <h4><span class="header-section-number">8.1.2.2</span> Hands-on exercise : varia
 <span id="cb175-8"><a href="pop-genetics.html#cb175-8" tabindex="-1"></a><span class="fu">summary</span>(linAD5)<span class="sc">$</span>r.squared<span class="sc">*</span>var_pheno    <span class="co"># (raw) variance component of total genetic component</span></span>
 <span id="cb175-9"><a href="pop-genetics.html#cb175-9" tabindex="-1"></a><span class="co">#&gt; [1] 3.519363</span></span></code></pre></div>
 </div>
-<div id="hands-on-exercise-variance-explained-using-a-classical-twin-design." class="section level4 hasAnchor" number="8.1.2.3">
-<h4><span class="header-section-number">8.1.2.3</span> Hands-on exercise : variance explained using a classical twin design.<a href="pop-genetics.html#hands-on-exercise-variance-explained-using-a-classical-twin-design." class="anchor-section" aria-label="Anchor link to header"></a></h4>
+<div id="hands-on-exercise-variance-explained-using-a-classical-twin-design." class="section level4 hasAnchor" number="7.1.2.3">
+<h4><span class="header-section-number">7.1.2.3</span> Hands-on exercise : variance explained using a classical twin design.<a href="pop-genetics.html#hands-on-exercise-variance-explained-using-a-classical-twin-design." class="anchor-section" aria-label="Anchor link to header"></a></h4>
 <p>Based on our regression results, we have estimates of the total genetic variance as well as the A and D components for phenotype 1. In practice, it is impossible to know all the variants associated with any polygenic trait.</p>
 <p>Given <code>rMZ &gt; 2*rDZ</code>, we can use Falconer’s formula based on ADE model to estimate the A (additive genetic) and D (dominance) variance with the classical twin design for phenotype 1 without genotypes.</p>
 <strong>Q5.</strong> Compute rMZ and rDZ.
@@ -929,8 +928,8 @@ <h4><span class="header-section-number">8.1.2.3</span> Hands-on exercise : varia
 <span id="cb177-12"><a href="pop-genetics.html#cb177-12" tabindex="-1"></a><span class="fu">print</span>(<span class="fu">c</span>(sA2, sC2, sE2))</span></code></pre></div>
 </div>
 </div>
-<div id="references" class="section level3 hasAnchor" number="8.1.3">
-<h3><span class="header-section-number">8.1.3</span> References<a href="pop-genetics.html#references" class="anchor-section" aria-label="Anchor link to header"></a></h3>
+<div id="references" class="section level3 hasAnchor" number="7.1.3">
+<h3><span class="header-section-number">7.1.3</span> References<a href="pop-genetics.html#references" class="anchor-section" aria-label="Anchor link to header"></a></h3>
 <ol style="list-style-type: decimal">
 <li><p>Evans DM, Gillespie NA, Martin NG. Biometrical genetics. Biol Psychol. 2002 Oct;61(1-2):33-51. doi: 10.1016/s0301-0511(02)00051-0. PMID: 12385668. [Review article]</p></li>
 <li><p>Falconer, D.S. and Mackay, T.F.C. (1996) Introduction to Quantitative Genetics. 4th Edition, Addison Wesley Longman, Harlow. [Most classical; a lot of online version]</p></li>
diff --git a/docs/preface.html b/docs/preface.html
index c6d0631..a168367 100644
--- a/docs/preface.html
+++ b/docs/preface.html
@@ -23,7 +23,7 @@
 <meta name="author" content="BIOF1001 teaching team" />
 
 
-<meta name="date" content="2023-11-06" />
+<meta name="date" content="2024-08-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -56,7 +56,7 @@
 
 <style type="text/css">
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span { line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -278,51 +278,52 @@
 </ul></li>
 <li class="part"><span><b>II Biomedical Data Modules</b></span></li>
 <li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
-<li class="chapter" data-level="6" data-path="infectious-dis.html"><a href="infectious-dis.html"><i class="fa fa-check"></i><b>6</b> Infectious Disease Informatics</a></li>
-<li class="chapter" data-level="7" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>7</b> Cancer genomics and epidemiology</a>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
 <ul>
-<li class="chapter" data-level="7.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>7.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
 <ul>
-<li class="chapter" data-level="7.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>7.1.1</b> Exploratory analysis</a></li>
-<li class="chapter" data-level="7.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>7.1.2</b> Statistical analysis</a></li>
-<li class="chapter" data-level="7.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>7.1.3</b> Literature search</a></li>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
 </ul></li>
-<li class="chapter" data-level="7.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>7.2</b> Case study 2: Cancer Epidemiology</a></li>
-<li class="chapter" data-level="7.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>7.3</b> 1. Scenario</a></li>
-<li class="chapter" data-level="7.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>7.4</b> 2. Hong Kong population</a>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
 <ul>
-<li class="chapter" data-level="7.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>7.4.1</b> Download population data</a></li>
-<li class="chapter" data-level="7.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>7.4.2</b> Format data for plotting</a></li>
-<li class="chapter" data-level="7.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>7.4.3</b> Plotting population data</a></li>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
 </ul></li>
-<li class="chapter" data-level="7.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>7.5</b> 3. Cancer registry data</a>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
 <ul>
-<li class="chapter" data-level="7.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>7.5.1</b> Download cancer registry data</a></li>
-<li class="chapter" data-level="7.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>7.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
-<li class="chapter" data-level="7.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>7.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
-<li class="chapter" data-level="7.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>7.5.4</b> 3c. Mortality-incidence ratio</a></li>
-<li class="chapter" data-level="7.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>7.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
-<li class="chapter" data-level="7.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>7.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
 </ul></li>
-<li class="chapter" data-level="7.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>7.6</b> 4. Existing cancer funding and publication data</a>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
 <ul>
-<li class="chapter" data-level="7.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>7.6.1</b> Download HMRF grants and Pubmed data</a></li>
-<li class="chapter" data-level="7.6.2" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>7.6.2</b> Make compare grant funding with incidence and mortality</a></li>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
 </ul></li>
-<li class="chapter" data-level="7.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>7.7</b> 5. Open disucssion</a></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
 </ul></li>
-<li class="chapter" data-level="8" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>8</b> Population Genetics and Diseases</a>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
 <ul>
-<li class="chapter" data-level="8.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>8.1</b> Case study 1: Heritability and human traits</a>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
 <ul>
-<li class="chapter" data-level="8.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>8.1.1</b> Part 1</a></li>
-<li class="chapter" data-level="8.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>8.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
 </ul></li>
 </ul></li>
 <li class="part"><span><b>III Appendix</b></span></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
 <ul>
-<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r"><i class="fa fa-check"></i>A.1 Install R</a>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
 <ul>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
@@ -338,7 +339,7 @@
 </ul></li>
 <li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
 </ul></li>
-<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
 <li class="divider"></li>
 <li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
 
@@ -388,9 +389,8 @@ <h3>What you will learn from this course/book<a href="preface.html#what-you-will
 problem-based learning format:</p>
 <ol style="list-style-type: decimal">
 <li>Medical imaging and digital health, by Dr Joshua Ho and Dr Rachel Kwan</li>
-<li>Infectious disease informatics, by Dr Tommy Lam and Dr Kathy Leung</li>
 <li>Cancer genomics and epidemiology, by Dr David Shih and Dr Jason Wong</li>
-<li>Population genetics and diseases, by Dr Clara Tang and Dr Asif Javed</li>
+<li>Population genetics and diseases, by Dr Clara Tang and Dr Yuanhua Huang</li>
 </ol>
 </div>
 <div id="what-we-recommend-you-do-while-reading-this-book" class="section level3 unnumbered hasAnchor">
@@ -414,9 +414,13 @@ <h2>Other reference books<a href="preface.html#other-reference-books" class="anc
 </div>
 <div id="acknowledgements" class="section level2 unnumbered hasAnchor">
 <h2>Acknowledgements<a href="preface.html#acknowledgements" class="anchor-section" aria-label="Anchor link to header"></a></h2>
-<p>We thank all teachers contributing to this course across all years, including
-Dr Lequan Yu (2022-23) and Dr Carlos Wong (2022-23) and student helpers serving
-as demonstrators, including Mr Mingze Gao and Ms Fangxin Cai.</p>
+<p>We thank all teachers and student helpers contributing to this course across
+all years, including</p>
+<ul>
+<li>2022: Dr Lequan Yu and Dr Carlos Wong</li>
+<li>2022 &amp; 2023: Dr Asif Javed, Dr Tommy Lam, and Dr Kathy Leung</li>
+<li>Student helpers: Mr Mingze Gao, Ms Fangxin Cai, and Mr Hoi Man Chung.</li>
+</ul>
 <!-- ## Last notes {-} -->
 <!-- # About the authors {-} -->
 <!-- The authors are the teaching team for the BIOF1001 course (ordered by teaching  -->
diff --git a/docs/reference-keys.txt b/docs/reference-keys.txt
index 4709ada..3755748 100644
--- a/docs/reference-keys.txt
+++ b/docs/reference-keys.txt
@@ -99,7 +99,6 @@ two-types-of-error
 roc-curve
 homework-1
 image-digital
-infectious-dis
 cancer
 cancer-case1
 exploratory-analysis
@@ -120,6 +119,7 @@ d.-paired-t-test-on-mortality-incidence-ratio-change
 e.-childhood-versus-elderly-cancers
 existing-cancer-funding-and-publication-data
 download-hmrf-grants-and-pubmed-data
+make-word-cloud-for-grants
 make-compare-grant-funding-with-incidence-and-mortality
 open-disucssion
 pop-genetics
@@ -129,4 +129,6 @@ questions-for-discussion
 hands-on-exercise-association-test
 part-2
 questions-for-discussions
-hands-on-exercise-variance-explained
+hands-on-exercise-variance-explained-using-regression-based-method
+hands-on-exercise-variance-explained-using-a-classical-twin-design.
+references
diff --git a/docs/references-1.html b/docs/references-1.html
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+  <meta property="og:description" content="This is a minimal example of using the bookdown package to write a book. The output format for this example is bookdown::gitbook." />
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+  <meta name="twitter:title" content="References | Biomedical Data Science - introduction with case studies" />
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+
+    <div class="book-summary">
+      <nav role="navigation">
+
+<ul class="summary">
+<li><a href="./index.html">Biomedical Data Science</a></li>
+
+<li class="divider"></li>
+<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Welcome</a></li>
+<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html"><i class="fa fa-check"></i>Preface</a>
+<ul>
+<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#introduction-for-readers"><i class="fa fa-check"></i>Introduction for readers</a>
+<ul>
+<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#what-you-will-learn-from-this-coursebook"><i class="fa fa-check"></i>What you will learn from this course/book</a></li>
+<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#what-we-recommend-you-do-while-reading-this-book"><i class="fa fa-check"></i>What we recommend you do while reading this book</a></li>
+</ul></li>
+<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#other-reference-books"><i class="fa fa-check"></i>Other reference books</a></li>
+<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#acknowledgements"><i class="fa fa-check"></i>Acknowledgements</a></li>
+</ul></li>
+<li class="part"><span><b>I Data Science Foundations</b></span></li>
+<li class="chapter" data-level="1" data-path="introR.html"><a href="introR.html"><i class="fa fa-check"></i><b>1</b> Introduction to R programming</a>
+<ul>
+<li class="chapter" data-level="1.1" data-path="introR.html"><a href="introR.html#data-types"><i class="fa fa-check"></i><b>1.1</b> Data types</a>
+<ul>
+<li class="chapter" data-level="1.1.1" data-path="introR.html"><a href="introR.html#nemeric-or-double"><i class="fa fa-check"></i><b>1.1.1</b> nemeric (or double)</a></li>
+<li class="chapter" data-level="1.1.2" data-path="introR.html"><a href="introR.html#integer"><i class="fa fa-check"></i><b>1.1.2</b> integer</a></li>
+<li class="chapter" data-level="1.1.3" data-path="introR.html"><a href="introR.html#logical"><i class="fa fa-check"></i><b>1.1.3</b> logical</a></li>
+<li class="chapter" data-level="1.1.4" data-path="introR.html"><a href="introR.html#character"><i class="fa fa-check"></i><b>1.1.4</b> character</a></li>
+<li class="chapter" data-level="1.1.5" data-path="introR.html"><a href="introR.html#memeory-usage"><i class="fa fa-check"></i><b>1.1.5</b> Memeory usage</a></li>
+</ul></li>
+<li class="chapter" data-level="1.2" data-path="introR.html"><a href="introR.html#data-structures"><i class="fa fa-check"></i><b>1.2</b> Data structures</a>
+<ul>
+<li class="chapter" data-level="1.2.1" data-path="introR.html"><a href="introR.html#vector"><i class="fa fa-check"></i><b>1.2.1</b> Vector</a></li>
+<li class="chapter" data-level="1.2.2" data-path="introR.html"><a href="introR.html#matrix"><i class="fa fa-check"></i><b>1.2.2</b> Matrix</a></li>
+<li class="chapter" data-level="1.2.3" data-path="introR.html"><a href="introR.html#list"><i class="fa fa-check"></i><b>1.2.3</b> List</a></li>
+<li class="chapter" data-level="1.2.4" data-path="introR.html"><a href="introR.html#data-frame"><i class="fa fa-check"></i><b>1.2.4</b> Data Frame</a></li>
+<li class="chapter" data-level="1.2.5" data-path="introR.html"><a href="introR.html#factor-vs-vector"><i class="fa fa-check"></i><b>1.2.5</b> Factor vs vector</a></li>
+</ul></li>
+<li class="chapter" data-level="1.3" data-path="introR.html"><a href="introR.html#read-and-write-files-tables"><i class="fa fa-check"></i><b>1.3</b> Read and write files (tables)</a>
+<ul>
+<li class="chapter" data-level="1.3.1" data-path="introR.html"><a href="introR.html#read-file"><i class="fa fa-check"></i><b>1.3.1</b> Read file</a></li>
+<li class="chapter" data-level="1.3.2" data-path="introR.html"><a href="introR.html#write-file"><i class="fa fa-check"></i><b>1.3.2</b> Write file</a></li>
+</ul></li>
+<li class="chapter" data-level="1.4" data-path="introR.html"><a href="introR.html#functions-and-packages"><i class="fa fa-check"></i><b>1.4</b> Functions and Packages</a>
+<ul>
+<li class="chapter" data-level="1.4.1" data-path="introR.html"><a href="introR.html#install-packages"><i class="fa fa-check"></i><b>1.4.1</b> Install packages</a></li>
+<li class="chapter" data-level="1.4.2" data-path="introR.html"><a href="introR.html#apply-function-repeatly"><i class="fa fa-check"></i><b>1.4.2</b> Apply function repeatly</a></li>
+<li class="chapter" data-level="1.4.3" data-path="introR.html"><a href="introR.html#pattern-match"><i class="fa fa-check"></i><b>1.4.3</b> Pattern match</a></li>
+</ul></li>
+<li class="chapter" data-level="1.5" data-path="introR.html"><a href="introR.html#flow-control"><i class="fa fa-check"></i><b>1.5</b> Flow Control</a>
+<ul>
+<li class="chapter" data-level="1.5.1" data-path="introR.html"><a href="introR.html#logical-operator"><i class="fa fa-check"></i><b>1.5.1</b> Logical operator</a></li>
+<li class="chapter" data-level="1.5.2" data-path="introR.html"><a href="introR.html#if-else-statements"><i class="fa fa-check"></i><b>1.5.2</b> if-else statements</a></li>
+<li class="chapter" data-level="1.5.3" data-path="introR.html"><a href="introR.html#for-loop"><i class="fa fa-check"></i><b>1.5.3</b> for-loop</a></li>
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+<li class="chapter" data-level="1.6" data-path="introR.html"><a href="introR.html#plotting"><i class="fa fa-check"></i><b>1.6</b> Plotting</a>
+<ul>
+<li class="chapter" data-level="1.6.1" data-path="introR.html"><a href="introR.html#datasets"><i class="fa fa-check"></i><b>1.6.1</b> datasets</a></li>
+<li class="chapter" data-level="1.6.2" data-path="introR.html"><a href="introR.html#basic-plotting"><i class="fa fa-check"></i><b>1.6.2</b> Basic plotting</a></li>
+<li class="chapter" data-level="1.6.3" data-path="introR.html"><a href="introR.html#ggplot2"><i class="fa fa-check"></i><b>1.6.3</b> ggplot2</a></li>
+</ul></li>
+<li class="chapter" data-level="1.7" data-path="introR.html"><a href="introR.html#scientific-computating"><i class="fa fa-check"></i><b>1.7</b> Scientific computating</a>
+<ul>
+<li class="chapter" data-level="1.7.1" data-path="introR.html"><a href="introR.html#orders-of-operators"><i class="fa fa-check"></i><b>1.7.1</b> Orders of operators</a></li>
+<li class="chapter" data-level="1.7.2" data-path="introR.html"><a href="introR.html#functions-for-statistics"><i class="fa fa-check"></i><b>1.7.2</b> Functions for statistics</a></li>
+<li class="chapter" data-level="1.7.3" data-path="introR.html"><a href="introR.html#correlation"><i class="fa fa-check"></i><b>1.7.3</b> Correlation</a></li>
+<li class="chapter" data-level="1.7.4" data-path="introR.html"><a href="introR.html#hypothesis-testing-t-test"><i class="fa fa-check"></i><b>1.7.4</b> Hypothesis testing (t test)</a></li>
+<li class="chapter" data-level="1.7.5" data-path="introR.html"><a href="introR.html#regression"><i class="fa fa-check"></i><b>1.7.5</b> Regression</a></li>
+<li class="chapter" data-level="1.7.6" data-path="introR.html"><a href="introR.html#resource-links"><i class="fa fa-check"></i><b>1.7.6</b> Resource links</a></li>
+<li class="chapter" data-level="1.7.7" data-path="introR.html"><a href="introR.html#coding-styling"><i class="fa fa-check"></i><b>1.7.7</b> Coding styling</a></li>
+</ul></li>
+<li class="chapter" data-level="1.8" data-path="introR.html"><a href="introR.html#exercises"><i class="fa fa-check"></i><b>1.8</b> Exercises</a>
+<ul>
+<li class="chapter" data-level="1.8.1" data-path="introR.html"><a href="introR.html#exercises-p1"><i class="fa fa-check"></i><b>1.8.1</b> Part 1. Basics (~40min)</a></li>
+<li class="chapter" data-level="1.8.2" data-path="introR.html"><a href="introR.html#exercises-p2"><i class="fa fa-check"></i><b>1.8.2</b> Part 2. Making plotting (~40min)</a></li>
+<li class="chapter" data-level="1.8.3" data-path="introR.html"><a href="introR.html#exercises-p3"><i class="fa fa-check"></i><b>1.8.3</b> Part 3. For loop and repeating processing (~40min)</a></li>
+</ul></li>
+</ul></li>
+<li class="chapter" data-level="2" data-path="introHypoTest.html"><a href="introHypoTest.html"><i class="fa fa-check"></i><b>2</b> Introduction to Hypothesis testing</a>
+<ul>
+<li class="chapter" data-level="2.1" data-path="introHypoTest.html"><a href="introHypoTest.html#hypothesis-testing-and-p-value"><i class="fa fa-check"></i><b>2.1</b> Hypothesis testing and <em>p</em> value</a>
+<ul>
+<li class="chapter" data-level="2.1.1" data-path="introHypoTest.html"><a href="introHypoTest.html#example-1-probability-of-rolling-a-six"><i class="fa fa-check"></i><b>2.1.1</b> Example 1: probability of rolling a six?</a></li>
+</ul></li>
+<li class="chapter" data-level="2.2" data-path="introHypoTest.html"><a href="introHypoTest.html#permutation-test"><i class="fa fa-check"></i><b>2.2</b> Permutation test</a>
+<ul>
+<li class="chapter" data-level="2.2.1" data-path="introHypoTest.html"><a href="introHypoTest.html#example-2-difference-in-birth-weight"><i class="fa fa-check"></i><b>2.2.1</b> Example 2: difference in birth weight</a></li>
+<li class="chapter" data-level="2.2.2" data-path="introHypoTest.html"><a href="introHypoTest.html#null-distribution-approximated-by-resampling"><i class="fa fa-check"></i><b>2.2.2</b> Null distribution approximated by resampling</a></li>
+</ul></li>
+<li class="chapter" data-level="2.3" data-path="introHypoTest.html"><a href="introHypoTest.html#t-test"><i class="fa fa-check"></i><b>2.3</b> <em>t</em> test</a>
+<ul>
+<li class="chapter" data-level="2.3.1" data-path="introHypoTest.html"><a href="introHypoTest.html#derivation-of-t-distribution"><i class="fa fa-check"></i><b>2.3.1</b> Derivation of t distribution</a></li>
+<li class="chapter" data-level="2.3.2" data-path="introHypoTest.html"><a href="introHypoTest.html#direct-use-of-t.test"><i class="fa fa-check"></i><b>2.3.2</b> Direct use of <code>t.test()</code></a></li>
+</ul></li>
+<li class="chapter" data-level="2.4" data-path="introHypoTest.html"><a href="introHypoTest.html#glm-test"><i class="fa fa-check"></i><b>2.4</b> GLM test</a></li>
+<li class="chapter" data-level="2.5" data-path="introHypoTest.html"><a href="introHypoTest.html#multiple-testing"><i class="fa fa-check"></i><b>2.5</b> Multiple testing</a>
+<ul>
+<li class="chapter" data-level="2.5.1" data-path="introHypoTest.html"><a href="introHypoTest.html#null-distribution-of-test-statistic"><i class="fa fa-check"></i><b>2.5.1</b> Null distribution (of test statistic)</a></li>
+<li class="chapter" data-level="2.5.2" data-path="introHypoTest.html"><a href="introHypoTest.html#null-distribution-of-p-value"><i class="fa fa-check"></i><b>2.5.2</b> Null distribution of p value</a></li>
+<li class="chapter" data-level="2.5.3" data-path="introHypoTest.html"><a href="introHypoTest.html#minimal-p-values-in-10-tests"><i class="fa fa-check"></i><b>2.5.3</b> Minimal p values in 10 tests</a></li>
+<li class="chapter" data-level="2.5.4" data-path="introHypoTest.html"><a href="introHypoTest.html#homework"><i class="fa fa-check"></i><b>2.5.4</b> Homework</a></li>
+</ul></li>
+</ul></li>
+<li class="chapter" data-level="3" data-path="introLinearReg.html"><a href="introLinearReg.html"><i class="fa fa-check"></i><b>3</b> Introduction to Linear Regression</a>
+<ul>
+<li class="chapter" data-level="3.1" data-path="introLinearReg.html"><a href="introLinearReg.html#linear-regression-using-simulated-data"><i class="fa fa-check"></i><b>3.1</b> Linear Regression Using Simulated Data</a>
+<ul>
+<li class="chapter" data-level="3.1.1" data-path="introLinearReg.html"><a href="introLinearReg.html#simulating-data"><i class="fa fa-check"></i><b>3.1.1</b> Simulating data:</a></li>
+<li class="chapter" data-level="3.1.2" data-path="introLinearReg.html"><a href="introLinearReg.html#model-efficacy"><i class="fa fa-check"></i><b>3.1.2</b> Model efficacy</a></li>
+<li class="chapter" data-level="3.1.3" data-path="introLinearReg.html"><a href="introLinearReg.html#r-squared"><i class="fa fa-check"></i><b>3.1.3</b> <em>R-Squared</em></a></li>
+</ul></li>
+<li class="chapter" data-level="3.2" data-path="introLinearReg.html"><a href="introLinearReg.html#least-squares-using-simulated-data"><i class="fa fa-check"></i><b>3.2</b> Least Squares Using Simulated Data</a></li>
+<li class="chapter" data-level="3.3" data-path="introLinearReg.html"><a href="introLinearReg.html#diagnostic-check-of-a-fitted-regression-model"><i class="fa fa-check"></i><b>3.3</b> Diagnostic check of a fitted regression model</a>
+<ul>
+<li class="chapter" data-level="3.3.1" data-path="introLinearReg.html"><a href="introLinearReg.html#residual-standard-errors-rse"><i class="fa fa-check"></i><b>3.3.1</b> Residual Standard Errors (RSE)</a></li>
+<li class="chapter" data-level="3.3.2" data-path="introLinearReg.html"><a href="introLinearReg.html#p-values"><i class="fa fa-check"></i><b>3.3.2</b> p-values</a></li>
+<li class="chapter" data-level="3.3.3" data-path="introLinearReg.html"><a href="introLinearReg.html#f-statistics"><i class="fa fa-check"></i><b>3.3.3</b> F-statistics</a></li>
+</ul></li>
+<li class="chapter" data-level="3.4" data-path="introLinearReg.html"><a href="introLinearReg.html#simple-linear-regression-with-lm-function"><i class="fa fa-check"></i><b>3.4</b> Simple Linear Regression with <code>lm</code> function</a></li>
+<li class="chapter" data-level="3.5" data-path="introLinearReg.html"><a href="introLinearReg.html#multiple-regression-with-lm-function"><i class="fa fa-check"></i><b>3.5</b> Multiple Regression with <code>lm</code> function</a></li>
+</ul></li>
+<li class="chapter" data-level="4" data-path="introClassifier.html"><a href="introClassifier.html"><i class="fa fa-check"></i><b>4</b> Introduction to Classification</a>
+<ul>
+<li class="chapter" data-level="4.1" data-path="introClassifier.html"><a href="introClassifier.html#visualise-logistic-and-logit-functions"><i class="fa fa-check"></i><b>4.1</b> Visualise logistic and logit functions</a>
+<ul>
+<li class="chapter" data-level="4.1.1" data-path="introClassifier.html"><a href="introClassifier.html#logistic-function"><i class="fa fa-check"></i><b>4.1.1</b> Logistic function</a></li>
+<li class="chapter" data-level="4.1.2" data-path="introClassifier.html"><a href="introClassifier.html#logit-function"><i class="fa fa-check"></i><b>4.1.2</b> Logit function</a></li>
+<li class="chapter" data-level="4.1.3" data-path="introClassifier.html"><a href="introClassifier.html#visualise-the-distribution"><i class="fa fa-check"></i><b>4.1.3</b> Visualise the distribution</a></li>
+</ul></li>
+<li class="chapter" data-level="4.2" data-path="introClassifier.html"><a href="introClassifier.html#logistic-regression-on-diabetes"><i class="fa fa-check"></i><b>4.2</b> Logistic regression on Diabetes</a>
+<ul>
+<li class="chapter" data-level="4.2.1" data-path="introClassifier.html"><a href="introClassifier.html#load-pima-indians-diabetes-database"><i class="fa fa-check"></i><b>4.2.1</b> Load Pima Indians Diabetes Database</a></li>
+<li class="chapter" data-level="4.2.2" data-path="introClassifier.html"><a href="introClassifier.html#fit-logistic-regression"><i class="fa fa-check"></i><b>4.2.2</b> Fit logistic regression</a></li>
+<li class="chapter" data-level="4.2.3" data-path="introClassifier.html"><a href="introClassifier.html#assess-on-test-data"><i class="fa fa-check"></i><b>4.2.3</b> Assess on test data</a></li>
+<li class="chapter" data-level="4.2.4" data-path="introClassifier.html"><a href="introClassifier.html#model-selection-and-diagnosis"><i class="fa fa-check"></i><b>4.2.4</b> Model selection and diagnosis</a></li>
+</ul></li>
+<li class="chapter" data-level="4.3" data-path="introClassifier.html"><a href="introClassifier.html#cross-validation"><i class="fa fa-check"></i><b>4.3</b> Cross-validation</a></li>
+<li class="chapter" data-level="4.4" data-path="introClassifier.html"><a href="introClassifier.html#more-assessment-metrics"><i class="fa fa-check"></i><b>4.4</b> More assessment metrics</a>
+<ul>
+<li class="chapter" data-level="4.4.1" data-path="introClassifier.html"><a href="introClassifier.html#two-types-of-error"><i class="fa fa-check"></i><b>4.4.1</b> Two types of error</a></li>
+<li class="chapter" data-level="4.4.2" data-path="introClassifier.html"><a href="introClassifier.html#roc-curve"><i class="fa fa-check"></i><b>4.4.2</b> ROC curve</a></li>
+<li class="chapter" data-level="4.4.3" data-path="introClassifier.html"><a href="introClassifier.html#homework-1"><i class="fa fa-check"></i><b>4.4.3</b> Homework</a></li>
+</ul></li>
+</ul></li>
+<li class="part"><span><b>II Biomedical Data Modules</b></span></li>
+<li class="chapter" data-level="5" data-path="image-digital.html"><a href="image-digital.html"><i class="fa fa-check"></i><b>5</b> Medical Image and Digital Health</a></li>
+<li class="chapter" data-level="6" data-path="cancer.html"><a href="cancer.html"><i class="fa fa-check"></i><b>6</b> Cancer genomics and epidemiology</a>
+<ul>
+<li class="chapter" data-level="6.1" data-path="cancer.html"><a href="cancer.html#cancer-case1"><i class="fa fa-check"></i><b>6.1</b> Case study 1: analysis of cBioportal mutation data</a>
+<ul>
+<li class="chapter" data-level="6.1.1" data-path="cancer.html"><a href="cancer.html#exploratory-analysis"><i class="fa fa-check"></i><b>6.1.1</b> Exploratory analysis</a></li>
+<li class="chapter" data-level="6.1.2" data-path="cancer.html"><a href="cancer.html#statistical-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Statistical analysis</a></li>
+<li class="chapter" data-level="6.1.3" data-path="cancer.html"><a href="cancer.html#literature-search"><i class="fa fa-check"></i><b>6.1.3</b> Literature search</a></li>
+</ul></li>
+<li class="chapter" data-level="6.2" data-path="cancer.html"><a href="cancer.html#cancer-case2"><i class="fa fa-check"></i><b>6.2</b> Case study 2: Cancer Epidemiology</a></li>
+<li class="chapter" data-level="6.3" data-path="cancer.html"><a href="cancer.html#scenario"><i class="fa fa-check"></i><b>6.3</b> 1. Scenario</a></li>
+<li class="chapter" data-level="6.4" data-path="cancer.html"><a href="cancer.html#hong-kong-population"><i class="fa fa-check"></i><b>6.4</b> 2. Hong Kong population</a>
+<ul>
+<li class="chapter" data-level="6.4.1" data-path="cancer.html"><a href="cancer.html#download-population-data"><i class="fa fa-check"></i><b>6.4.1</b> Download population data</a></li>
+<li class="chapter" data-level="6.4.2" data-path="cancer.html"><a href="cancer.html#format-data-for-plotting"><i class="fa fa-check"></i><b>6.4.2</b> Format data for plotting</a></li>
+<li class="chapter" data-level="6.4.3" data-path="cancer.html"><a href="cancer.html#plotting-population-data"><i class="fa fa-check"></i><b>6.4.3</b> Plotting population data</a></li>
+</ul></li>
+<li class="chapter" data-level="6.5" data-path="cancer.html"><a href="cancer.html#cancer-registry-data"><i class="fa fa-check"></i><b>6.5</b> 3. Cancer registry data</a>
+<ul>
+<li class="chapter" data-level="6.5.1" data-path="cancer.html"><a href="cancer.html#download-cancer-registry-data"><i class="fa fa-check"></i><b>6.5.1</b> Download cancer registry data</a></li>
+<li class="chapter" data-level="6.5.2" data-path="cancer.html"><a href="cancer.html#a.-visualise-changes-in-incidence-and-mortality"><i class="fa fa-check"></i><b>6.5.2</b> 3a. Visualise changes in incidence and mortality</a></li>
+<li class="chapter" data-level="6.5.3" data-path="cancer.html"><a href="cancer.html#b.-calculate-cancer-risk-and-mortality-rate"><i class="fa fa-check"></i><b>6.5.3</b> 3b. Calculate cancer risk and mortality rate</a></li>
+<li class="chapter" data-level="6.5.4" data-path="cancer.html"><a href="cancer.html#c.-mortality-incidence-ratio"><i class="fa fa-check"></i><b>6.5.4</b> 3c. Mortality-incidence ratio</a></li>
+<li class="chapter" data-level="6.5.5" data-path="cancer.html"><a href="cancer.html#d.-paired-t-test-on-mortality-incidence-ratio-change"><i class="fa fa-check"></i><b>6.5.5</b> 3d. Paired t-test on mortality-incidence ratio change</a></li>
+<li class="chapter" data-level="6.5.6" data-path="cancer.html"><a href="cancer.html#e.-childhood-versus-elderly-cancers"><i class="fa fa-check"></i><b>6.5.6</b> 3e. Childhood versus elderly cancers</a></li>
+</ul></li>
+<li class="chapter" data-level="6.6" data-path="cancer.html"><a href="cancer.html#existing-cancer-funding-and-publication-data"><i class="fa fa-check"></i><b>6.6</b> 4. Existing cancer funding and publication data</a>
+<ul>
+<li class="chapter" data-level="6.6.1" data-path="cancer.html"><a href="cancer.html#download-hmrf-grants-and-pubmed-data"><i class="fa fa-check"></i><b>6.6.1</b> Download HMRF grants and Pubmed data</a></li>
+<li class="chapter" data-level="6.6.2" data-path="cancer.html"><a href="cancer.html#make-word-cloud-for-grants"><i class="fa fa-check"></i><b>6.6.2</b> Make word cloud for grants</a></li>
+<li class="chapter" data-level="6.6.3" data-path="cancer.html"><a href="cancer.html#make-compare-grant-funding-with-incidence-and-mortality"><i class="fa fa-check"></i><b>6.6.3</b> Make compare grant funding with incidence and mortality</a></li>
+</ul></li>
+<li class="chapter" data-level="6.7" data-path="cancer.html"><a href="cancer.html#open-disucssion"><i class="fa fa-check"></i><b>6.7</b> 5. Open disucssion</a></li>
+</ul></li>
+<li class="chapter" data-level="7" data-path="pop-genetics.html"><a href="pop-genetics.html"><i class="fa fa-check"></i><b>7</b> Population Genetics and Diseases</a>
+<ul>
+<li class="chapter" data-level="7.1" data-path="pop-genetics.html"><a href="pop-genetics.html#case-study-1-heritability-and-human-traits"><i class="fa fa-check"></i><b>7.1</b> Case study 1: Heritability and human traits</a>
+<ul>
+<li class="chapter" data-level="7.1.1" data-path="pop-genetics.html"><a href="pop-genetics.html#part-1"><i class="fa fa-check"></i><b>7.1.1</b> Part 1</a></li>
+<li class="chapter" data-level="7.1.2" data-path="pop-genetics.html"><a href="pop-genetics.html#part-2"><i class="fa fa-check"></i><b>7.1.2</b> Part 2</a></li>
+<li class="chapter" data-level="7.1.3" data-path="pop-genetics.html"><a href="pop-genetics.html#references"><i class="fa fa-check"></i><b>7.1.3</b> References</a></li>
+</ul></li>
+</ul></li>
+<li class="part"><span><b>III Appendix</b></span></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html"><i class="fa fa-check"></i>Appendix A: Install R &amp; RStudio</a>
+<ul>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.1-install-r-4.3.1"><i class="fa fa-check"></i>A.1 Install R (&gt;=4.3.1)</a>
+<ul>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-windows"><i class="fa fa-check"></i>R on Windows</a></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-macos"><i class="fa fa-check"></i>R on macOS</a></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-on-linux-ubuntu"><i class="fa fa-check"></i>R on Linux (Ubuntu)</a></li>
+</ul></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.2-install-rstudio"><i class="fa fa-check"></i>A.2 Install RStudio</a></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a.3-use-r-inside-rstudio"><i class="fa fa-check"></i>A.3 Use R inside RStudio</a>
+<ul>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#r-studio"><i class="fa fa-check"></i>R studio</a></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#set-working-directory"><i class="fa fa-check"></i>Set working directory</a></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#some-general-knowledge"><i class="fa fa-check"></i>Some general knowledge</a></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#install-packages-1"><i class="fa fa-check"></i>Install packages</a></li>
+</ul></li>
+<li class="chapter" data-level="" data-path="install.html"><a href="install.html#a4.-cloud-computing"><i class="fa fa-check"></i>A4. Cloud computing</a></li>
+</ul></li>
+<li class="chapter" data-level="" data-path="references-1.html"><a href="references-1.html"><i class="fa fa-check"></i>References</a></li>
+<li class="divider"></li>
+<li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
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-[["index.html", "Biomedical Data Science - introduction with case studies Welcome", " Biomedical Data Science - introduction with case studies BIOF1001 teaching team 2023-11-06 Welcome Welcome to the book Biomedical Data Science - an introduction with case studies. Most contents are demonstrated with R programming language. This book is designed as a collection of R Markdown notebooks, as supplementary to the lecture notes for the course BIOF1001: Introduction to Biomedical Data Science, an undergraduate course (Year 1) at the University of Hong Kong. Note: Most contents may be only updated before or right after the lectures, so please refer to the updated version. GitHub Repository: you can find the source files on StatBiomed/BMDS-book and the way to re-build this book. "],["preface.html", "Preface Introduction for readers Other reference books Acknowledgements", " Preface This book is designed as the lecture notes and textbook for BIOF1001: Introduction to Biomedical Data Science, an undergraduate course (Year 1) at the University of Hong Kong. This book is not aimed to be a comprehensive textbook, but rather more Rmarkdown notebooks as supplementary to lecture notes so that students can reproduce the teaching contents more easily. Introduction for readers What you will learn from this course/book In part I, you will find a general introduction to data science (by Dr YH Huang): Basic programming and visualisation skills: R scripts for the quantitative methods and data visualisation. Quantitative methods: t-test, correlation analysis, clustering, linear regression, linear classification. Gain familiarity with common databases in the biomedical domain. Introduce ethical, legal, social and technological issues related to biomedical data sciences. Introduce good practice in managing a data science project and communicate results to key stakeholders. In part II, you will experience data types in four different biomedical topics, which will be illustrated with both introduction and cases that are suitable for problem-based learning format: Medical imaging and digital health, by Dr Joshua Ho and Dr Rachel Kwan Infectious disease informatics, by Dr Tommy Lam and Dr Kathy Leung Cancer genomics and epidemiology, by Dr David Shih and Dr Jason Wong Population genetics and diseases, by Dr Clara Tang and Dr Asif Javed What we recommend you do while reading this book To enhance the knowledge and skills learned from this book, we recommend that readers Read the materials/slides provided in each module Practice quantitative skills by solving problems using R Other reference books Besides this online book as a collection of R materials for the teaching contents, we also recommend the following online books as reference: Introduction to Data Science: Data Wrangling and Visualization with R by Rafeal A. Irizarry Advanced Data Science: Statistics and Prediction Algorithms Through Case Studies by Rafeal A. Irizarry Acknowledgements We thank all teachers contributing to this course across all years, including Dr Lequan Yu (2022-23) and Dr Carlos Wong (2022-23) and student helpers serving as demonstrators, including Mr Mingze Gao and Ms Fangxin Cai. "],["introR.html", "Chapter 1 Introduction to R programming 1.1 Data types 1.2 Data structures 1.3 Read and write files (tables) 1.4 Functions and Packages 1.5 Flow Control 1.6 Plotting 1.7 Scientific computating 1.8 Exercises", " Chapter 1 Introduction to R programming This notebook collects the scripts used for teaching in BIOF1001 for Introduction to R (1 hour teaching). You can get this Rmd file on Moodle or here (right-click and “save link as” to download). R is a programming language, particularly popular for its power in statistical computing, elegant graphics, and also genomic data analysis. It is a free and open-source software, with active support and development from the community. Additionally, R is relatively easy to get started for scientific computing. Note To learn and practice R programming, you need to install R and RStudio on your computer. You can follow the instructions for installation in the Appendix A chapter. 1.1 Data types In R language setting (similar to some other programming languages), there are a few commonly used data types that are predefined in the built-in environment. You can use the class() and typeof() functions to check the class and data type of any variable. In total, R has five data types: Numeric Integers Complex Logical Characters 1.1.1 nemeric (or double) The numeric is for numeric values, as the most common and the default data type. The numeric datatype saves values in double precision (double number of bytes in memory), so the type is also double. x &lt;- c(1.0, 2.0, 5.0, 7.0) x #&gt; [1] 1 2 5 7 class(x) #&gt; [1] &quot;numeric&quot; typeof(x) #&gt; [1] &quot;double&quot; 1.1.2 integer The integer is another data type used for the set of all integers. You can use the capital ‘L’ notation as a suffix to specify a particular value as the integer data type. Also, you can convert a value into an integer type using the as.integer() function. y &lt;- c(1L, 2L, 5L, 7L) y #&gt; [1] 1 2 5 7 class(y) #&gt; [1] &quot;integer&quot; typeof(y) #&gt; [1] &quot;integer&quot; # Assign a integer value to y y = 5 # is y an integer? print(is.integer(y)) #&gt; [1] FALSE 1.1.3 logical In R, the logical data type takes either a value of true or false. A logical value is often generated when comparing variables. z &lt;- c(TRUE, TRUE, TRUE, FALSE) z #&gt; [1] TRUE TRUE TRUE FALSE typeof(z) #&gt; [1] &quot;logical&quot; 1.1.4 character In R, the character is a data type where you have all the alphabets and special characters. It stores character values or strings. Strings in R can contain alphabets, numbers, and symbols. The character type is usually denoted by wrapping the value inside single or double inverted commas. w &lt;- c(&quot;aa&quot;, &quot;bb&quot;, &quot;5&quot;, &quot;7&quot;) w #&gt; [1] &quot;aa&quot; &quot;bb&quot; &quot;5&quot; &quot;7&quot; typeof(w) #&gt; [1] &quot;character&quot; 1.1.5 Memeory usage Each data type is explicitly defined, especially the size of the memory. When initializing a certain data type, there are a few small bytes used to store basic information. Let’s look at the empty values. object.size(numeric()) #&gt; 48 bytes object.size(integer()) #&gt; 48 bytes object.size(logical()) #&gt; 48 bytes object.size(character()) #&gt; 48 bytes To illustrate, let’s use 1000 elements below to show the memory size usage for each data type. As we will see, integer and logical use 4 bytes per element, which is only half of the memory usage by double (numeric) and character of 8 bytes. object.size(rep(1, 1000)) #&gt; 8048 bytes object.size(rep(1L, 1000)) #&gt; 4048 bytes object.size(rep(TRUE, 1000)) #&gt; 4048 bytes object.size(rep(&quot;aa&quot;, 1000)) #&gt; 8104 bytes 1.2 Data structures Data structure is one of the most important features in programming. It involves how the data is organised and can be accessed and modified. Using an appropriate data structure may largely improve computing efficiency. 1.2.1 Vector Vector is a basic data structure in R. It contains elements in the same data type (no matter double, integer, character or others). You can check the data type by using typeof() function and the length of the vector by length() function. Since a vector has elements of the same type, this function will try and coerce elements to the same type, if they are different. Coercion is from lower to higher types, i.e., from logical to integer to double to a character. See more introduction here. x &lt;- c(1, 2, 5, 7) x #&gt; [1] 1 2 5 7 typeof(x) #&gt; [1] &quot;double&quot; x &lt;- rep(3, 5) x #&gt; [1] 3 3 3 3 3 typeof(x) #&gt; [1] &quot;double&quot; x &lt;- 1:12 # integer x #&gt; [1] 1 2 3 4 5 6 7 8 9 10 11 12 typeof(x) #&gt; [1] &quot;integer&quot; 1.2.2 Matrix Matrix is a two-dimensional data structure. It is in principle built based on vector but has more convenient built-in functions for computation. It has rows and columns, both of which can also have names. To check the dimensions, you can use the dim() function. See more introduction here. A &lt;- matrix(1:12, nrow=3) A #&gt; [,1] [,2] [,3] [,4] #&gt; [1,] 1 4 7 10 #&gt; [2,] 2 5 8 11 #&gt; [3,] 3 6 9 12 B &lt;- matrix(1:12, nrow=3, byrow=TRUE) B #&gt; [,1] [,2] [,3] [,4] #&gt; [1,] 1 2 3 4 #&gt; [2,] 5 6 7 8 #&gt; [3,] 9 10 11 12 colnames(A) &lt;- c(&quot;C1&quot;,&quot;C2&quot;,&quot;C3&quot;,&quot;C4&quot;) rownames(A) &lt;- c(&quot;R1&quot;,&quot;R2&quot;,&quot;R3&quot;) A #&gt; C1 C2 C3 C4 #&gt; R1 1 4 7 10 #&gt; R2 2 5 8 11 #&gt; R3 3 6 9 12 1.2.2.1 Index Vector and Matrix To index vector, you can use logical or integer, or the element name if it has. Note, when using an integer for indexing, the index starts from 1 in R, unlike most programming languages where the index starts from 0. We can also use negative integers to return all elements except those specified. But we cannot mix positive and negative integers while indexing and real numbers if used are truncated to integers. N.B., when using logical as the index, be careful if the index length is different from the vector. x &lt;- 1:12 x[3] #&gt; [1] 3 x[2:5] #&gt; [1] 2 3 4 5 x[c(2, 5, 6)] # index with integer #&gt; [1] 2 5 6 x[c(TRUE, FALSE, FALSE, TRUE)] # index with logical value #&gt; [1] 1 4 5 8 9 12 Now, let’s index a matrix. It is very similar to vector, but it has both rows and columns. A &lt;- matrix(1:12, nrow=3) colnames(A) &lt;- c(&quot;C1&quot;,&quot;C2&quot;,&quot;C3&quot;,&quot;C4&quot;) rownames(A) &lt;- c(&quot;R1&quot;,&quot;R2&quot;,&quot;R3&quot;) A #&gt; C1 C2 C3 C4 #&gt; R1 1 4 7 10 #&gt; R2 2 5 8 11 #&gt; R3 3 6 9 12 A[1, 2] #&gt; [1] 4 A[1, &quot;C2&quot;] #&gt; [1] 4 A[1, c(2, 3)] #&gt; C2 C3 #&gt; 4 7 A[1:2, c(2, 3)] #&gt; C2 C3 #&gt; R1 4 7 #&gt; R2 5 8 Single row or column matrix will become a vector, unless using drop=FALSE A[1, 2:4] #&gt; C2 C3 C4 #&gt; 4 7 10 dim(A[1, 2:4]) #&gt; NULL A[1, 2:4, drop=FALSE] #&gt; C2 C3 C4 #&gt; R1 4 7 10 dim(A[1, 2:4, drop=FALSE]) #&gt; [1] 1 3 1.2.2.2 Modify values A[1, 2:4] &lt;- c(-3, -5, 20) A #&gt; C1 C2 C3 C4 #&gt; R1 1 -3 -5 20 #&gt; R2 2 5 8 11 #&gt; R3 3 6 9 12 1.2.3 List Different from vector that has all elements in the same data type, the list data structure can have components of mixed data types. More broadly, a list can contain a list of any data structure: value, vector, matrix, etc. We can use str() function to view the structure of a list (or any object). x &lt;- list(2.5, TRUE, 1:3) x #&gt; [[1]] #&gt; [1] 2.5 #&gt; #&gt; [[2]] #&gt; [1] TRUE #&gt; #&gt; [[3]] #&gt; [1] 1 2 3 str(x) #&gt; List of 3 #&gt; $ : num 2.5 #&gt; $ : logi TRUE #&gt; $ : int [1:3] 1 2 3 We can also have a name for each element: x &lt;- list(&quot;a&quot; = 2.5, &quot;b&quot; = TRUE, &quot;c&quot; = 1:3) x #&gt; $a #&gt; [1] 2.5 #&gt; #&gt; $b #&gt; [1] TRUE #&gt; #&gt; $c #&gt; [1] 1 2 3 str(x) #&gt; List of 3 #&gt; $ a: num 2.5 #&gt; $ b: logi TRUE #&gt; $ c: int [1:3] 1 2 3 1.2.3.1 Indexing list Different from vector and matrix, for a list, you need to use double-layer square brackets, either by numeric index or name. Alternatively, you can also use $ symbol with the name. x[[3]] #&gt; [1] 1 2 3 x[[&quot;c&quot;]] #&gt; [1] 1 2 3 x$c #&gt; [1] 1 2 3 1.2.4 Data Frame Data frame is widely used for rectangular data, where each column has the same data type (vector) but different columns can have different data types (like Excel) As you guess, the data frame is a special type of list: A list of vectors with the same length. df &lt;- data.frame(&quot;SN&quot; = 1:2, &quot;Age&quot; = c(21,15), &quot;Name&quot; = c(&quot;John&quot;,&quot;Dora&quot;)) df #&gt; SN Age Name #&gt; 1 1 21 John #&gt; 2 2 15 Dora df$Age[2] #&gt; [1] 15 # View(df) 1.2.5 Factor vs vector For vector, if it only contains pre-defined values (which can have specified orders), you may consider using factor. Factor is a data structure used for fields that takes only predefined, finite number of values (categorical data) The order of predefined values can be specified, instead of alphabetic by default x = c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;) # vector x #&gt; [1] &quot;single&quot; &quot;married&quot; &quot;married&quot; &quot;single&quot; class(x) #&gt; [1] &quot;character&quot; typeof(x) #&gt; [1] &quot;character&quot; y = factor(c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;)) y #&gt; [1] single married married single #&gt; Levels: married single class(y) #&gt; [1] &quot;factor&quot; typeof(y) #&gt; [1] &quot;integer&quot; 1.2.5.1 Change the order of factor levels z &lt;- factor(c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;) , levels=c(&quot;single&quot;, &quot;married&quot;)) z #&gt; [1] single married married single #&gt; Levels: single married 1.2.5.2 Smaller memory as categorical data type x = c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;) # vector y = factor(c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;)) object.size(rep(x, 1000)) #&gt; 32160 bytes object.size(rep(y, 1000)) #&gt; 16560 bytes 1.3 Read and write files (tables) Besides operating in the R environment, we also want to read data from files or write results into files. For tables, R has convenient built-in function read.table() and write.table(). 1.3.1 Read file We can use read.table() function to read tables, e.g., in comma separated values (csv) or tab separated values (tsv) formats. See full manuals: help(read.table) or ?read.table or its online manual help(&quot;read.table&quot;) ?read.table Here, let’s read an example file. Data is available on Moodle and on the github repository df = read.table(&quot;./SRP029880.colData.tsv&quot;, sep=&quot;\\t&quot;) df #&gt; source_name group #&gt; CASE_1 metastasized cancer CASE #&gt; CASE_2 metastasized cancer CASE #&gt; CASE_3 metastasized cancer CASE #&gt; CASE_4 metastasized cancer CASE #&gt; CASE_5 metastasized cancer CASE #&gt; CTRL_1 normal colon CTRL #&gt; CTRL_2 normal colon CTRL #&gt; CTRL_3 normal colon CTRL #&gt; CTRL_4 normal colon CTRL #&gt; CTRL_5 normal colon CTRL 1.3.2 Write file The above file is loaded as a data frame. Here, let’s add an extra column to indicate if the sample is frozen or not, then save it into a file. df$frozen &lt;- c(1, 1, 0, 0, 0, 1, 1, 0, 0, 0) write.table(df, &quot;./SRP029880.colData.add_frozen.tsv&quot;, sep=&quot;\\t&quot;, quote=FALSE) 1.4 Functions and Packages As experienced above, we have used function multiple times, e.g., read.table and typeof. As one more example mean() is a function here and it is from the base package x &lt;- 4:10 mean(x) #&gt; [1] 7 base::mean(x) #&gt; [1] 7 Generally speaking, A function is a set of statements organized together to perform a specific task. Many lines of codes are packed into one function &amp; it’s reusable. A function can be written in the same R file and loaded, or it can be distributed as part of a package. For using such functions, we need to install the corresponding package and load it. 1.4.1 Install packages It depends on where the package is stored. Please refers to the documentation of the specific package you want to install and use. CRAN (the Comprehensive R Archive Network): main platform For example: install.packages(\"ggplot2\") Bioconductor: primarily for biology related packages For example: BiocManager::install(\"DESeq2\") As an example, we can install the powerful plotting package ggplot2 from CRAN. #install.packages(&quot;ggplot2&quot;) 1.4.2 Apply function repeatly We may often want to use a certain function for multiple times, e.g., calculate the sample mean for many genes. There are multiple ways to achieve it, e.g., via a for loop. Here, we will introduce apply and its variants for this purpose. See more introductions here. 1.4.2.1 apply, lapply, sapply and vapply In short, the apply() function and its variants apply a certain function to each element of a vector, a matrix, or a list. 1.4.2.1.1 apply for matrix The apply(X, MARGIN, FUN) function works for matrix (or array) for rows or columns. For example, calculating the median of each column: my.matrx &lt;- matrix(1:15, nrow = 5, ncol = 3) my.matrx #&gt; [,1] [,2] [,3] #&gt; [1,] 1 6 11 #&gt; [2,] 2 7 12 #&gt; [3,] 3 8 13 #&gt; [4,] 4 9 14 #&gt; [5,] 5 10 15 apply(my.matrx, 2, median) #&gt; [1] 3 8 13 1.4.2.1.2 lapply, sapply, and vapply for list or vector The above apply function requires MARGIN, hence won’t work for vector or list. There are a few variants to support lists or vectors for different purposes. From the manual, we can find out the arguments for these three functions: lapply(X, FUN, …) sapply(X, FUN, …, simplify = TRUE, USE.NAMES = TRUE) vapply(X, FUN, FUN.VALUE, …, USE.NAMES = TRUE) Let’s look at examples. The lapply works for vector and list and returns a list: A&lt;-c(1:9) B&lt;-c(1:12) C&lt;-c(1:15) my.lst&lt;-list(A,B,C) lapply(my.lst, median) #&gt; [[1]] #&gt; [1] 5 #&gt; #&gt; [[2]] #&gt; [1] 6.5 #&gt; #&gt; [[3]] #&gt; [1] 8 If you want the return as a vector, you can use sapply() for simplified output: sapply(my.lst, median) #&gt; [1] 5.0 6.5 8.0 If you want to check the data type of the return, you can further use the vapply function. An error will be raised if the data type does not match. Note, the FUN.VALUE argument takes the value as a template, so the use of numeric(1) or any numeric value, e.g., 3 is the same. vapply(my.lst, median, numeric(1)) #&gt; [1] 5.0 6.5 8.0 vapply(my.lst, median, 3) #&gt; [1] 5.0 6.5 8.0 # try this # vapply(my.lst, median, character(1)) 1.4.3 Pattern match Matching patterns between two vectors is a very common task, for example matching the gene names of two files or matching students IDs in two courses. Two commonly used functions for pattern match are match() and %in%, see the match() documentation: match returns a vector of the positions of (first) matches of its first argument in its second. %in% is a more intuitive interface as a binary operator, which returns a logical vector indicating if there is a match or not for its left operand. They work for any data type: numeric and character 1:6 %in% c(1,3,5,9) #&gt; [1] TRUE FALSE TRUE FALSE TRUE FALSE match(c(3, 4, 5), c(5, 3, 1, 9)) #&gt; [1] 2 NA 1 idx = match(c(3, 4, 5), c(5, 3, 1, 9)) c(5, 3, 1, 9)[idx] #&gt; [1] 3 NA 5 1.5 Flow Control 1.5.1 Logical operator The common logical operators are shown in the following table. Operator Description Associativity ! Logical NOT Left to right &amp; Element-wise logical AND Left to right &amp;&amp; Logical AND Left to right | Element-wise logical OR Left to right || Logical OR Left to right A few notes: Zero is considered FALSE and non-zero numbers are taken as TRUE. Operators &amp; and | perform element-wise operation, returning length of the longer operand. For operators &amp;&amp; and ||, it depends on the R version. In R&lt;=4.2.3, it examines only the first element of the operands, returning a single value, while in R=4.3.1, &amp;&amp; and || only compare single values and will return errors if input vectors. x &lt;- c(TRUE, FALSE, 0, 6) y &lt;- c(FALSE, TRUE, FALSE, TRUE) !x #&gt; [1] FALSE TRUE TRUE FALSE x &amp; y #&gt; [1] FALSE FALSE FALSE TRUE x | y #&gt; [1] TRUE TRUE FALSE TRUE # try it yourself # x &amp;&amp; y # x || y 1.5.2 if-else statements The if-else statement allows us to control when and how particular parts of our code are executed. # In Q10 in Section 1.8 we have x_mean and x_sd x_mean = 1.7 x_sd = 2.9 if ( (x_mean &gt; 0.1) &amp;&amp; (x_sd &lt; 2.0) ) { trend = &quot;increase&quot; } else{ trend = &quot;not_increase&quot; } print(trend) #&gt; [1] &quot;not_increase&quot; x_mean = 1.7 x_st = 2.9 trend = &quot;not_increase&quot; if ( (x_mean &gt; 0.1) &amp;&amp; (x_sd &lt; 2.0) ) { trend = &quot;increase&quot; } print(trend) #&gt; [1] &quot;not_increase&quot; 1.5.3 for-loop Loops, including for loop and while loop are used in programming to repeat a specific block of code, commonly with if-else statements. For example, calculate the sum from 1 to 10: sum_val = 0 for (val in seq(1, 10)) { # print(val) sum_val = sum_val + val } print(sum_val) #&gt; [1] 55 Or detect the differential expressed genes. Note, NA value may exist in the padj column: is_DE = rep(FALSE, nrow(df_DEG)) for (i in 1:nrow(df_DEG)) { if (df_DEG$padj[i] &lt;= 0.05) { is_DE[i] = TRUE } } print(sum(is_DE)) 1.6 Plotting 1.6.1 datasets Let’s use a built-in dataset for illustration: iris (4 flower features in 3 plants) head(iris) #&gt; Sepal.Length Sepal.Width Petal.Length Petal.Width Species #&gt; 1 5.1 3.5 1.4 0.2 setosa #&gt; 2 4.9 3.0 1.4 0.2 setosa #&gt; 3 4.7 3.2 1.3 0.2 setosa #&gt; 4 4.6 3.1 1.5 0.2 setosa #&gt; 5 5.0 3.6 1.4 0.2 setosa #&gt; 6 5.4 3.9 1.7 0.4 setosa summary(iris) #&gt; Sepal.Length Sepal.Width Petal.Length Petal.Width #&gt; Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100 #&gt; 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300 #&gt; Median :5.800 Median :3.000 Median :4.350 Median :1.300 #&gt; Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199 #&gt; 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800 #&gt; Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500 #&gt; Species #&gt; setosa :50 #&gt; versicolor:50 #&gt; virginica :50 #&gt; #&gt; #&gt; There are two common ways of plotting: the built-in plotting functions the ggplot format 1.6.2 Basic plotting 1.6.2.1 Histogram hist(iris$Sepal.Length) 1.6.2.2 Scatter plot plot(x=iris$Sepal.Length, y=iris$Sepal.Width) 1.6.2.3 boxplot x1 &lt;- iris$Sepal.Length[iris$Species == &quot;setosa&quot;] x2 &lt;- iris$Sepal.Length[iris$Species == &quot;versicolor&quot;] x3 &lt;- iris$Sepal.Length[iris$Species == &quot;virginica&quot;] boxplot(x1, x2, x3) 1.6.3 ggplot2 See more instructions: http://www.sthda.com/english/wiki/ggplot2-essentials 1.6.3.1 Install and load package if (!requireNamespace(&quot;ggplot2&quot;, quietly = TRUE)) install.packages(&quot;ggplot2&quot;) library(ggplot2) #&gt; RStudio Community is a great place to get help: #&gt; https://community.rstudio.com/c/tidyverse 1.6.3.2 Histogram ggplot(iris, aes(x=Sepal.Length)) + geom_histogram(bins = 8) 1.6.3.3 Scatter plot ggplot(iris, aes(x=Sepal.Length, y=Sepal.Width)) + geom_point() 1.6.3.4 Box plot ggplot(iris, aes(x=Species, y=Sepal.Length)) + geom_boxplot() 1.7 Scientific computating 1.7.1 Orders of operators See lecture slides. If you are not sure about a certain ordering, use brackets! 5 * 2 &gt; 4 #&gt; [1] TRUE 5 * (2 &gt; 4) #&gt; [1] 0 1.7.2 Functions for statistics More theory and practice to come in next session 1.7.3 Correlation cor(iris$Sepal.Length, iris$Petal.Length) #&gt; [1] 0.8717538 cor.test(iris$Sepal.Length, iris$Petal.Length) #&gt; #&gt; Pearson&#39;s product-moment correlation #&gt; #&gt; data: iris$Sepal.Length and iris$Petal.Length #&gt; t = 21.646, df = 148, p-value &lt; 2.2e-16 #&gt; alternative hypothesis: true correlation is not equal to 0 #&gt; 95 percent confidence interval: #&gt; 0.8270363 0.9055080 #&gt; sample estimates: #&gt; cor #&gt; 0.8717538 1.7.4 Hypothesis testing (t test) x1 &lt;- iris$Sepal.Length[iris$Species == &quot;setosa&quot;] x2 &lt;- iris$Sepal.Length[iris$Species == &quot;versicolor&quot;] x3 &lt;- iris$Sepal.Length[iris$Species == &quot;virginica&quot;] t.test(x2, x3) #&gt; #&gt; Welch Two Sample t-test #&gt; #&gt; data: x2 and x3 #&gt; t = -5.6292, df = 94.025, p-value = 1.866e-07 #&gt; alternative hypothesis: true difference in means is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.8819731 -0.4220269 #&gt; sample estimates: #&gt; mean of x mean of y #&gt; 5.936 6.588 1.7.5 Regression fit &lt;- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, data=iris) summary(fit) # show results #&gt; #&gt; Call: #&gt; lm(formula = Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, #&gt; data = iris) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -0.82816 -0.21989 0.01875 0.19709 0.84570 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 1.85600 0.25078 7.401 9.85e-12 *** #&gt; Sepal.Width 0.65084 0.06665 9.765 &lt; 2e-16 *** #&gt; Petal.Length 0.70913 0.05672 12.502 &lt; 2e-16 *** #&gt; Petal.Width -0.55648 0.12755 -4.363 2.41e-05 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 0.3145 on 146 degrees of freedom #&gt; Multiple R-squared: 0.8586, Adjusted R-squared: 0.8557 #&gt; F-statistic: 295.5 on 3 and 146 DF, p-value: &lt; 2.2e-16 This means the fitted regression is: Sepal.Length ~ 1.856 + 0.65*Sepal.Width + 0.709*Petal.Length - 0.556*Petal.Width We can check how good the regression is by plotting it out y_pred &lt;- fit$coefficients[1] + fit$coefficients[2] * iris$Sepal.Width + fit$coefficients[3] * iris$Petal.Length + fit$coefficients[4] * iris$Petal.Width cor(iris$Sepal.Length, y_pred) #&gt; [1] 0.926613 plot(iris$Sepal.Length, y_pred) 1.7.6 Resource links This notebook adapts contents from these resources: https://www.datamentor.io/r-programming/ https://www.geeksforgeeks.org/r-data-types/ https://data-flair.training/blogs/r-data-types/ http://www.sthda.com/english/wiki/ggplot2-essentials 1.7.7 Coding styling Elegant styling is crucial for maintenance and collaboration. Here is a highly recommended guideline: http://adv-r.had.co.nz/Style.html 1.8 Exercises This list of exercises will serve as a 2-hour demonstration in the BIOF1001 course. For other learners, you can go through it as homework. The expected time is around two hours if you have read the R materials carefully together with trying them with your own R environment. Note, before you get started, please make sure that you are familiar with the panels in RStudio. You may watch this YouTube Video or check this RStudio cheatsheet. 1.8.1 Part 1. Basics (~40min) Q1: We have 25 students in BIOF1001, to store the final marks (0 to 100 with a precision of 0.1), what data type will we use? Q2: For the grades (A+ to F), what data type and data structure can be used to keep the memory minimal? Q3: Make a matrix with name my_matrix, shape of 5 rows and 2 columns and values from 3 to 12. The first row is 3 and 4. Hint: for making a vector from 3 to 12, you may use seq() or :. Q4: Based on Q3, add the row names to Day1 to Day5 and column names to Lunch and Dinner. Q5: Based on Q4, get a matrix with shape of 3x1 and values of 6, 8, 10 from the matrix my_matrix. Q6: What will you get for my_matrix[c(TRUE, FALSE, FALSE, TRUE), ]? Hint: think of recycling if the index length is different from the query dimension (Over-flexibility comes with a price of wrong use). Q7: If you have two vectors the BIOF1001 marks and grades and one character for teaching performance \"good\", and you want to store them into one variable, which data structure will you use? Q8: Now, on your Desktop folder, make a subfolder with name R_exercises and download this file of differentailly expressed genes results Diff_Expression_results.tsv to the folder. Check your current work directory by getwd() function and change the work directory to the folder you just created. Hint: you may use setwd() to change the work directory or use the Session button of RStudio. Q9: Related to Q8, use the read.table() function to load the file into a data frame with the variable name df_DEG. Hint: You may consider using the full path or just the file name if it’s in the same work directory. Please keep header=TRUE for the argument. Think how to find help page for a certain function. Q10: Can you calculate the mean and standard deviation of the log2FoldChange? If the mean &gt;0.1 and the standard deviation &lt; 3, set the trend variable as “increase”, otherwise “not_increase”. What will happen if you add this trend variable to the data frame, and why? Hint: use mean() and st() functions for calculating mean and standard deviation. 1.8.2 Part 2. Making plotting (~40min) Q11: Keep use the df_DEG from part 1 Q9. Now, make a histogram of the log2FoldChange with both basic plotting function hist() and ggplot2. Q12: Make a plot with x-axis of log10(baseMean) and y-axis of log2FoldChange. Please try both the basic plot() function and ggplot2. Q13: Now, manipulate the dataframe by adding two columns: Add a column log2FC_clip for clipping log2FoldChange to [-5, +5] Add a column is_DE for padj &lt; 0.05 Q14: Try the summary() function with the above df_DEG data frame, and also table() function for the is_DE column. Q15: Based on ggplot2, add the color by the newly added column is_DE. Q16: Set the colors to “red” and “grey”, and make it in the order of TRUE and FALSE. Hint: use factor and set the levels parameter. Q17: Save the generated figure into “My_DEG_results.pdf”. Use the ggsave() function. Please set width = 5, height = 4. You are expected a figure like this DEG figure If you want to change labels on x-axis or y-axis and font size, etc., you can simply Google and find examples. 1.8.3 Part 3. For loop and repeating processing (~40min) Q18: Load the following table from this file on GitHub and View it in RStudio. It contains expressoon of 619 transcription factors from 7 Nasopharyngeal carcinoma (NPC) samples and 3 nasopharyngeal lymphatic hyperplasia (NLH) samples. https://github.com/StatBiomed/NegabinGLM/blob/main/data/NPC_NLH-Tcell-donorX.tsv df_NPC = read.table(\"https://github.com/StatBiomed/NegabinGLM/raw/main/data/NPC_NLH-Tcell-donorX.tsv\", sep=\"\\t\", header=TRUE) Q19: Extract the column 5 (HES5) to 623 (LEK4) and make it into a matrix TF_mat Hint: how to index a data frame like index a matrix. Q20: perform normalization. Divide the TF_mat by the df_NPC$total_counts and multiply by 1000000, and assign it to a new matrix named TF_mat_norm. You may further consider transformation by log1p(), i.e., log(TF_mat_norm + 1). Q21: calculate the log fold change on the first gene TP73 in TF_mat_norm between NPC (row 1 to 7) and NLH (row 8 to 10) and perform t-test return the p value and log fold change. Q22: perform t-test on the all gene in TF_mat_norm between NPC (row 1 to 7) and NLH (row 8 to 10). Hint: think of for loop or apply() function. "],["introHypoTest.html", "Chapter 2 Introduction to Hypothesis testing 2.1 Hypothesis testing and p value 2.2 Permutation test 2.3 t test 2.4 GLM test 2.5 Multiple testing", " Chapter 2 Introduction to Hypothesis testing 2.1 Hypothesis testing and p value How surprising is my result? Calculating a p-value There are many circumstances where we simply want to check whether an observation looks like it is compatible with the null hypothesis, \\(H_{0}\\). Having decided on a significance level \\(\\alpha\\) and whether the situation warrants a one-tailed or a two-tailed test, we can use the cdf of the null distribution to calculate a p-value for the observation. Acknowledgement: examples are from Dr John Pinney link here 2.1.1 Example 1: probability of rolling a six? Your arch-nemesis Blofeld always seems to win at ludo, and you have started to suspect him of using a loaded die. You observe the following outcomes from 100 rolls of his die: data = c(6, 1, 5, 6, 2, 6, 4, 3, 4, 6, 1, 2, 5, 6, 6, 3, 6, 2, 6, 4, 6, 2, 5, 4, 2, 3, 3, 6, 6, 1, 2, 5, 6, 4, 6, 2, 1, 3, 6, 5, 4, 5, 6, 3, 6, 6, 1, 4, 6, 6, 6, 6, 6, 2, 3, 1, 6, 4, 3, 6, 2, 4, 6, 6, 6, 5, 6, 2, 1, 6, 6, 4, 3, 6, 5, 6, 6, 2, 6, 3, 6, 6, 1, 4, 6, 4, 2, 6, 6, 5, 2, 6, 6, 4, 3, 1, 6, 6, 5, 5) Do you have enough evidence to confront him? # We will work with the binomial distribution for the observed number of sixes # Write down the hypotheses # H0: p = 1/6 # H1: p &gt; 1/6 # choose a significance level # alpha = 0.01 # number of sixes # number of trials stat_k = sum(data == 6) trials = length(data) print(paste(&quot;number of sixes:&quot;, stat_k)) #&gt; [1] &quot;number of sixes: 43&quot; print(paste(&quot;number of trials:&quot;, trials)) #&gt; [1] &quot;number of trials: 100&quot; # test statistic: number of sixes out of 100 trials # null distribution: dbinom(x, size=100, prob=1/6) # calculate p value p_val = 1 - pbinom(stat_k - 1, size=trials, prob=1/6) print(paste(&quot;Observed statistic is&quot;, stat_k)) #&gt; [1] &quot;Observed statistic is 43&quot; print(paste(&quot;p value is&quot;, p_val)) #&gt; [1] &quot;p value is 5.43908695860296e-10&quot; 2.1.1.1 Visualize the null distribution and the test statistic # plot the probability mass function of null distribution x = seq(0, 101) pmf = dbinom(x, size=100, prob=1/6) df = data.frame(x=x, pmf=pmf, extreme=(x &gt;= stat_k)) library(ggplot2) ggplot(df, aes(x=x)) + geom_point(aes(y=pmf, color=extreme)) + scale_color_manual(values=c(&quot;black&quot;, &quot;red&quot;)) + xlab(&#39;Number of sixes&#39;) + ylab(&#39;Probability Mass Function&#39;) + ggtitle(&#39;Distribution of n_six under the null hypothesis&#39;) 2.2 Permutation test 2.2.1 Example 2: difference in birth weight The birth weights of babies (in kg) have been measured for a sample of mothers split into two categories: nonsmoking and heavy smoking. The two categories are measured independently from each other. Both come from normal distributions The two groups are assumed to have the same unknown variance. data_heavysmoking = c(3.18, 2.84, 2.90, 3.27, 3.85, 3.52, 3.23, 2.76, 3.60, 3.75, 3.59, 3.63, 2.38, 2.34, 2.44) data_nonsmoking = c(3.99, 3.79, 3.60, 3.73, 3.21, 3.60, 4.08, 3.61, 3.83, 3.31, 4.13, 3.26, 3.54) We want to know whether there is a significant difference in mean birth weight between the two categories. # Write down the hypotheses # H0: there is no difference in mean birth weight between groups: d == 0 # H1: there is a difference, d != 0 # choose a significance level # alpha = 0.05 # Define test statistic: difference of group mean stat_mu = mean(data_heavysmoking) - mean(data_nonsmoking) stat_mu #&gt; [1] -0.5156923 2.2.2 Null distribution approximated by resampling #&#39; Simple function to generate permutation distribution get_permutation_null &lt;- function(x1, x2, n_permute=1000) { n1 = length(x1) n2 = length(x2) # pool data sets x_pool = c(x1, x2) null_distr = rep(0, n_permute) for (i in seq(n_permute)) { # split idx = sample(n1 + n2, size=n1) x1_perm = x_pool[idx] x2_perm = x_pool[-idx] # calculate test statistic null_distr[i] = mean(x1_perm) - mean(x2_perm) } return(null_distr) } set.seed(1) perm_null = get_permutation_null(data_heavysmoking, data_nonsmoking) We can plot the histogram of the null distribution obtained by resampling. We can also add line(s) for the values as extreme as observed statistic mu, where we can consider one side or both side as extreme values. df_perm = data.frame(perm_null = perm_null) ggplot(df_perm, aes(x=perm_null)) + geom_histogram(bins=20) + geom_vline(xintercept=stat_mu, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + geom_vline(xintercept=-stat_mu, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + xlab(&#39;Difference of group mean&#39;) + ylab(&#39;Resampling frequency&#39;) + ggtitle(&#39;Distribution of mu under the null hypothesis&#39;) ## Two tailed p value p_two_tailed = mean(abs(perm_null) &gt;= abs(stat_mu)) p_one_tailed = mean(perm_null &lt; stat_mu) print(paste(&quot;Two tailed p value:&quot;, round(p_two_tailed, 5))) #&gt; [1] &quot;Two tailed p value: 0.003&quot; print(paste(&quot;One (left) tailed p value:&quot;, round(p_one_tailed, 5))) #&gt; [1] &quot;One (left) tailed p value: 0.002&quot; 2.3 t test 2.3.1 Derivation of t distribution Null distribution approximated by \\(t\\) distribution We use the t test to assess whether two samples taken from normal distributions have significantly different means. The test statistic follows a Student’s t-distribution, provided that the variances of the two groups are equal. Other variants of the t-test are applicable under different conditions. The test statistic is \\[ t = \\frac{\\bar{X}_{1} - \\bar{X}_{2}}{s_p \\cdot \\sqrt{\\frac{1}{n_{1}} + \\frac{1}{n_{2}}}} \\] where \\[ s_p = \\sqrt{\\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} \\] is an estimator of the pooled standard deviation. Under the null hypothesis of equal means, the statistic follows a Student’s t-distribution with \\((n_{1} + n_{2} - 2)\\) degrees of freedom. # Same test statistic: difference of group mean stat_t = mean(data_heavysmoking) - mean(data_nonsmoking) stat_t #&gt; [1] -0.5156923 Calculate parameters for approximate t distribution n_ns = length(data_nonsmoking) n_hs = length(data_heavysmoking) s_ns = sd(data_nonsmoking) # degree of freedom: n-1 s_hs = sd(data_heavysmoking) # the pooled standard deviation sp = sqrt(((n_ns - 1)*s_ns**2 + (n_hs - 1)*s_hs**2) / (n_ns + n_hs - 2)) print(paste0(&quot;Pooled standard deviation:&quot;, sp)) #&gt; [1] &quot;Pooled standard deviation:0.428057812829366&quot; my_std = sp * sqrt(1/n_ns + 1/n_hs) print(paste(&quot;Estimated standard error of mean difference:&quot;, my_std)) #&gt; [1] &quot;Estimated standard error of mean difference: 0.162204962956089&quot; stat_t_scaled = stat_t / my_std print(paste(&quot;Rescaled t statistic:&quot;, stat_t_scaled)) #&gt; [1] &quot;Rescaled t statistic: -3.17926343494134&quot; print(paste(&quot;degree of freedom&quot;, n_hs+n_ns-2)) #&gt; [1] &quot;degree of freedom 26&quot; Here, we focusing the standardized \\(t\\) distribution, namely the variance=1, so let’s re-scale the test statistic by dividing the standard error my_std. xx = seq(-4.5, 4.5, 0.05) xx_pdf = dt(xx, df=n_hs+n_ns-2) df_t_dist = data.frame(x=xx, pdf=xx_pdf) ggplot(df_t_dist, aes(x=x)) + geom_line(aes(y=pdf)) + geom_vline(xintercept=stat_t_scaled, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + geom_vline(xintercept=-stat_t_scaled, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + xlab(&#39;Difference of group mean&#39;) + ylab(&#39;PDF approximated by t distr.&#39;) + ggtitle(&#39;Distribution of t under the null hypothesis&#39;) # Note, we used multiply 2 just because the t distribution is symmetric, # otherwise, we need calculate both side and add them. pval_t_twoside = pt(stat_t_scaled, df=n_hs+n_ns-2) * 2 print(paste(&#39;t-test p value (two-tailed):&#39;, round(pval_t_twoside, 6))) #&gt; [1] &quot;t-test p value (two-tailed): 0.003793&quot; 2.3.2 Direct use of t.test() In course and most of your future analyses, you can directly use the built-in t.test() function. # Note, we assumed the variance in both groups are the same, # we so need to set var.equal = TRUE t.test(data_nonsmoking, data_heavysmoking, var.equal = TRUE) #&gt; #&gt; Two Sample t-test #&gt; #&gt; data: data_nonsmoking and data_heavysmoking #&gt; t = 3.1793, df = 26, p-value = 0.003793 #&gt; alternative hypothesis: true difference in means is not equal to 0 #&gt; 95 percent confidence interval: #&gt; 0.1822752 0.8491094 #&gt; sample estimates: #&gt; mean of x mean of y #&gt; 3.667692 3.152000 2.4 GLM test We can also perform t-test in a Generalised linear model (GLM) setting to test if a coefficient is zero or not. Here, we simply use the marketing dataset as an example. # Install datarium library if you haven&#39;t if (!requireNamespace(&quot;datarium&quot;, quietly = TRUE)) { install.packages(&quot;datarium&quot;) } library(datarium) # Load data: then we will have a data.frame with name marketing data(marketing) head(marketing) #&gt; youtube facebook newspaper sales #&gt; 1 276.12 45.36 83.04 26.52 #&gt; 2 53.40 47.16 54.12 12.48 #&gt; 3 20.64 55.08 83.16 11.16 #&gt; 4 181.80 49.56 70.20 22.20 #&gt; 5 216.96 12.96 70.08 15.48 #&gt; 6 10.44 58.68 90.00 8.64 ggplot(marketing, aes(x=newspaper, y=sales)) + geom_point() + geom_smooth(method=lm) #&gt; `geom_smooth()` using formula = &#39;y ~ x&#39; # Fit linear regression res.lm &lt;- lm(sales ~ newspaper, data = marketing) # We can check the test via the summary() function summary(res.lm) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ newspaper, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -13.473 -4.065 -1.007 4.207 15.330 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 14.82169 0.74570 19.88 &lt; 2e-16 *** #&gt; newspaper 0.05469 0.01658 3.30 0.00115 ** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 6.111 on 198 degrees of freedom #&gt; Multiple R-squared: 0.05212, Adjusted R-squared: 0.04733 #&gt; F-statistic: 10.89 on 1 and 198 DF, p-value: 0.001148 glm_t_val = summary(res.lm)$coefficients[&quot;newspaper&quot;, &quot;t value&quot;] xx = seq(-5, 5, 0.01) yy = dt(xx, 198) df_ttest &lt;- data.frame(x=xx, PDF=yy) ggplot(df_ttest, aes(x=x, y=PDF)) + geom_line() + geom_vline(xintercept = glm_t_val, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + geom_vline(xintercept = -glm_t_val, linetype=&quot;dashed&quot;, color=&#39;tomato&#39;) 2.5 Multiple testing Hypothetical null distribution. Feel feel to try any null distribution, examples below ## Example null distributions # t, normal or anything. we use chi-squared distribution as an example x_random = rchisq(n=1000, df=3) any_null_dist = dchisq(x_random, df=3) pvals_null = 1 - pchisq(x_random, df=3) 2.5.1 Null distribution (of test statistic) # Null distribution of test statistic hist(x_random) 2.5.2 Null distribution of p value # Null distribution of test statistic hist(pvals_null) 2.5.3 Minimal p values in 10 tests # We use matrix to group 100 trials into a column # We then use apply() to calculate min value for each column pval_null_mtx = matrix(pvals_null, nrow=10) p_min_in10 = apply(pval_null_mtx, MARGIN=2, FUN=min) hist(p_min_in10) print(paste(&#39;Proportion of tests with min(p) &lt; 0.05:&#39;, mean(p_min_in10 &lt; 0.05))) #&gt; [1] &quot;Proportion of tests with min(p) &lt; 0.05: 0.43&quot; 2.5.4 Homework Make a simulation of score: group A and B B follows normal(mean=0, std=1); A follows normal(mean=0.1, std=1) Generate 100 samples for each group, and do a t test, is difference significant? Please use set.seed(0) beforehand. Try 3) again but general 3,00 samples this time, later 1,000 samples. What do you find? Think the relation between power and sample size. set.seed(0) n_sample = 100 # change this value to 1000 and 10000 xB = rnorm(n_sample) xA = rnorm(n_sample, mean=0.1) t.test(xA, xB, var.equal = TRUE) #&gt; #&gt; Two Sample t-test #&gt; #&gt; data: xA and xB #&gt; t = 0.24294, df = 198, p-value = 0.8083 #&gt; alternative hypothesis: true difference in means is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.2261882 0.2897482 #&gt; sample estimates: #&gt; mean of x mean of y #&gt; 0.05444844 0.02266845 "],["introLinearReg.html", "Chapter 3 Introduction to Linear Regression 3.1 Linear Regression Using Simulated Data 3.2 Least Squares Using Simulated Data 3.3 Diagnostic check of a fitted regression model 3.4 Simple Linear Regression with lm function 3.5 Multiple Regression with lm function", " Chapter 3 Introduction to Linear Regression Acknowledgements: this chapter is adapted and updated from the materials originally produced by STAT1005 teaching team, especially Prof. Jeff Yao. 3.1 Linear Regression Using Simulated Data Let’s first simulate some data and look at how the predicted values (Ye) differ from the actual value (Y). 3.1.1 Simulating data: For X, we generate 100 normally distributed random numbers with mean 1.5 and standard deviation 2.5. For predicted value Ye, we assume an intercept (α) of 2 and a slope (β) of 0.3 and we write \\(Y_e = 2 + 0.3 x\\) Later, we will estimate the values of α and β using the least squares method and see how that changes the efficacy of the model. Though we estimate \\(Y_e = \\alpha + \\beta X\\), in reality Y is rarely perfectly linear. It usually has an error component or residual: \\(Y = \\alpha + \\beta X + R\\), where R is a random variable and is assumed to be normally distributed. Therefore for the actual value Y, we add a residual term (res), a random variable distributed normally with mean 0 and a standard deviation of 0.5. The following cell shows the code snippet to generate these numbers and convert these three columns in a data frame. Read through the code carefully and run the cell to output a sample of our simulated data. # Fix seed: each run gives the same random numbers so the same outputs. # Commenting out this line would read similar but different outputs at each run. # Try it out! set.seed(0) # Generate data X = 2.5 * rnorm(100) + 1.5 # Array of 100 values with mean = 1.5, stddev = 2.5 ypred = 2 + 0.3 * X # Prediction of Y, assuming a = 2, b = 0.3 res = 0.5 * rnorm(100) # Generate 100 residual terms yact = 2 + 0.3 * X + res # Actual values of Y # Create dataframe to store our X, ypred, and yact values df = data.frame(&#39;X&#39; = X, &#39;ypred&#39; = ypred, &#39;yact&#39; = yact) # Show the first six rows of our dataframe head(df) #&gt; X ypred yact #&gt; 1 4.6573857 3.397216 3.788145 #&gt; 2 0.6844166 2.205325 1.816937 #&gt; 3 4.8244982 3.447349 3.139354 #&gt; 4 4.6810733 3.404322 3.427612 #&gt; 5 2.5366036 2.760981 2.195788 #&gt; 6 -2.3498751 1.295037 1.583397 Now let’s plot both the actual output (yact) and predicted output (ypred) against the input variable (X) to see what the difference between yact and ypred is, and therefore, to see how accurately the proposed equation (ypred = 2 + 0.3 * X) has been able to predict the value of the output: # You can use basic plotting functions # plot(x=df$X, y=df$yact, col=&quot;red&quot;) # lines(x=df$X, y=df$ypred, col=&quot;darkgreen&quot;) # But let&#39;s use ggplot2 for higher flexibility library(ggplot2) ggplot(df, aes(X)) + # basic graphical object geom_point(aes(y=yact), colour=&quot;black&quot;) + # first layer geom_line(aes(y=ypred), colour=&quot;darkgreen&quot;) + # second layer ggtitle(&#39;Actual vs Predicted values from the dummy dataset&#39;) 3.1.2 Model efficacy How do we know the values we calculate for α and β are giving us a good model? We can explain the total variability in our model with the Total Sum of Squares or SST: \\[SST = \\sum_{i=1}^n\\Bigl(\\text{yact}_i - \\text{yavg}\\Bigr)^2, \\qquad\\qquad \\text{yavg}=\\frac1n \\sum_{i=1}^n \\text{yact}_i\\] Mathematically, we have \\[ \\sum_{i=1}^n\\Bigl(\\text{yact}_i - \\text{yavg}\\Bigr)^2 = \\sum_{i=1}^n\\Bigl(\\text{ypred}_i -\\text{yavg} \\Bigr)^2 + \\sum_{i=1}^n\\Bigl(\\text{yact}_i - \\text{ypred}_i\\Bigr)^2\\] The identity reads as Sum of Squares Total = Sum of Squares Regression + Sum of Squares Error, or simply , SST = SSR + SSE. The Regression Sum of Squares or SSR measures the variation of the regression/predicted values, and the Sum of Squares Error SSE the variation between the actual and the predicted values. An alternative saying is that SSR is the difference explained by the model, SSE is the difference not explained by the model and is random, and SST is the total error. Note, we often use SSE (Sum of Squares Error) and SSD (Sum of Squares Difference) interchangeably. 3.1.3 R-Squared The higher the ratio of SSR to SST, the better the model is. This ratio is quantified by the coefficient of determination (also known as R2 or R-squared): \\[ R^2= \\frac{SSR}{SST}\\] Since \\(SST= SSR+SSE\\), \\(\\qquad 0\\le R^2\\le 1\\). The closer it is to 1, the better the model. Note that there are many other factors that we need to analyse before we can conclude a linear regression model is effective, but a high \\(R^2\\) is a pretty good indicator. Let’s see what the value of \\(R^2\\) is for our simulated dataset. # Calculate the mean of Y ymean = mean(df$yact) print(paste(&#39;Mean of Y =&#39;, ymean)) # paste brings a white space by default #&gt; [1] &quot;Mean of Y = 2.44422555811815&quot; # Calculate SSR and SST df[&#39;SSR&#39;] = (df[&#39;ypred&#39;] - ymean)**2 df[&#39;SST&#39;] = (df[&#39;yact&#39;] - ymean)**2 SSR = sum(df[&#39;SSR&#39;]) SST = sum(df[&#39;SST&#39;]) # Calculate R-squared R2 = SSR / SST print(paste(&#39;R2 =&#39;, R2)) #&gt; [1] &quot;R2 = 0.583160943681119&quot; The value of \\(R^2=0.583\\) suggests that ypred provides a decent prediction of the yact. We have randomly assumed some values for \\(\\alpha\\) and \\(\\beta\\), but these may or may not be the best values. In the next step, we will use the least sum of square method to calculate the optimum value for \\(\\alpha\\) and \\(\\beta\\) to see if there is an improvement in \\(R^2\\). To get started on the next step, open the notebook called 02-linearReg-02.Rmd. 3.2 Least Squares Using Simulated Data Now, using our simulated data from the previous step, let’s estimate the optimum values of our variable coefficients, \\(\\alpha\\) and \\(\\beta\\). Using the predictor variable, X, and the output variable, yact, we will calculate the values of \\(\\alpha\\) and \\(\\beta\\) using the Least Squares method described in the lecture. The cell below creates the same dataframe as previously. Run the cell to get started! set.seed(0) # Generate data X = 2.5 * rnorm(100) + 1.5 # Array of 100 values with mean = 1.5, stddev = 2.5 ypred = 2 + 0.3 * X # Prediction of Y, assuming a = 2, b = 0.3 res = 0.5 * rnorm(100) # Generate 100 residual terms yact = 2 + 0.3 * X + res # Actual values of Y # Create dataframe to store our X, ypred, and yact values df = data.frame(&#39;X&#39; = X, &#39;ypred&#39; = ypred, &#39;yact&#39; = yact) Just to reiterate, here are the formulas for \\(\\alpha\\) and \\(\\beta\\) again: \\[\\hat\\beta=\\frac{\\sum_{i=1}^n(X_i-\\bar X)(Y_i-\\bar Y)}{\\sum_{i=1}^n(X_i-\\bar X)^2}=\\frac{\\text{cov}(X,Y)}{\\text{var}(X)}\\] \\[\\hat\\alpha=\\bar Y-\\hat\\beta * \\bar X\\] To calculate these coefficients, we will create a few more columns in our df data frame. We need to calculate xmean and ymean to calculate the covariance of X and Y (xycov) and the variance of X (xvar) before we can work out the values for alpha and beta. # Calculate the mean of X and Y xmean = mean(X) ymean = mean(yact) # Calculate the terms needed for the numator and denominator of beta df[&#39;xycov&#39;] = (df[&#39;X&#39;] - xmean) * (df[&#39;yact&#39;] - ymean) df[&#39;xvar&#39;] = (df[&#39;X&#39;] - xmean)**2 # Calculate beta and alpha beta = sum(df[&#39;xycov&#39;]) / sum(df[&#39;xvar&#39;]) alpha = ymean - (beta * xmean) print(paste(&#39;alpha =&#39;, alpha, &#39;;&#39;, &#39;beta =&#39;, beta)) #&gt; [1] &quot;alpha = 1.93401265576322 ; beta = 0.327758955833308&quot; As we can see, the values are only a little different from what we had assumed earlier. Let’s see how the value of \\(R^2\\) changes if we use the new values of \\(\\alpha\\) and \\(\\beta\\). The equation for the new model can be written as: \\[ y=1.934 + 0.328 * x \\] Let’s create a new column in df to accommodate the values generated by this equation and call this ypred2, and calculate the new \\(R^2\\). # Create new column to store new predictions df[&#39;ypred2&#39;] = alpha + beta * df[&#39;X&#39;] # Calculate new SSR with new predictions of Y. # Note that SST remains the same since yact and ymean do not change. df[&#39;SSR2&#39;] = (df[&#39;ypred2&#39;] - ymean)**2 df[&#39;SST&#39;] = (df[&#39;yact&#39;] - ymean)**2 SSR2 = sum(df[&#39;SSR2&#39;]) SST = sum(df[&#39;SST&#39;]) # Calculate new R2 R2_2 = SSR2 / SST print(paste(&#39;New R2 =&#39;, R2_2)) #&gt; [1] &quot;New R2 = 0.69524214766491&quot; The new value of \\(R^2= 0.695\\) shows a slight improvement from the previous value of \\(R^2=0.583\\) (obtained with \\(\\alpha=2,~\\beta=0.3\\)). Let’s also plot our new prediction model against the actual values and our earlier assumed model, just to get a better visual understanding. library(ggplot2) # Put color into aes ggplot(df, aes(X)) + # basic graphical object geom_point(aes(y=yact), colour=&quot;black&quot;) + # first layer geom_line(aes(y=ypred, colour=&quot;Guess&quot;)) + # second layer geom_line(aes(y=ypred2, colour=&quot;OLS&quot;)) + # third layer scale_colour_manual(name=&quot;Models&quot;, values = c(&quot;Guess&quot;=&quot;darkgreen&quot;, &quot;OLS&quot;=&quot;red&quot;)) + ggtitle(&#39;Actual vs Predicted with guessed parameters vs Predicted with calculated parameters&#39;) As we can see, the ypred2 and ypred are more or less overlapping since the respective values of ɑ and β are not very different. Next, we will explore other methods of determining model efficacy by using the notebook called 02-linearReg-03.Rmd. 3.3 Diagnostic check of a fitted regression model Apart from the \\(R^2\\) statistic, there are other statistics and parameters that you need to look at in order to determine if the model is efficient. We will discuss some commonly used statistics – Residual Standard Errors, \\(p\\)-values, and \\(F\\)-statistics. 3.3.1 Residual Standard Errors (RSE) RSE is a common statistic used to calculate the accuracy of values predicted by a model. It is an estimate of the variance of the error term, res. For a simple linear regression model, RSE is defined as: \\[ RSE^2 = \\frac{SSE}{n-2} = \\frac1{n-2} \\sum_{i=1}^n \\Bigl(\\text{yact}_i - \\text{ypred}_i \\Bigr)^2. \\] In general, \\[ RSE^2 = \\frac{SSE}{n-p-1} = \\frac1{n-p-1} \\sum_{i=1}^n \\Bigl(\\text{yact}_i - \\text{ypred}_i \\Bigr)^2. \\] where \\(p\\) is the number of predictor variables in a model where we have more than one predictor variables. A multiple linear regression model is a linear regression model with multiple predictors, written as \\[ Y_e = \\alpha +\\beta_1 * X_1 +\\cdots +\\beta_p X_p. \\] As you see, the parameters and predictors are subscripted from 1 up to the number of predictors \\(p\\). In multiple regression, the value of RSE generally decreases as we add variables that are more significant predictors of the output variable. Using our simulated data from the previous steps, the following code snippet shows how the RSE for a model can be calculated: set.seed(0) # Generate data X = 2.5 * rnorm(100) + 1.5 # Array of 100 values with mean = 1.5, stddev = 2.5 res = 0.5 * rnorm(100) # Generate 100 residual terms yact = 2 + 0.3 * X + res # Actual values of Y # Create dataframe to store our X, ypred, and yact values df = data.frame(&#39;X&#39; = X, &#39;yact&#39; = yact) # Calculate the mean of X and Y xmean = mean(X) ymean = mean(yact) # Calculate the terms needed for the numator and denominator of beta df[&#39;xycov&#39;] = (df[&#39;X&#39;] - xmean) * (df[&#39;yact&#39;] - ymean) df[&#39;xvar&#39;] = (df[&#39;X&#39;] - xmean)**2 # Calculate beta and alpha beta = sum(df[&#39;xycov&#39;]) / sum(df[&#39;xvar&#39;]) alpha = ymean - (beta * xmean) print(paste(&#39;alpha =&#39;, alpha, &#39;;&#39;, &#39;beta =&#39;, beta)) #&gt; [1] &quot;alpha = 1.93401265576322 ; beta = 0.327758955833308&quot; # Store predictions as in previous step df[&#39;ypred&#39;] = alpha + beta * df[&#39;X&#39;] # Show first five rows of dataframe head(df) #&gt; X yact xycov xvar ypred #&gt; 1 4.6573857 3.788145 4.1671116 9.6144310 3.460513 #&gt; 2 0.6844166 1.816937 0.5471556 0.7608280 2.158336 #&gt; 3 4.8244982 3.139354 2.2715611 10.6786935 3.515285 #&gt; 4 4.6810733 3.427612 3.0724952 9.7618890 3.468276 #&gt; 5 2.5366036 2.195788 -0.2434518 0.9602676 2.765407 #&gt; 6 -2.3498751 1.583397 3.3628671 15.2611034 1.163820 # Calculate SSE df[&#39;SSE&#39;] = (df[&#39;yact&#39;] - df[&#39;ypred&#39;])**2 SSE = sum(df[&#39;SSE&#39;]) # Calculate RSE RSE = sqrt(SSE / 98) # n = 100 print(paste(&#39;RSE =&#39;, RSE)) #&gt; [1] &quot;RSE = 0.481279277134956&quot; The value of RSE comes out to be 0.48. As you might have guessed, the smaller the residual standard errors, the better the model is. The benchmark to compare this to is the mean of the actual values, yact. As shown previously, this value is ymean = 2.54. In plain English, this means we observe an error of 0.48 over 2.44 - approximately 19.69%. error = RSE / ymean print(paste(&#39;Mean Y =&#39;, ymean)) #&gt; [1] &quot;Mean Y = 2.44422555811815&quot; print(paste(&#39;Error =&#39;, error)) #&gt; [1] &quot;Error = 0.196904608716023&quot; 3.3.2 p-values The calculation of \\(\\alpha\\) and \\(\\beta\\) are estimates, not exact calculations. Whether their values are significant or not needs to be tested using a hypothesis test. In the equation, \\(Y = \\alpha + \\beta X\\), if we set \\(\\beta=0\\), there will be no relation between \\(Y\\) and \\(X\\). Therefore, the hypothesis tests whether the value of \\(\\beta\\) is non-zero or not. \\[\\begin{align*} \\text{Null hypothesis}~ H_0~:~ \\beta=0, &amp; \\quad \\text{versus} \\\\ \\text{Alternative hypothesis}~ H_1~:~ \\beta\\ne 0.&amp; \\end{align*} \\] Whenever a regression task is performed and \\(\\beta\\) is calculated, there will be an accompanying p-value corresponding to this hypothesis test. We will not go through how this is calculated in this course (you can learn more here), since it is calculated automatically by ready-made methods in R. If the p-value is less than a chosen significance level (e.g. 0.05) then the null hypothesis that \\(\\beta = 0\\) is rejected and \\(\\beta\\) is said to be significant and non-zero. In the case of multiple linear regression, the p-value associated with each \\(\\beta_k\\) can be used to weed out insignificant predictors from the model. The higher the p-value for \\(\\beta_k\\), the less significant \\(X_k\\) is to the model. 3.3.3 F-statistics In a multiple regression model, apart from testing the significance of individual variables by checking the p-values, it is also necessary to check whether, as a group all the predictors are significant. This can be done using the following hypothesis: \\[\\begin{align*} \\text{Null hypothesis}~ H_0~:~ &amp; \\beta_1=\\beta_2=\\cdots=\\beta_p=0, \\quad \\text{versus} \\\\ \\text{Alternative hypothesis}~ H_1~:~&amp; \\text{at least one of the} ~\\beta_k&#39;s ~ \\text{is non zero}. \\end{align*} \\] The statistic that is used to test this hypothesis is called the F-statistic and is defined as follows: \\[ F\\text{-statistic} = \\text{Fisher statistic}= \\frac{ (SST-SSE)/p}{ SSE/(n-p-1)} \\] where \\(n\\) = number of rows (sample points) in the dataset and \\(p\\) = number of predictor variables in the model. There is a \\(p\\)-value that is associated with this \\(F\\)-statistic. If the \\(p\\)-value is smaller than the chosen significance level, the null hypothesis can be rejected. It is important to look at the F-statistic because: p-values are about individual relationships between predictors and the outcome variable. However, one predictor’s relationship with the output might be impacted by the presence of other variables. When the number of predictors in the model is very large and all the \\(\\beta_i\\) are very close to zero, the individual p-values associated with the predictors might give very small values so we might incorrectly conclude that there is a relationship between the predictors and the outcome. 3.4 Simple Linear Regression with lm function There are a few R packages, e.g., the built-in stat package have a lm (linear model) function to fit linear regression very easy - much easier than implementing from scratch like we did in the last lesson. See more details in the lm manual. We will start with the datarium library which contain the advertising data. # Install datarium library if you haven&#39;t if (!requireNamespace(&quot;datarium&quot;, quietly = TRUE)) { install.packages(&quot;datarium&quot;) } library(datarium) # Load data: then we will have a data.frame with name marketing data(marketing) head(marketing) #&gt; youtube facebook newspaper sales #&gt; 1 276.12 45.36 83.04 26.52 #&gt; 2 53.40 47.16 54.12 12.48 #&gt; 3 20.64 55.08 83.16 11.16 #&gt; 4 181.80 49.56 70.20 22.20 #&gt; 5 216.96 12.96 70.08 15.48 #&gt; 6 10.44 58.68 90.00 8.64 We can also check summary statistics of each column summary(marketing) #&gt; youtube facebook newspaper sales #&gt; Min. : 0.84 Min. : 0.00 Min. : 0.36 Min. : 1.92 #&gt; 1st Qu.: 89.25 1st Qu.:11.97 1st Qu.: 15.30 1st Qu.:12.45 #&gt; Median :179.70 Median :27.48 Median : 30.90 Median :15.48 #&gt; Mean :176.45 Mean :27.92 Mean : 36.66 Mean :16.83 #&gt; 3rd Qu.:262.59 3rd Qu.:43.83 3rd Qu.: 54.12 3rd Qu.:20.88 #&gt; Max. :355.68 Max. :59.52 Max. :136.80 Max. :32.40 This dataset contains data about the advertising budget spent on YouTub, Radio, and Newspapers for a particular product and the resulting sales. We expect a positive correlation between such advertising costs and sales. Let’s start with YouTub advertising costs to create a simple linear regression model. First let’s plot the variables to get a better sense of their relationship: # Create scatter plot library(ggplot2) ggplot(marketing, aes(x=youtube, y=sales)) + geom_point(colour=&quot;black&quot;) + ggtitle(&#39;YouTube vs Sales&#39;) As YouTube advertisement cost increases, sales also increase – they are positively correlated! Now with the linear model lm function, let’s create a line of best fit using the least sum of square method. # Fit linear regression # By default it include an incepter, so it is equvialent to add &quot;+ 1&quot; # res.lm &lt;- lm(sales ~ youtube + 1, data = marketing) res.lm &lt;- lm(sales ~ youtube, data = marketing) In the above code, we used lm to fit our simple linear regression model. This takes the formula y ~ X, where X is the predictor variable (YouTube advertising costs) and y is the output variable (Sales). Then, this function will return fitted model via a ordinary least squares (OLS) method. The res.lm is a list, you can get the it attributes by e.g., res.lm$coefficients res.lm$coefficients #&gt; (Intercept) youtube #&gt; 8.43911226 0.04753664 In the notation that we have been using, \\(\\alpha\\) is the intercept and \\(\\beta\\) is the slope i.e.: \\(\\alpha = 8.439, \\quad \\beta = 0.048\\) Thus, the equation for the model will be: \\(\\text{Sales} = 8.439 + 0.048*\\text{YouTube}\\) Let’s also check an indicator of the model efficacy, R2. Luckily, summary function can calculate it from the lm output and gives us a ready-made method for doing this so we don’t need to code all the math ourselves: res_summary = summary(res.lm) # Again, res_summary is also a list res_summary$r.squared #&gt; [1] 0.6118751 We can also take a look at the model summary by writing this snippet: # Print out the summary summary(res.lm) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ youtube, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -10.0632 -2.3454 -0.2295 2.4805 8.6548 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 8.439112 0.549412 15.36 &lt;2e-16 *** #&gt; youtube 0.047537 0.002691 17.67 &lt;2e-16 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.91 on 198 degrees of freedom #&gt; Multiple R-squared: 0.6119, Adjusted R-squared: 0.6099 #&gt; F-statistic: 312.1 on 1 and 198 DF, p-value: &lt; 2.2e-16 There is a lot here. Of these results, we have discussed: R-squared F-statistic Prob (F-statistic) - this is the p-value of the F-statistic Intercept coef - this is alpha YouTub coef - this is beta for predictor YouTub P&gt;|t| - this is the p-value for our coefficients Now that we’ve fit a simple regression model, we can try to predict the values of sales based on the equation we just derived! sales_pred = predict(res.lm, newdata = marketing[c(&#39;youtube&#39;)]) marketing[&#39;sales_pred&#39;] = sales_pred The predict fucntion predicts sales value for each row based on the model equation using YouTub costs. This is the equivalent of manually typing out our equation: sales_pred = 8.439 + 0.048*(advert['youtube']). We can visualise our regression model by plotting sales_pred against the YouTube advertising costs to find the line of best fit: library(ggplot2) ggplot(marketing, aes(x=youtube)) + geom_point(aes(y=sales), colour=&quot;black&quot;) + geom_line(aes(y=sales_pred), colour=&quot;red&quot;) + ggtitle(&#39;YouTube vs Sales&#39;) In the next step, we will add more features as predictors and see whether it improves our model. Go to the the notebook called 02-linearReg-05.Rmd. 3.5 Multiple Regression with lm function A multiple linear regression is simply a linear regression that involves more than one predictor variable. It is represented as: \\[\\qquad Y_e = \\alpha + \\beta_1*X_1 + \\beta_2*X_2 + \\dots + \\beta_p*X_p\\] Each βi will be estimated using the least sum of squares method. The data set is \\[ \\begin{array} {~~} Y_1, &amp; X_1^{(1)}, &amp; \\ldots, &amp; X_p^{(1)} \\\\ Y_2, &amp; X_1^{(2)}, &amp; \\ldots, &amp; X_p^{(2)} \\\\ \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\ Y_n, &amp; X_1^{(n)}, &amp; \\ldots, &amp; X_p^{(n)} \\end{array} \\] For each sample \\(i\\), the predicted value by the model is: \\(\\qquad Y_{i,e} = \\alpha + \\beta_1*X_1^{(i)} + \\beta_2*X_2^{(i)} + \\dots + \\beta_p*X_p^{(i)}\\) Define the sum of squares \\[ S(\\alpha,\\beta_1,\\ldots,\\beta_p) = \\sum_{i=1}^n \\left\\{ Y_i -Y_{i,e}\\right\\}^2 =\\sum_{i=1}^n \\left\\{ Y_i -\\left( \\alpha + \\beta_1*X_1^{(i)} + \\beta_2*X_2^{(i)} + \\dots + \\beta_p*X_p^{(i)}\\right)\\right\\}^2 \\] Least squares estimators: solve \\[ \\frac{\\partial S(\\alpha,\\beta_1,\\ldots,\\beta_p)}{\\partial \\alpha}=0,\\quad \\frac{\\partial S (\\alpha,\\beta_1,\\ldots,\\beta_p)}{\\partial \\beta_1}=0,\\quad \\ldots,\\quad \\frac{\\partial S (\\alpha,\\beta_1,\\ldots,\\beta_p)}{\\partial \\beta_p}=0. \\] to obtain the least squares estimators of the parameters \\[ \\hat\\alpha, \\hat\\beta_1,\\ldots,\\hat\\beta_p. \\] Note that be definition, \\[ SSE = S(\\hat\\alpha, \\hat\\beta_1,\\ldots,\\hat\\beta_p). \\] In other words, the fitted SSE (sum of squares error) is the minimized value of the sum squares with the estimated values of the parameters. The more varibles, the smaller the \\(R^2\\) Consider two regression models \\(\\quad ~ Y_e = \\alpha + \\beta_1*X_1\\) \\(\\quad \\tilde Y_e = \\alpha + \\beta_1*X_1 + \\beta_2*X_2\\) The model (II) has one more input variable \\(X_2\\). The \\(SSE_I\\) of Model (I) is the minimum of \\[ S_I(\\alpha,\\beta_1) = \\sum_{i=1}^n \\left\\{ Y_i -\\left( \\alpha + \\beta_1*X_1^{(i)} \\right)\\right\\}^2 \\] over all possible values of \\((\\alpha,\\beta_1)\\). The \\(SSE_{II}\\) of Model (II) is the minimum of \\[ S_{II}(\\alpha,\\beta_1,\\beta_2) = \\sum_{i=1}^n \\left\\{ Y_i -\\left( \\alpha + \\beta_1*X_1^{(i)} +\\beta_2*X_2^{(i)} \\right)\\right\\}^2. \\] over all possible values of \\((\\alpha,\\beta_1,\\beta_2)\\). Because \\(\\quad S_I(\\alpha,\\beta_1) = S_{II}(\\alpha,\\beta_1,\\beta_2=0 )\\), we find that \\(SSE_{II}\\le SSE_I\\), so \\[ R^2_{II} = SST - SSE_{II} \\ge SST - SSE_{I} = R^2_{I}. \\] With this simple dataset of three predictor variables, there can be seven possible models: Sales ~ YouTube Sales ~ Newspaper Sales ~ Facebook Sales ~ YouTube + Facebook Sales ~ YouTube + Newspaper Sales ~ Newspaper + Facebook Sales ~ YouTube + Facebook + Newspaper Generally, if there are p possible predictor variables, there can be (2p - 1) possible models – this can get large very quickly! Thankfully, there are a few guidelines to filter some of these and then navigate towards the most efficient one. Keep variables with low p-values and eliminate ones with high p-values Keep variables that increase the value of adjusted-R2 – this penalizes the model for adding insignificant variables and increases when we add significant variables. It is calculated by: \\[ R^2_{adj} = 1- (1-R^2) \\frac{n-1}{n-p-1}\\] Based on these guidelines, there are two approaches to select the predictor variables in the final model: Forward selection: start with a null model (no predictors), then add predictors one by one. If the p-value for the variable is small enough and the value of the adjusted-R2 goes up, the predictor is included in the model. Otherwise, it is not included. Backward selection: starts with a model that has all the possible predictors and discard some of them. If the p-value of a predictor variable is large and adjusted-R2 is lower when removed, it is discarded from the model. Otherwise, it remains a part of the model. Many statistical programs give us an option to select from these approaches while implementing multiple linear regression. For now, let’s manually add a few variables and see how it changes the model parameters and efficacy. First, add the newspaper variable to the model: library(datarium) data(marketing) head(marketing) #&gt; youtube facebook newspaper sales #&gt; 1 276.12 45.36 83.04 26.52 #&gt; 2 53.40 47.16 54.12 12.48 #&gt; 3 20.64 55.08 83.16 11.16 #&gt; 4 181.80 49.56 70.20 22.20 #&gt; 5 216.96 12.96 70.08 15.48 #&gt; 6 10.44 58.68 90.00 8.64 res_lm2 = lm(sales ~ youtube + newspaper, data=marketing) summary(res_lm2) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ youtube + newspaper, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -10.3477 -2.0815 -0.1138 2.2711 10.1415 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 6.929938 0.630405 10.993 &lt; 2e-16 *** #&gt; youtube 0.046901 0.002581 18.173 &lt; 2e-16 *** #&gt; newspaper 0.044219 0.010174 4.346 2.22e-05 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.745 on 197 degrees of freedom #&gt; Multiple R-squared: 0.6458, Adjusted R-squared: 0.6422 #&gt; F-statistic: 179.6 on 2 and 197 DF, p-value: &lt; 2.2e-16 As you see, the p-values for the coefficients are very small, suggesting that all the estimates are significant. The equation for this model will be: \\[ \\text{Sales} = 6.93+0.046* \\text{YouTube} + 0.044 * \\text{Newspaper}\\] The values of R2 and adjusted R2 are 0.646 and 0.642, which is just a minor improvement from before (0.612 and 0.610, respectively). Similarly for RSE (3.745). Only a small decrease in RSE and error… Let’s take a closer look at the summary above. The Adj-R2 increases slightly, but the F-statistic decreases (from 312.1 to 179.6), as does the associated p-value. This suggests that adding newspaper didn’t improve the model significantly. Let’s try adding facebook instead: # Initialise and fit new model with TV and Radio as predictors # model3 = smf.ols(&#39;Sales ~ TV + Radio&#39;, data=advert).fit() # print(model3.summary()) res_lm3 = lm(sales ~ youtube + facebook, data=marketing) summary(res_lm3) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ youtube + facebook, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -10.5572 -1.0502 0.2906 1.4049 3.3994 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 3.50532 0.35339 9.919 &lt;2e-16 *** #&gt; youtube 0.04575 0.00139 32.909 &lt;2e-16 *** #&gt; facebook 0.18799 0.00804 23.382 &lt;2e-16 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 2.018 on 197 degrees of freedom #&gt; Multiple R-squared: 0.8972, Adjusted R-squared: 0.8962 #&gt; F-statistic: 859.6 on 2 and 197 DF, p-value: &lt; 2.2e-16 This gives us the model: \\[ \\text{Sales} = 3.51+0.046* \\text{YouTube} + 0.188 * \\text{Facebook}\\] The adjusted R2 value has improved considerably, as did the RSE and F-statistic, indicating an efficient model. Thus, we can conclude that facebook is a great addition to the model. YouTube and facebook advertising costs together are able to predict sales well. But, can we improve it a bit further by combining all three predictor variables? Try it out: see if you can figure out how to do this on your own! # Initialise and fit new model with TV, Newspaper, and Radio as predictors # Print summary of regression results # Calculate RSE - don&#39;t forget that the number of predictors p is now 3 You should get the equation: \\[ \\text{Sales} = 3.53+0.046*\\text{YouTube} -0.001*\\text{Newspaper} +0.188*\\text{Facebook}\\] You should also find that: RSE increases slightly, the coefficient for newspaper is negative, and the F-statistic decreases considerably from 859.6 to 570.3. All these suggest that the model actually became less efficient on addition of newspaper. Why? This step shows clearly that adding one more input variable Newspaper in Model 3 does not lead to any improvement. "],["introClassifier.html", "Chapter 4 Introduction to Classification 4.1 Visualise logistic and logit functions 4.2 Logistic regression on Diabetes 4.3 Cross-validation 4.4 More assessment metrics", " Chapter 4 Introduction to Classification 4.1 Visualise logistic and logit functions In this chapter, we will focus on logistic regression for classification. Let’s first look at what logistic and logit function look like. 4.1.1 Logistic function Let’s write our first function logestic() as follows. # Write your first function logistic &lt;- function(y) { exp(y) / (1 + exp(y)) } # Try it with different values: logistic(0.1) #&gt; [1] 0.5249792 logistic(c(-3, -2, 0.5, 3, 5)) #&gt; [1] 0.04742587 0.11920292 0.62245933 0.95257413 0.99330715 This is the equivalent to the built-in plogis() function in the stat package for the logistic distribution: plogis(0.1) #&gt; [1] 0.5249792 plogis(c(-3, -2, 0.5, 3, 5)) #&gt; [1] 0.04742587 0.11920292 0.62245933 0.95257413 0.99330715 4.1.2 Logit function Now, let look at the logistic’s inverse function logit(), and let’s define it manually. Note, this function only support input between 0 and 1. # Write your first function logit &lt;- function(x) { log(x / (1 - x)) } # Try it with different values: logit(0.4) #&gt; [1] -0.4054651 logit(c(0.2, 0.3, 0.5, 0.7, 0.9)) #&gt; [1] -1.3862944 -0.8472979 0.0000000 0.8472979 2.1972246 logit(c(-1, 2, 0.4)) #&gt; Warning in log(x/(1 - x)): NaNs produced #&gt; [1] NaN NaN -0.4054651 Again, the built-in stat package’s logistic distribution has an equivalent function qlogis(), though with a different name. qlogis(0.4) #&gt; [1] -0.4054651 qlogis(c(0.2, 0.3, 0.5, 0.7, 0.9)) #&gt; [1] -1.3862944 -0.8472979 0.0000000 0.8472979 2.1972246 qlogis(c(-1, 2, 0.4)) #&gt; Warning in qlogis(c(-1, 2, 0.4)): NaNs produced #&gt; [1] NaN NaN -0.4054651 4.1.3 Visualise the distribution Logisitc function # You can use seq() function to generate a vector # Check how to use it by help(seq) or ?seq x = seq(-7, 7, 0.3) df = data.frame(&#39;x&#39;=x, &#39;logistic&#39;=plogis(x)) # You can plot by plot function # plot(x=df$x, y=df$logistic, type=&#39;o&#39;) # Or ggplot2 library(ggplot2) ggplot(df, aes(x=x, y=logistic)) + geom_point() + geom_line() Logit function x = seq(0.001, 0.999, 0.01) df = data.frame(&#39;x&#39;=x, &#39;logit&#39;=qlogis(x)) ggplot(df, aes(x=x, y=logit)) + geom_point() + geom_line() 4.2 Logistic regression on Diabetes 4.2.1 Load Pima Indians Diabetes Database This dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. The objective of the dataset is to diagnostically predict whether or not a patient has diabetes, based on certain diagnostic measurements included in the dataset. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage. The datasets consist of several medical predictor (independent) variables and one target (dependent) variable, Outcome. Independent variables include the number of pregnancies the patient has had, their BMI, insulin level, age, and so on. Acknowledgement: This notebook is adapted and updated from STAT1005. # Install the mlbench library for loading the datasets if (!requireNamespace(&quot;mlbench&quot;, quietly = TRUE)) { install.packages(&quot;mlbench&quot;) } # Load data library(mlbench) data(PimaIndiansDiabetes) # Check the first few lines dim(PimaIndiansDiabetes) #&gt; [1] 768 9 head(PimaIndiansDiabetes) #&gt; pregnant glucose pressure triceps insulin mass pedigree age diabetes #&gt; 1 6 148 72 35 0 33.6 0.627 50 pos #&gt; 2 1 85 66 29 0 26.6 0.351 31 neg #&gt; 3 8 183 64 0 0 23.3 0.672 32 pos #&gt; 4 1 89 66 23 94 28.1 0.167 21 neg #&gt; 5 0 137 40 35 168 43.1 2.288 33 pos #&gt; 6 5 116 74 0 0 25.6 0.201 30 neg Now, let’s check two potential features: glucose and age, colored by the diabetes labels. library(ggplot2) ggplot(data=PimaIndiansDiabetes, aes(x=glucose, y=age)) + geom_point(aes(color=diabetes)) Before we start fit models, let’s split the data into training and test sets in a 4:1 ratio. Let define it manually, though there are functions to do it automatically. set.seed(0) idx_train = sample(nrow(PimaIndiansDiabetes), size=0.75*nrow(PimaIndiansDiabetes), replace = FALSE) df_train = PimaIndiansDiabetes[idx_train, ] df_test = PimaIndiansDiabetes[-idx_train, ] # recall the meaning of negative symbol 4.2.2 Fit logistic regression In logistic regression, the predicted probability to be class 1 is: \\[P(y=1|X, W) = \\sigma(w_0, x_1 * w_1 + ... + x_p * w_p)\\] where the \\(\\sigma()\\) denotes the logistic function. In R, the built-in package stats already have functions to fit generalised linear model (GLM), including logistic regression, a type of GML. Here, let’s start with the whole dataset to fit a logistic regression. Note, we will specify the model family as binomial, as the likelihood we are using in logistic regression is a Bernoulli likelihood, a special case of binomial likelihood when the total trial n=1. # Define formula in different ways # my_formula = as.formula(diabetes ~ glucose + age) # my_formula = as.formula(paste(colnames(PimaIndiansDiabetes)[1:8], collapse= &quot; + &quot;)) # my_formula = as.formula(diabetes ~ .) # Fit logistic regression glm_res &lt;- glm(diabetes ~ ., data=df_train, family = binomial) # We can use the logLik() function to obtain the log likelihood logLik(glm_res) #&gt; &#39;log Lik.&#39; -281.9041 (df=9) We can use summary() function to see more details about the model fitting. summary(glm_res) #&gt; #&gt; Call: #&gt; glm(formula = diabetes ~ ., family = binomial, data = df_train) #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error z value Pr(&gt;|z|) #&gt; (Intercept) -8.044602 0.826981 -9.728 &lt; 2e-16 *** #&gt; pregnant 0.130418 0.036080 3.615 0.000301 *** #&gt; glucose 0.032196 0.004021 8.007 1.18e-15 *** #&gt; pressure -0.017158 0.006103 -2.811 0.004934 ** #&gt; triceps -0.003425 0.007659 -0.447 0.654752 #&gt; insulin -0.001238 0.001060 -1.169 0.242599 #&gt; mass 0.104029 0.018119 5.741 9.39e-09 *** #&gt; pedigree 0.911030 0.344362 2.646 0.008156 ** #&gt; age 0.012980 0.010497 1.237 0.216267 #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; (Dispersion parameter for binomial family taken to be 1) #&gt; #&gt; Null deviance: 756.83 on 575 degrees of freedom #&gt; Residual deviance: 563.81 on 567 degrees of freedom #&gt; AIC: 581.81 #&gt; #&gt; Number of Fisher Scoring iterations: 5 4.2.3 Assess on test data Now, we can evaluate the accuracy of the model on the 25% test data. # Train the full model on the training data glm_train &lt;- glm(diabetes ~ ., data=df_train, family = binomial) # Predict the probability of being diabeties on test data # We can also set a threshold, e.g., 0.5 for the predicted label pred_prob = predict(glm_train, df_test, type = &quot;response&quot;) pred_label = pred_prob &gt;= 0.5 # Observed label obse_label = df_test$diabetes == &#39;pos&#39; # Calculate the accuracy on test data # think how accuracy is defined # we can use (TN + TP) / (TN + TP + FN + FP) # we can also directly compare the proportion of correctness accuracy = mean(pred_label == obse_label) print(paste(&quot;Accuracy on test set:&quot;, accuracy)) #&gt; [1] &quot;Accuracy on test set: 0.796875&quot; 4.2.4 Model selection and diagnosis 4.2.4.1 Model2: New feature set by removing triceps # Train the full model on the training data glm_mod2 &lt;- glm(diabetes ~ pregnant + glucose + pressure + insulin + mass + pedigree + age, data=df_train, family = binomial) logLik(glm_mod2) #&gt; &#39;log Lik.&#39; -282.0038 (df=8) summary(glm_mod2) #&gt; #&gt; Call: #&gt; glm(formula = diabetes ~ pregnant + glucose + pressure + insulin + #&gt; mass + pedigree + age, family = binomial, data = df_train) #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error z value Pr(&gt;|z|) #&gt; (Intercept) -8.0317567 0.8251403 -9.734 &lt; 2e-16 *** #&gt; pregnant 0.1308094 0.0361230 3.621 0.000293 *** #&gt; glucose 0.0324606 0.0039854 8.145 3.80e-16 *** #&gt; pressure -0.0175651 0.0060269 -2.914 0.003563 ** #&gt; insulin -0.0014402 0.0009593 -1.501 0.133291 #&gt; mass 0.1018155 0.0173811 5.858 4.69e-09 *** #&gt; pedigree 0.9000134 0.3428652 2.625 0.008665 ** #&gt; age 0.0131238 0.0105147 1.248 0.211982 #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; (Dispersion parameter for binomial family taken to be 1) #&gt; #&gt; Null deviance: 756.83 on 575 degrees of freedom #&gt; Residual deviance: 564.01 on 568 degrees of freedom #&gt; AIC: 580.01 #&gt; #&gt; Number of Fisher Scoring iterations: 5 # Predict the probability of being diabeties on test data # We can also set a threshold, e.g., 0.5 for the predicted label pred_prob2 = predict(glm_mod2, df_test, type = &quot;response&quot;) pred_label2 = pred_prob2 &gt;= 0.5 accuracy2 = mean(pred_label2 == obse_label) print(paste(&quot;Accuracy on test set with model2:&quot;, accuracy2)) #&gt; [1] &quot;Accuracy on test set with model2: 0.807291666666667&quot; 4.2.4.2 Model3: New feature set by removing triceps and insulin # Train the full model on the training data glm_mod3 &lt;- glm(diabetes ~ pregnant + glucose + pressure + mass + pedigree + age, data=df_train, family = binomial) logLik(glm_mod3) #&gt; &#39;log Lik.&#39; -283.1342 (df=7) summary(glm_mod3) #&gt; #&gt; Call: #&gt; glm(formula = diabetes ~ pregnant + glucose + pressure + mass + #&gt; pedigree + age, family = binomial, data = df_train) #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error z value Pr(&gt;|z|) #&gt; (Intercept) -7.797803 0.802287 -9.719 &lt; 2e-16 *** #&gt; pregnant 0.130990 0.035957 3.643 0.00027 *** #&gt; glucose 0.030661 0.003755 8.164 3.23e-16 *** #&gt; pressure -0.017847 0.005953 -2.998 0.00272 ** #&gt; mass 0.097356 0.016969 5.737 9.61e-09 *** #&gt; pedigree 0.824150 0.338299 2.436 0.01484 * #&gt; age 0.015134 0.010426 1.452 0.14663 #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; (Dispersion parameter for binomial family taken to be 1) #&gt; #&gt; Null deviance: 756.83 on 575 degrees of freedom #&gt; Residual deviance: 566.27 on 569 degrees of freedom #&gt; AIC: 580.27 #&gt; #&gt; Number of Fisher Scoring iterations: 5 # Predict the probability of being diabeties on test data # We can also set a threshold, e.g., 0.5 for the predicted label pred_prob3 = predict(glm_mod3, df_test, type = &quot;response&quot;) pred_label3 = pred_prob3 &gt;= 0.5 accuracy3 = mean(pred_label3 == obse_label) print(paste(&quot;Accuracy on test set with model3:&quot;, accuracy3)) #&gt; [1] &quot;Accuracy on test set with model3: 0.786458333333333&quot; 4.3 Cross-validation In last section, we split the whole dataset into 75% for training and 25% for testing. However, when the dataset is small, the test set may not be big enough and introduce high variance on the assessment. One way to reduce this variance in assessment is performing cross-validation, where we split the data into K folds and use K-1 folds for training and the remaining fold for testing. This procedure will be repeated for fold 1 to fold K as testing fold and all folds will be aggregated for joint assessment. K is usually taken 3, 5 or 10. In extreme case that K=n_sample, we call it leave-one-out cross-validation (LOOCV). Let’s load the dataset (again) first. # Load data library(mlbench) data(PimaIndiansDiabetes) Besides implement the cross-validation from scratch, there are packages supporting it well, including caret package. We will install it and use it for cross-validation here. # Install the caret library for cross-validation if (!requireNamespace(&quot;caret&quot;, quietly = TRUE)) { install.packages(&quot;caret&quot;) } library(caret) #&gt; Loading required package: lattice # Define training control # We also want to have savePredictions=TRUE &amp; classProbs=TRUE set.seed(0) my_trControl &lt;- trainControl(method = &quot;cv&quot;, number = 5, classProbs = TRUE, savePredictions = TRUE) # Train the model cv_model &lt;- train(diabetes ~ ., data = PimaIndiansDiabetes, method = &quot;glm&quot;, family=binomial(), trControl = my_trControl) # Summarize the results print(cv_model) #&gt; Generalized Linear Model #&gt; #&gt; 768 samples #&gt; 8 predictor #&gt; 2 classes: &#39;neg&#39;, &#39;pos&#39; #&gt; #&gt; No pre-processing #&gt; Resampling: Cross-Validated (5 fold) #&gt; Summary of sample sizes: 615, 614, 615, 614, 614 #&gt; Resampling results: #&gt; #&gt; Accuracy Kappa #&gt; 0.7708344 0.4695353 We can also access to detailed prediction results after concatenating the K folds: head(cv_model$pred) #&gt; pred obs neg pos rowIndex parameter Resample #&gt; 1 neg neg 0.9656694 0.03433058 4 none Fold1 #&gt; 2 neg neg 0.8581071 0.14189290 6 none Fold1 #&gt; 3 neg pos 0.9508306 0.04916940 7 none Fold1 #&gt; 4 neg pos 0.6541361 0.34586388 17 none Fold1 #&gt; 5 neg pos 0.7675666 0.23243342 20 none Fold1 #&gt; 6 neg pos 0.6132685 0.38673152 26 none Fold1 We can double check the accuracy: CV_acc = mean(cv_model$pred$pred == cv_model$pred$obs) print(paste(&quot;Accuracy via 5-fold cross-validation&quot;, CV_acc)) #&gt; [1] &quot;Accuracy via 5-fold cross-validation 0.770833333333333&quot; 4.4 More assessment metrics 4.4.1 Two types of error In the above sections, we used the accuracy to perform model diagnosis, either only on one testing dataset or aggregating cross multiple folds in cross- validation. Accuracy is a widely used metric for model evaluation, on the averaged error rate. However, this metric still have limitations when assessing the model performance, especially the following two: When the samples are highly imbalance, high accuracy may not mean a good model. For example, for a sample with 990 negative samples and 10 positive samples, a simple model by predicting for all sample as negative will give an accuracy of 0.99. Thus, for highly imbalanced samples, we should be careful when interpreting the accuracy. In many scenarios, our tolerance on false positive errors and false negative errors may be different and we want to know both for a certain model. They are often called as type I and II errors: Type I error: false positive (rate) Type II error: false negative (rate) - a joke way to remember what type II mean Negative has two stripes. Here, we use the diabetes dataset and their cross-validation results above to illustrate the two types of errors and the corresponding model performance evaluation. # Let&#39;s start to define the values for the confusion matrix first # Recall what the difference between &amp; vs &amp;&amp; # Read more: https://stat.ethz.ch/R-manual/R-devel/library/base/html/Logic.html TP = sum((cv_model$pred$obs == &#39;pos&#39;) &amp; (cv_model$pred$pred == &#39;pos&#39;)) FN = sum((cv_model$pred$obs == &#39;pos&#39;) &amp; (cv_model$pred$pred == &#39;neg&#39;)) FP = sum((cv_model$pred$obs == &#39;neg&#39;) &amp; (cv_model$pred$pred == &#39;pos&#39;)) TN = sum((cv_model$pred$obs == &#39;neg&#39;) &amp; (cv_model$pred$pred == &#39;neg&#39;)) print(paste(&#39;TP, FN, FP, TN:&#39;, TP, FN, FP, TN)) #&gt; [1] &quot;TP, FN, FP, TN: 151 117 59 441&quot; We can also use the table() function to get the whole confusion matrix. Read more about the table function for counting the frequency of each element. A similar way is the confusionMatrix() in caret package. # Calculate confusion matrix confusion_mtx = table(cv_model$pred[, c(&quot;obs&quot;, &quot;pred&quot;)]) confusion_mtx #&gt; pred #&gt; obs neg pos #&gt; neg 441 59 #&gt; pos 117 151 # similar function confusionMatrix # conf_mat = confusionMatrix(cv_model$pred$pred, cv_model$pred$obs) # conf_mat$table We can also plot out the confusion matrix # Change to data.frame before using ggplot confusion_df = as.data.frame(confusion_mtx) ggplot(confusion_df, aes(pred, obs, fill= Freq)) + geom_tile() + geom_text(aes(label=Freq)) + scale_fill_gradient(low=&quot;white&quot;, high=&quot;darkgreen&quot;) Also the false positive rate, false negative rate and true negative rate. Note, the denominator is always the number of observed samples with the same label, namely they are a constant for a specific dataset. FPR = FP / sum(cv_model$pred$obs == &#39;neg&#39;) FNR = FN / sum(cv_model$pred$obs == &#39;pos&#39;) TPR = TP / sum(cv_model$pred$obs == &#39;pos&#39;) print(paste(&quot;False positive rate:&quot;, FPR)) #&gt; [1] &quot;False positive rate: 0.118&quot; print(paste(&quot;False negative rate:&quot;, FNR)) #&gt; [1] &quot;False negative rate: 0.436567164179104&quot; print(paste(&quot;True positive rate:&quot;, TPR)) #&gt; [1] &quot;True positive rate: 0.563432835820896&quot; 4.4.2 ROC curve In the above assessment, we only used \\(P&gt;0.5\\) to denote predicted label as positive. We can imagine if we a lower cutoff lower, we will have more false positives and fewer false negatives. Indeed, in different scenarios, people may choose different level of cutoff for their tolerance of different types of errors. Let’s try cutoff \\(P&gt;0.4\\). Think what will you expect. # Original confusion matrix table(cv_model$pred[, c(&quot;obs&quot;, &quot;pred&quot;)]) #&gt; pred #&gt; obs neg pos #&gt; neg 441 59 #&gt; pos 117 151 # New confusion matrix with cutoff 0.4 cv_model$pred$pred_new = as.integer(cv_model$pred$pos &gt;= 0.4) table(cv_model$pred[, c(&quot;obs&quot;, &quot;pred_new&quot;)]) #&gt; pred_new #&gt; obs 0 1 #&gt; neg 408 92 #&gt; pos 89 179 Therefore, we may want to assess the model performance by varying the cutoffs and obtain a more systematic assessment. Actually, the Receiver operating characteristic (ROC) curve is what you need. It presents the TPR (sensitivity) vs the FPR (i.e., 1 - TNR or 1 - specificity) when varying the cutoffs. In order to achieve this, we can calculate FPR and TPR manually by varying the cutoff through a for loop. Read more about for loop and you may try write your own and here is an example from the cardelino package. For simplicity, let use an existing tool implemented in the plotROC package: plotROC::geom_roc() that is compatible with ggplot2. # Install the plotROC library for plotting ROC curve if (!requireNamespace(&quot;plotROC&quot;, quietly = TRUE)) { install.packages(&quot;plotROC&quot;) } library(ggplot2) library(plotROC) # You can set the n.cuts to show the cutoffs on the curve g = ggplot(cv_model$pred, aes(m = pos, d = as.integer(obs==&#39;pos&#39;))) + geom_roc(n.cuts=7, hjust = -0.4, vjust = 1.5) + coord_equal() + ggtitle(&quot;ROC curve&quot;) # Calculate AUC from the graph AUC_val = calc_auc(g)$AUC #&gt; Warning: The following aesthetics were dropped during statistical transformation: m, d #&gt; ℹ This can happen when ggplot fails to infer the correct grouping structure in #&gt; the data. #&gt; ℹ Did you forget to specify a `group` aesthetic or to convert a numerical #&gt; variable into a factor? # Display the plot g + annotate(&quot;text&quot;, x=0.8, y=0.1, label=paste(&quot;AUC =&quot;, round(AUC_val, 4))) #&gt; Warning: The following aesthetics were dropped during statistical transformation: m, d #&gt; ℹ This can happen when ggplot fails to infer the correct grouping structure in #&gt; the data. #&gt; ℹ Did you forget to specify a `group` aesthetic or to convert a numerical #&gt; variable into a factor? 4.4.3 Homework Now, try another model with removing triceps and plot the ROC curve and calculate the AUC score. Is it higher or lower than using the full features? "],["image-digital.html", "Chapter 5 Medical Image and Digital Health", " Chapter 5 Medical Image and Digital Health Contents to be added. "],["infectious-dis.html", "Chapter 6 Infectious Disease Informatics", " Chapter 6 Infectious Disease Informatics Contents to be added. "],["cancer.html", "Chapter 7 Cancer genomics and epidemiology 7.1 Case study 1: analysis of cBioportal mutation data 7.2 Case study 2: Cancer Epidemiology 7.3 1. Scenario 7.4 2. Hong Kong population 7.5 3. Cancer registry data 7.6 4. Existing cancer funding and publication data 7.7 5. Open disucssion", " Chapter 7 Cancer genomics and epidemiology 7.1 Case study 1: analysis of cBioportal mutation data Non-small cell lung cancer is a deadly disease, and we would like to identify mutations in genes that drive its formation and progression. George et al. (2015) has sequenced 120 small cell lung cancer samples and this data is available from cBioportal. The original data is in the MAF, and we have selected a subset of the columns, normalized the column names, and made the data available as an RDS file. In this exercise, we will explore the mutation data and examine genes that are frequently mutated in non-small cell lung cancer samples. We will implement a simple method for identifying candidate tumour suppressors based on loss-of-function mutations. 7.1.1 Exploratory analysis Q1. Load the data named mutations_sclc_ucologne_2015.rds into R. Examine it using head. In this data.frame, each row is a mutation detected in a particular gene from a particular sample in the study. For more information on the columns, see the MAF specification. ?readRDS ?head Q2. Identify the top 10 most frequently mutated genes. # calculate count frequencies using table ?table # freqs &lt;- ??? # sort the frequency vector in decreasing order ?sort # freqs &lt;- ??? # select the first 10 genes in the freqs # freqs.top &lt;- ??? # obtain the gene names # genes &lt;- names(freqs.top); # print(freqs.top) Q3. Tabulate the count frequencies of variant_class. What proportion of variants are Silent or inside an Intron? ?table Q4. A variant class value frame_shift_del appears to be misspelt due to case sensitivity. Correct this error. # x$variant_class[x$variant_class == &quot;frame_shift_del&quot;] &lt;- ???; Q5. To help us simplify the variant classes into loss-of-function or neutral, let us import the mutation_effects.tsv data. ?read.table # Hint: You need to set the `header` and `sep` arguments Q6. Define a new column in x that converts the variant classes to effects. ?match Q7. Create a subset of the data for the most frequently mutated genes, and tabulate the mutation count frequencies of variant classes for each gene. # x.sub &lt;- x[???, ] # order the factor levels based on `genes`, # which was previously sorted in decreasing order of frequency # x.sub$gene &lt;- factor(x.sub$gene, levels=genes); ?table Q8. Determine the number of mutations in each effect category, across all genes. Save the result in a variable named overall.counts. # overall.counts &lt;- table(???); # overall.counts Q9. Tabulate the mutation count frequencies for each gene and effect. Save the results in a variable named gene.counts. Look up the frequently mutated genes in this matrix. # gene.counts &lt;- table(???, ???); # gene.counts[???, ] 7.1.2 Statistical analysis Here, we implemented a simple statistical test for assessing whether a gene is significantly frequently targeted by loss-of-function mutations, based on the Fisher’s exact test. # Test whether a query gene has significantly more loss-of-function # mutations compared with other genes. # Requires global variables `gene.counts` and `overall.counts` lof_test &lt;- function(gene) { # Construct the following contingency table: # neutral lof # other genes a b # query gene c d cols &lt;- c(&quot;neutral&quot;, &quot;loss_of_function&quot;); gene.counts.sel &lt;- gene.counts[gene, cols]; ct &lt;- matrix( c( overall.counts[cols] - gene.counts.sel, gene.counts.sel ), byrow=TRUE, ncol=2 ); # Test whether the lof mutations are greater in frequency compared # to neutral mutations in the query gene, in comparison to all other genes fisher.test(ct, alternative=&quot;greater&quot;) } Q10. Subset the gene.counts table for the TP53 gene. Run lof_test on this gene. # gene.counts[???, ] # lof_test(???) Q11. Now, test to see if TTN and MUC16 are significantly frequently targeted by loss-of-function mutations. # similar to above Q12. Apply the loss-of-function test to all frequently mutated genes. ?lapply Q13. Extract odds ratio and p-values from the test results. # odds.ratios &lt;- vapply(hs, function(h) h$estimate, 0); # ps &lt;- vapply(hs, function(h) ???, 0); Q14. Since we tested many genes, we need to adjust for multiple hypothesis testing so that we can control the false discovery rate. So, adjust the p-values to obtain q-values. ?p.adjust Q15. Construct a results data.frame with gene names, odds ratio, p-values, and q-values that summarize the loss-of-function test results. # res &lt;- data.frame( # gene = ???, # odds_ratio = ???, # p = ???, # q = ??? # ); ?order #res &lt;- res[order(???), ]; Q16. Identify the significant genes from the results data.frame at a false discovery rate of 5% (i.e. q-value threshold of 0.05). Q17. Look up the significant genes in the gene.counts matrix. 7.1.3 Literature search Q18. Do the significant genes appear to be involved in cancer? What general roles do they play? Q19. How do these genes contribute specifically to the formation or progression of small cell lung cancer? Q20. What are some possible ways of identifying oncogenes that are activated by mutations or other genomic alterations? 7.2 Case study 2: Cancer Epidemiology by Dr Jason Wong Date: 6-11-2023 The RMarkdown notebook to run your own code can be downloaded here 7.3 1. Scenario You are a grants officer working for the Hong Kong Health Bureau. The HK government has recently announced new special funding in cancer research to be administered by the Bureau. You are tasked with coming up with a proposal for distribution of funding to specific cancer types that are in most need of research. Discussion points: What is important to consider when selecting a cancer type in need of research? What type of data is required? 7.4 2. Hong Kong population You are aware that generally cancer is disease that affects the elderly more than the young. You decide to first take a closer look at the structure of the population of Hong Kong. Historic population of Hong Kong can be obtained from the Census and Statistics Department. An abridged version of the full historic population of Hong Kong is provided here containing the population of Hong Kong from 1965, 1975, 1985, 1995, 2005, 2015 and 2022 categorised by sex and age (0-19, 20-44, 45-64, 65+). Discussion points: What is the trend in Hong Kong’s population over the past ~60 years? What is the best way to visualise this data? 7.4.1 Download population data HKPop&lt;- read.table(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HK_population_1965-2022.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = FALSE) HKPop #&gt; Sex Age 1965 1975 1985 1995 2005 2015 2022 #&gt; 1 male 0-19 901.9 989.7 909.0 835.6 719.0 613.8 530.6 #&gt; 2 male 20-44 607.4 795.6 1210.2 1363.7 1263.7 1146.9 1039.2 #&gt; 3 male 45-64 266.5 414.3 525.9 615.7 896.6 1084.9 1046.2 #&gt; 4 male 65+ 42.2 84.6 170.5 269.3 384.7 520.0 713.6 #&gt; 5 female 0-19 865.6 938.8 840.3 780.7 684.1 575.0 502.1 #&gt; 6 female 20-44 539.3 685.6 1093.7 1423.6 1530.4 1531.8 1338.7 #&gt; 7 female 45-64 286.3 400.7 470.7 535.0 884.7 1224.3 1314.7 #&gt; 8 female 65+ 88.7 152.3 235.9 332.5 450.0 594.6 806.5 7.4.2 Format data for plotting Here we convert the original dataframe into simplified format for ggplot2. male&lt;-data.frame(year = as.numeric(colnames(HKPop[1,3:9])), `0-19` = as.numeric(HKPop[1,3:9]), `20-44` = as.numeric(HKPop[2,3:9]), `45-64` = as.numeric(HKPop[3,3:9]), `65+` = as.numeric(HKPop[4,3:9]), check.names = FALSE) female&lt;-data.frame(year = as.numeric(colnames(HKPop[1,3:9])), `0-19` = as.numeric(HKPop[5,3:9]), `20-44` = as.numeric(HKPop[6,3:9]), `45-64` = as.numeric(HKPop[7,3:9]), `65+` = as.numeric(HKPop[8,3:9]), check.names = FALSE) if (!require(&quot;tidyverse&quot;)) install.packages(&quot;tidyverse&quot;) male&lt;-as_tibble(male) %&gt;% select(year,`0-19`,`20-44`,`45-64`,`65+`) %&gt;% gather (key=&quot;age&quot;,value=&quot;population (&#39;000s)&quot;,-year) female&lt;-as_tibble(female) %&gt;% select(year,`0-19`,`20-44`,`45-64`,`65+`) %&gt;% gather (key=&quot;age&quot;,value=&quot;population (&#39;000s)&quot;,-year) male #&gt; # A tibble: 28 × 3 #&gt; year age `population (&#39;000s)` #&gt; &lt;dbl&gt; &lt;chr&gt; &lt;dbl&gt; #&gt; 1 1965 0-19 902. #&gt; 2 1975 0-19 990. #&gt; 3 1985 0-19 909 #&gt; 4 1995 0-19 836. #&gt; 5 2005 0-19 719 #&gt; 6 2015 0-19 614. #&gt; 7 2022 0-19 531. #&gt; 8 1965 20-44 607. #&gt; 9 1975 20-44 796. #&gt; 10 1985 20-44 1210. #&gt; # ℹ 18 more rows female #&gt; # A tibble: 28 × 3 #&gt; year age `population (&#39;000s)` #&gt; &lt;dbl&gt; &lt;chr&gt; &lt;dbl&gt; #&gt; 1 1965 0-19 866. #&gt; 2 1975 0-19 939. #&gt; 3 1985 0-19 840. #&gt; 4 1995 0-19 781. #&gt; 5 2005 0-19 684. #&gt; 6 2015 0-19 575 #&gt; 7 2022 0-19 502. #&gt; 8 1965 20-44 539. #&gt; 9 1975 20-44 686. #&gt; 10 1985 20-44 1094. #&gt; # ℹ 18 more rows 7.4.3 Plotting population data Uses ggplot2 and gridExtra to make line plot of male and female population data side-by-side. if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) library(ggplot2) library(gridExtra) #Import the necessary packages and libraries pmale&lt;-ggplot(male,aes(x=year,y=`population (&#39;000s)`,group=age))+ geom_line(aes(color=age))+ geom_point(aes(color=age))+ scale_color_brewer(palette=&quot;Spectral&quot;)+ theme_classic()+ ylim(0,1600)+ theme(legend.position=&quot;none&quot;)+ scale_x_continuous(breaks = seq(1965, 2022, by = 10))+ ggtitle(&quot;male&quot;) pfemale&lt;-ggplot(female,aes(x=year,y=`population (&#39;000s)`,group=age))+ geom_line(aes(color=age))+ geom_point(aes(color=age))+ scale_color_brewer(palette=&quot;Spectral&quot;)+ theme_classic()+ ylim(0,1600)+ theme(legend.position=&quot;right&quot;,axis.title.y = element_blank())+ scale_x_continuous(breaks = seq(1965, 2022, by = 10))+ ggtitle(&quot;female&quot;) grid.arrange(pmale,pfemale,ncol=2,widths=c(3,3.75)) 7.5 3. Cancer registry data It is clear that Hong Kong has an aging population, thus cancer incidence would also likely increase. To examine cancer incidence and mortality in Hong Kong you obtain data from the Hong Kong Cancer Registry, which is maintained by the Hospital Authority. Cancer incidence data was summarised for the last three decades (1990-1999, 2000-2009 and 2010-2019). Discussion points: Has incidence been increasing for most cancers? How about mortality? How has cancer risk and mortality rate changed in the past 3 decades? Has the incidence-to-mortality ratio been decreasing generally? Is it statistically significant? Which cancer type has the highest incidence in children (0-19) when compared with the elderly (65+). Is this statistically significantly different to incidence of children versus elderly cancers in general? 7.5.1 Download cancer registry data HKCancer&lt;- read.table(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HK_cancer_incidence_mortality_1990-2020.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE) HKCancer #&gt; Type Sex Age Year Biliary Bladder Brain Breast Cervix #&gt; 1 incidence male 0-19 1990-1999 0 6 212 0 0 #&gt; 2 incidence male 20-44 1990-1999 36 165 368 6 0 #&gt; 3 incidence male 45-64 1990-1999 322 1266 393 28 0 #&gt; 4 incidence male 65+ 1990-1999 830 2920 318 35 0 #&gt; 5 incidence male 0-19 2000-2009 0 2 206 0 0 #&gt; 6 incidence male 20-44 2000-2009 31 103 267 9 0 #&gt; 7 incidence male 45-64 2000-2009 297 900 372 52 0 #&gt; 8 incidence male 65+ 2000-2009 1134 3103 299 96 0 #&gt; 9 incidence male 0-19 2010-2019 0 2 155 0 0 #&gt; 10 incidence male 20-44 2010-2019 28 18 276 14 0 #&gt; 11 incidence male 45-64 2010-2019 530 648 511 72 0 #&gt; 12 incidence male 65+ 2010-2019 1568 2399 380 107 0 #&gt; 13 incidence female 0-19 1990-1999 0 2 149 6 0 #&gt; 14 incidence female 20-44 1990-1999 52 62 283 4228 1263 #&gt; 15 incidence female 45-64 1990-1999 246 246 238 5311 1839 #&gt; 16 incidence female 65+ 1990-1999 909 1199 284 4122 1574 #&gt; 17 incidence female 0-19 2000-2009 0 0 132 4 4 #&gt; 18 incidence female 20-44 2000-2009 34 39 223 5887 1204 #&gt; 19 incidence female 45-64 2000-2009 287 179 265 11833 1676 #&gt; 20 incidence female 65+ 2000-2009 1190 1090 237 5774 1329 #&gt; 21 incidence female 0-19 2010-2019 0 2 119 1 0 #&gt; 22 incidence female 20-44 2010-2019 36 17 223 6658 1294 #&gt; 23 incidence female 45-64 2010-2019 452 188 394 22096 2288 #&gt; 24 incidence female 65+ 2010-2019 1500 872 283 10337 1269 #&gt; 25 mortality male 0-19 1990-1999 0 0 76 0 0 #&gt; Colorectum Eye Hodgkin.lymphoma Kaposi Kidney Larynx Leukaemia Liver Lung #&gt; 1 15 29 35 0 24 1 356 58 6 #&gt; 2 1087 8 64 0 141 86 509 1741 1036 #&gt; 3 4644 9 47 0 530 824 453 5702 8420 #&gt; 4 8058 21 41 0 721 1265 623 4806 15152 #&gt; 5 5 38 32 0 20 0 329 33 3 #&gt; 6 957 8 119 9 221 37 437 1116 772 #&gt; 7 6418 18 77 4 1071 658 642 6015 7909 #&gt; 8 13352 13 77 8 1275 1125 864 5808 18870 #&gt; 9 6 26 53 0 31 0 338 24 2 #&gt; 10 1005 10 163 25 293 29 401 659 541 #&gt; 11 10034 28 87 18 1978 684 1033 6500 9523 #&gt; 12 18003 15 114 12 1977 1043 1381 6716 20588 #&gt; 13 2 33 10 0 25 0 296 37 7 #&gt; 14 932 11 61 0 98 13 393 353 597 #&gt; 15 3166 9 19 0 256 59 312 1093 2629 #&gt; 16 7728 16 33 0 503 130 534 2244 8428 #&gt; 17 5 14 30 0 15 0 219 13 5 #&gt; 18 938 12 122 2 120 5 405 212 625 #&gt; 19 4430 10 33 0 482 37 469 1041 3397 #&gt; 20 10810 8 35 0 830 85 723 2637 9517 #&gt; 21 5 14 32 0 19 0 237 21 0 #&gt; 22 1057 9 174 0 135 7 443 168 647 #&gt; 23 7200 16 58 4 887 47 786 1168 6312 #&gt; 24 13119 20 58 5 1203 84 913 3007 10872 #&gt; 25 10 3 0 0 2 0 120 36 1 #&gt; Melanoma Mesothelioma Multiple.myeloma Nasal Nasopharynx #&gt; 1 3 0 1 4 33 #&gt; 2 50 0 43 53 3049 #&gt; 3 82 0 210 109 3724 #&gt; 4 107 0 421 120 1212 #&gt; 5 1 0 1 7 16 #&gt; 6 41 5 38 38 2114 #&gt; 7 98 34 326 161 3750 #&gt; 8 137 77 674 137 1177 #&gt; 9 0 0 0 3 21 #&gt; 10 47 4 26 41 1339 #&gt; 11 186 51 525 174 3653 #&gt; 12 195 154 910 154 1207 #&gt; 13 2 0 1 1 13 #&gt; 14 44 0 19 31 1380 #&gt; 15 58 0 150 57 1157 #&gt; 16 102 0 417 93 536 #&gt; 17 2 0 0 5 6 #&gt; 18 41 8 21 36 942 #&gt; 19 102 12 185 74 1187 #&gt; 20 118 14 559 92 465 #&gt; 21 3 0 0 6 6 #&gt; 22 70 10 24 37 583 #&gt; 23 128 34 399 105 1145 #&gt; 24 179 24 636 102 389 #&gt; 25 2 0 0 0 6 #&gt; Non.Hodgkin.lymphoma Non.melanoma.skin Oesophagus Oral Ovary Pancreas Penis #&gt; 1 137 8 0 18 0 4 2 #&gt; 2 596 211 158 324 0 106 19 #&gt; 3 997 613 1873 1165 0 514 78 #&gt; 4 1210 968 2203 1055 0 887 184 #&gt; 5 111 4 0 6 0 1 0 #&gt; 6 454 220 82 312 0 71 18 #&gt; 7 1216 917 1528 1354 0 780 71 #&gt; 8 1756 1835 2126 1416 0 1440 199 #&gt; 9 106 1 0 9 0 1 0 #&gt; 10 487 291 54 304 0 109 21 #&gt; 11 1910 1782 1321 1941 0 1402 154 #&gt; 12 2633 2975 1982 1813 0 2302 279 #&gt; 13 75 2 0 21 77 2 0 #&gt; 14 444 156 48 241 854 60 0 #&gt; 15 594 374 254 364 970 290 0 #&gt; 16 1120 1249 761 485 776 875 0 #&gt; 17 43 4 1 20 108 0 0 #&gt; 18 461 182 13 254 1299 62 0 #&gt; 19 888 580 190 454 1846 461 0 #&gt; 20 1409 2476 725 768 891 1329 0 #&gt; 21 57 4 0 9 84 3 0 #&gt; 22 475 303 16 259 1466 92 0 #&gt; 23 1561 1168 174 920 3166 923 0 #&gt; 24 1883 3268 624 1091 1128 2101 0 #&gt; 25 25 0 0 1 0 3 0 #&gt; Placenta Prostate Sarcoma Small.intestine Stomach Testis Thymus Thyroid #&gt; 1 0 0 137 0 5 61 12 22 #&gt; 2 0 10 320 31 429 275 71 250 #&gt; 3 0 481 281 102 1990 80 70 288 #&gt; 4 0 3073 261 131 3634 129 59 194 #&gt; 5 0 0 118 0 6 57 16 21 #&gt; 6 0 6 307 34 331 395 96 333 #&gt; 7 0 1588 367 113 1954 65 137 447 #&gt; 8 0 8676 316 163 4256 44 94 278 #&gt; 9 0 1 110 1 2 53 23 17 #&gt; 10 0 18 299 46 192 587 68 496 #&gt; 11 0 4128 527 293 2158 100 137 834 #&gt; 12 0 14703 507 336 4720 15 85 424 #&gt; 13 1 0 128 1 1 0 3 80 #&gt; 14 13 0 283 22 492 0 38 1294 #&gt; 15 0 0 232 53 826 0 38 788 #&gt; 16 0 0 232 116 2319 0 38 479 #&gt; 17 0 0 105 0 2 0 1 81 #&gt; 18 8 0 322 24 379 0 64 1659 #&gt; 19 3 0 300 80 971 0 116 1570 #&gt; 20 0 0 247 153 2512 0 65 595 #&gt; 21 0 0 86 1 0 0 5 103 #&gt; 22 12 0 330 38 318 0 30 2291 #&gt; 23 3 0 509 221 1653 0 81 3200 #&gt; 24 0 0 351 251 2809 0 67 940 #&gt; 25 0 0 41 1 0 2 7 1 #&gt; Uterus Vulva #&gt; 1 0 0 #&gt; 2 0 0 #&gt; 3 0 0 #&gt; 4 0 0 #&gt; 5 0 0 #&gt; 6 0 0 #&gt; 7 0 0 #&gt; 8 0 0 #&gt; 9 0 0 #&gt; 10 0 0 #&gt; 11 0 0 #&gt; 12 0 0 #&gt; 13 2 1 #&gt; 14 478 49 #&gt; 15 1362 96 #&gt; 16 729 235 #&gt; 17 2 2 #&gt; 18 821 44 #&gt; 19 3071 147 #&gt; 20 1130 336 #&gt; 21 3 1 #&gt; 22 1165 57 #&gt; 23 6582 235 #&gt; 24 1864 486 #&gt; 25 0 0 #&gt; [ reached &#39;max&#39; / getOption(&quot;max.print&quot;) -- omitted 23 rows ] 7.5.2 3a. Visualise changes in incidence and mortality # first plot incidence for each cancer type #Import the necessary packages and libraries if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) if (!require(&quot;ggpubr&quot;)) install.packages(&quot;ggpubr&quot;) library(ggplot2) library(gridExtra) library(ggpubr) HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] p&lt;-list() for (i in 1:(ncol(HKCancer_inc)-4)){ p[[i]]&lt;-ggplot(HKCancer_inc,aes_string(fill=names(HKCancer_inc)[3],x=names(HKCancer_inc)[4], y=names(HKCancer_inc)[i+4],group=names(HKCancer_inc)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;Incidence&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) # now plot mortality for each cancer type #Import the necessary packages and libraries if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) if (!require(&quot;ggpubr&quot;)) install.packages(&quot;ggpubr&quot;) if (!require(&quot;dplyr&quot;)) install.packages(&quot;dplyr&quot;) library(ggplot2) library(gridExtra) library(ggpubr) library(dplyr) HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] p&lt;-list() #(ncol(HKCancer_inc)-4) for (i in 1:(ncol(HKCancer_mort)-4)){ p[[i]]&lt;-ggplot(HKCancer_mort,aes_string(fill=names(HKCancer_mort)[3],x=names(HKCancer_mort)[4], y=names(HKCancer_mort)[i+4],group=names(HKCancer_mort)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_mort)[i+4])+ ylab(&quot;Mortality&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) 7.5.3 3b. Calculate cancer risk and mortality rate To calculate disease risk we need to calculated the number of new cases over the number of persons at risk over a specific time period. We have the incidence for each decade and can estimate the number of persons at risk based on the population in 1995, 2005 and 2015. # cancer risk calculation HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_inc_risk &lt;- HKCancer_inc[,1:5] risk &lt;- function(x,age,sex,year){ if (is.integer(x)){ pop_n &lt;- HKPop %&gt;% filter(Sex==sex &amp; Age==age) if (year == &quot;1990-1999&quot;){ return (as.double(x)/as.double(pop_n$`1995`)) } else if (year == &quot;2000-2009&quot;) {return (as.double(x)/as.double(pop_n$`2005`))} else { return (as.double(x)/as.double(pop_n$`2015`)) } } return (x) } for (i in 5:ncol(HKCancer_inc)){ HKCancer_inc_risk[names(HKCancer_inc)[i]] &lt;- mapply(risk,HKCancer_inc[,i],HKCancer_inc[,3],HKCancer_inc[,2],HKCancer_inc[,4]) } #visualise cancer risk p&lt;-list() for (i in 1:(ncol(HKCancer_inc_risk)-4)){ p[[i]]&lt;-ggplot(HKCancer_inc_risk,aes_string(fill=names(HKCancer_inc_risk)[3],x=names(HKCancer_inc_risk)[4], y=names(HKCancer_inc_risk)[i+4],group=names(HKCancer_inc_risk)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;incidence per 1000&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) # mortality rate calculation HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] HKCancer_mort_risk &lt;- HKCancer_mort[,1:5] risk &lt;- function(x,age,sex,year){ if (is.integer(x)){ pop_n &lt;- HKPop %&gt;% filter(Sex==sex &amp; Age==age) if (year == &quot;1990-1999&quot;){ return (as.double(x)/as.double(pop_n$`1995`)) } else if (year == &quot;2000-2009&quot;) {return (as.double(x)/as.double(pop_n$`2005`))} else { return (as.double(x)/as.double(pop_n$`2015`)) } } return (x) } for (i in 5:ncol(HKCancer_mort)){ HKCancer_mort_risk[names(HKCancer_mort)[i]] &lt;- mapply(risk,HKCancer_mort[,i],HKCancer_mort[,3],HKCancer_mort[,2],HKCancer_mort[,4]) } #visualise mortality rate p&lt;-list() for (i in 1:(ncol(HKCancer_mort_risk)-4)){ p[[i]]&lt;-ggplot(HKCancer_mort_risk,aes_string(fill=names(HKCancer_mort_risk)[3],x=names(HKCancer_mort_risk)[4], y=names(HKCancer_mort_risk)[i+4],group=names(HKCancer_mort_risk)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;mortality per 1000&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) 7.5.4 3c. Mortality-incidence ratio Cancer research can be focused on improving cancer outcomes in a number of ways. For example cancer prevention research that seeks to reduce cancer incidence which would also ultimately reduce cancer mortality. Another area is cancer therapy which would not affect incidence but seeks to reduce mortality, or at least prolong survival. We don’t go into survival analysis in this tutorial, but a way to get an idea whether treatment is improving by looking at the mortality-incidence ratio. HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] HKCancer_mort_inc &lt;- HKCancer_mort[,1:5] risk &lt;- function(mort,inc){ if (inc == 0){ return (0) } return (as.double(mort)/as.double(inc)) } for (i in 5:ncol(HKCancer_mort)){ HKCancer_mort_inc[names(HKCancer_mort)[i]] &lt;- mapply(risk,HKCancer_mort[,i],HKCancer_inc[,i]) } #visualise mortality incidence ratio p&lt;-list() for (i in 1:(ncol(HKCancer_mort_inc)-4)){ p[[i]]&lt;-ggplot(HKCancer_mort_inc,aes_string(fill=names(HKCancer_mort_inc)[3],x=names(HKCancer_mort_inc)[4], y=names(HKCancer_mort_inc)[i+4],group=names(HKCancer_mort_inc)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;mortality-incidence ratio&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) 7.5.5 3d. Paired t-test on mortality-incidence ratio change In general, across the different cancer types is cancer treatment improving? We can use a paired t-test comparing the mortality-incidence ratio of cancers from the 1990-1999 period with the 2010-2019 period. #First sum up all incidence and mortality data for each cancer type across age and sex HKCancer_inc_sum &lt;- aggregate(HKCancer_inc[,-(1:4)],list(HKCancer_inc$Year),FUN=sum) HKCancer_mort_sum &lt;- aggregate(HKCancer_mort[,-(1:4)],list(HKCancer_mort$Year),FUN=sum) HKCancer_mort_inc_year &lt;- data.frame(Year=HKCancer_mort_sum[,1]) risk &lt;- function(mort,inc){ return (as.double(mort)/as.double(inc)) } for (i in 2:ncol(HKCancer_mort_sum)){ HKCancer_mort_inc_year[names(HKCancer_mort_sum)[i]] &lt;- mapply(risk,HKCancer_mort_sum[,i],HKCancer_inc_sum[,i]) } HKCancer_mort_inc_year_m &lt;-data.frame(`1990-1999` = as.numeric(HKCancer_mort_inc_year[1,2:37]), `2000-2009` = as.numeric(HKCancer_mort_inc_year[2,2:37]), `2010-2019` = as.numeric(HKCancer_mort_inc_year[3,2:37]), check.names = FALSE) HKCancer_mort_inc_year_m$Cancer &lt;- names(HKCancer_mort_inc_year)[-1] HKCancer_mort_inc_year_t&lt;-as_tibble(HKCancer_mort_inc_year_m) %&gt;% select(`Cancer`,`1990-1999`,`2000-2009`,`2010-2019`)%&gt;% gather (key=&quot;Year&quot;,value=&quot;MIR&quot;,-Cancer) plot&lt;-ggplot(HKCancer_mort_inc_year_t,aes(x=Year,y=MIR, color=Year))+ geom_boxplot(na.rm=T) + theme_classic()+ scale_color_brewer(palette=&quot;Dark2&quot;)+ geom_jitter(shape=16, position=position_jitter(0.2),na.rm=T)+ ylab(&quot;mortality-incidence ratio&quot;)+ ylim(0,1.2) + geom_signif(comparisons = list(c(&quot;1990-1999&quot;, &quot;2010-2019&quot;)), map_signif_level=F, test= &quot;t.test&quot;,test.args = list(paired = TRUE), na.rm = T, y_position = c(1.1, 1.3)) + geom_signif(comparisons = list(c(&quot;1990-1999&quot;, &quot;2000-2009&quot;)), map_signif_level=F, test= &quot;t.test&quot;,test.args = list(paired = TRUE), na.rm = T) + geom_signif(comparisons = list(c(&quot;2000-2009&quot;, &quot;2010-2019&quot;)), map_signif_level=F, test= &quot;t.test&quot;,test.args = list(paired = TRUE), na.rm = T) plot p&lt;-list() p[[1]]&lt;-t.test(HKCancer_mort_inc_year_m$`1990-1999`,HKCancer_mort_inc_year_m$`2000-2009`,paired=TRUE,alternative_m = &quot;two.sided&quot;) p[[2]]&lt;-t.test(HKCancer_mort_inc_year_m$`1990-1999`,HKCancer_mort_inc_year_m$`2010-2019`,paired=TRUE,alternative_m = &quot;two.sided&quot;) p[[3]]&lt;-t.test(HKCancer_mort_inc_year_m$`2000-2009`,HKCancer_mort_inc_year_m$`2010-2019`,paired=TRUE,alternative_m = &quot;two.sided&quot;) p #&gt; [[1]] #&gt; #&gt; Paired t-test #&gt; #&gt; data: HKCancer_mort_inc_year_m$`1990-1999` and HKCancer_mort_inc_year_m$`2000-2009` #&gt; t = 0.79695, df = 33, p-value = 0.4312 #&gt; alternative hypothesis: true mean difference is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.01415536 0.03238636 #&gt; sample estimates: #&gt; mean difference #&gt; 0.009115498 #&gt; #&gt; #&gt; [[2]] #&gt; #&gt; Paired t-test #&gt; #&gt; data: HKCancer_mort_inc_year_m$`1990-1999` and HKCancer_mort_inc_year_m$`2010-2019` #&gt; t = 2.1861, df = 33, p-value = 0.036 #&gt; alternative hypothesis: true mean difference is not equal to 0 #&gt; 95 percent confidence interval: #&gt; 0.002055217 0.057209924 #&gt; sample estimates: #&gt; mean difference #&gt; 0.02963257 #&gt; #&gt; #&gt; [[3]] #&gt; #&gt; Paired t-test #&gt; #&gt; data: HKCancer_mort_inc_year_m$`2000-2009` and HKCancer_mort_inc_year_m$`2010-2019` #&gt; t = 1.5413, df = 35, p-value = 0.1322 #&gt; alternative hypothesis: true mean difference is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.005438019 0.039734021 #&gt; sample estimates: #&gt; mean difference #&gt; 0.017148 7.5.6 3e. Childhood versus elderly cancers Although it is clear that the incidence of cancer is typically higher in the elderly, some cancers affect children as well. What cancer types disproportionate affect children? For each cancer type, compare the proportion of 0-19 versus 65+ incidence against the 0-19 versus 65+ incidence for all other cancer types. # Examine the proportion of childhood HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_inc_age_sum &lt;- aggregate(HKCancer_inc[,-(1:4)],list(HKCancer_inc$Age),FUN=sum) HKCancer_inc_age_sum$Total&lt;- rowSums(HKCancer_inc_age_sum[,-1]) HKCancer_inc_age_sum_csq &lt;- data.frame(cancer=names(HKCancer_inc_age_sum[,2:ncol(HKCancer_inc_age_sum)])) pval &lt;- list() ratio &lt;- list() for (i in 2:(ncol(HKCancer_inc_age_sum))){ val = Map(&#39;-&#39;,HKCancer_inc_age_sum$Total,HKCancer_inc_age_sum[,i]) dat &lt;- data.frame(cancer=HKCancer_inc_age_sum[c(1,4),i], other =c(val[[1]],val[[2]])) pval &lt;- append(pval,fisher.test(dat)$p.val) ratio&lt;- append(ratio,log(as.double(dat[1,1]+0.1)/as.double(dat[2,1]+0.1))) } HKCancer_inc_age_sum_csq$pval &lt;- pval HKCancer_inc_age_sum_csq$ratio &lt;- ratio plot_child&lt;-ggplot(HKCancer_inc_age_sum_csq[-37,],aes(x=reorder(cancer,-as.numeric(ratio)),y=as.numeric(ratio)),fill=cancer)+ geom_bar(stat=&quot;identity&quot;,fill=&quot;red&quot;)+ geom_hline(yintercept=-4.12132318942113, linetype=&quot;dashed&quot;, color = &quot;black&quot;, linewidth=0.5)+ theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ #theme(text = element_text(size = 10))+ theme(axis.title.x=element_blank())+ theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) + ylab(&quot;log((child+0.1)/(elderly+0.1)&quot;) plot_child HKCancer_inc_age_sum_csq #&gt; cancer pval ratio #&gt; 1 Biliary 1.21618e-216 -11.17481 #&gt; 2 Bladder 9.601084e-314 -6.711128 #&gt; 3 Brain 0 -0.615666 #&gt; 4 Breast 0 -7.519824 #&gt; 5 Cervix 1.635299e-126 -6.925188 #&gt; 6 Colorectum 0 -7.531208 #&gt; 7 Eye 2.085337e-112 0.5039276 #&gt; 8 Hodgkin.lymphoma 3.658856e-81 -0.6227962 #&gt; 9 Kaposi 0.41662 -5.525453 #&gt; 10 Kidney 1.560619e-71 -3.882371 #&gt; 11 Larynx 1.963055e-113 -8.129416 #&gt; 12 Leukaemia 0 -1.043172 #&gt; 13 Liver 0 -4.909033 #&gt; 14 Lung 0 -8.191896 #&gt; 15 Melanoma 6.246412e-15 -4.324192 #&gt; 16 Mesothelioma 5.396388e-09 -7.897668 #&gt; 17 Multiple.myeloma 6.126613e-106 -7.062026 #&gt; 18 Nasal 0.0001285609 -3.286427 #&gt; 19 Nasopharynx 4.628193e-74 -3.95948 #&gt; 20 Non.Hodgkin.lymphoma 4.513518e-11 -2.940272 #&gt; 21 Non.melanoma.skin 0 -6.315107 #&gt; 22 Oesophagus 1.377432e-251 -8.943186 #&gt; 23 Oral 5.100139e-108 -4.379029 #&gt; 24 Ovary 0.0002847234 -2.34054 #&gt; 25 Pancreas 3.11451e-246 -6.690686 #&gt; 26 Penis 3.023792e-18 -5.753479 #&gt; 27 Placenta 0.07013259 2.397895 #&gt; 28 Prostate 0 -10.08778 #&gt; 29 Sarcoma 9.774701e-213 -1.028899 #&gt; 30 Small.intestine 1.479593e-31 -5.916202 #&gt; 31 Stomach 0 -7.137096 #&gt; 32 Testis 1.871184e-97 -0.09472556 #&gt; 33 Thymus 6.748934e-06 -1.915502 #&gt; 34 Thyroid 7.821825e-09 -2.194891 #&gt; 35 Uterus 1.457974e-105 -6.262217 #&gt; 36 Vulva 1.521831e-27 -5.552298 #&gt; 37 Total 1 -4.121323 7.6 4. Existing cancer funding and publication data The Hong Kong government established in Health and Medical Research Fund (HMRF) in 2011 to specifically provide research funding for health and medical research in Hong Kong. Since 2016 over 370 projects in the category of Cancer has been funded for a total of ~$400 M dollars. A list of all funded projects can be found on the Health Bureau webpage. You would like to use this data to see if there is any association between previous project funding and the epidemiology of cancers in Hong Kong. We can also do a similar thing with publications and ask if the research publications in Hong Kong have been aligned with the incidence and mortality. We can obtain this data from PubMed using the following terms: (“Hong Kong”[Affiliation]) AND (neoplasms[MeSH Terms]) The data has been predownloaded as the Pubmed API via R is a bit slow. Discussion points: Why has research publications increased dramatically in recent years? Is there something unsual with the dataset? What are the main cancer types being researched in Hong Kong? Is there any correlation between funding and cancer incidence and mortality? 7.6.1 Download HMRF grants and Pubmed data HMRF&lt;- read.delim(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HMRF_cancer_grants.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = TRUE) #HMRF pubmed&lt;- read.delim(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/pubmed__neoplasm_hongkong.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = TRUE) #pubmed hist(pubmed$Publication.Year) 7.6.2 Make compare grant funding with incidence and mortality if (!require(&quot;ggrepel&quot;)) install.packages(&quot;ggrepel&quot;) if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) library(ggrepel) library(ggplot2) library(gridExtra) grantpmsum&lt;- read.delim(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/Grants_pubmed_summary.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = TRUE) grantpmsum #&gt; Cancer Grants Pubmed #&gt; 1 Biliary 0 72 #&gt; 2 Bladder 0 141 #&gt; 3 Brain 2 294 #&gt; 4 Breast 34 1147 #&gt; 5 Cervix 9 408 #&gt; 6 Colorectum 40 857 #&gt; 7 Eye 2 27 #&gt; 8 Hodgkin lymphoma 0 21 #&gt; 9 Kaposi 0 6 #&gt; 10 Kidney 0 133 #&gt; 11 Larynx 0 8 #&gt; 12 Leukaemia 18 515 #&gt; 13 Liver 97 2077 #&gt; 14 Lung 22 773 #&gt; 15 Melanoma 0 99 #&gt; 16 Mesothelioma 6 58 #&gt; 17 Multiple myeloma 0 104 #&gt; 18 Nasal 0 14 #&gt; 19 Nasopharynx 24 1113 #&gt; 20 Non-Hodgkin lymphoma 0 55 #&gt; 21 Skin 0 32 #&gt; 22 Oesophagus 7 404 #&gt; 23 Oral 5 229 #&gt; 24 Ovary 14 354 #&gt; 25 Pancreas 2 141 #&gt; 26 Penis 0 7 #&gt; 27 Placenta 0 9 #&gt; 28 Prostate 6 322 #&gt; 29 Sarcoma 2 216 #&gt; 30 Small intestine 0 11 #&gt; 31 Stomach 5 455 #&gt; 32 Testis 0 18 #&gt; 33 Thymus 0 3 #&gt; 34 Thyroid 2 231 #&gt; 35 Uterus 0 72 #&gt; 36 Vulva 0 8 HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_inc_sum &lt;- data.frame(incidence=colSums(HKCancer_inc[,-(1:4)])) HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] HKCancer_mort_sum &lt;- data.frame(mortality=colSums(HKCancer_inc[,-(1:4)])) HKCancer_compare &lt;-data.frame(cancer=grantpmsum$Cancer, grants=grantpmsum$Grants, pubmed=grantpmsum$Pubmed, incidence=colSums(HKCancer_inc[,-(1:4)]), mortality=colSums(HKCancer_mort[,-(1:4)])) gp&lt;-ggplot(HKCancer_compare, aes(y=grants, x=pubmed)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 45, box.padding = 0.4) + stat_cor(method = &quot;pearson&quot;, label.x = 3, label.y = 90) pinc&lt;-ggplot(HKCancer_compare, aes(y=pubmed, x=incidence)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 15, box.padding = 0.5)+ stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) pmor&lt;-ggplot(HKCancer_compare, aes(y=pubmed, x=mortality)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 15, box.padding = 0.5) + stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) ginc&lt;-ggplot(HKCancer_compare, aes(y=grants, x=incidence)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 40, box.padding = 0.4) + stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) gmor&lt;-ggplot(HKCancer_compare, aes(y=grants, x=mortality)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 40, box.padding = 0.4) + stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) grid.arrange(gp,ginc,gmor,pinc, pmor, ncol=3) 7.7 5. Open disucssion As a group discuss what cancer type would be most worthy of funding in Hong Kong. Statistics and figures should be used to support your decision. If possible also discuss other data/analyses that can be performed and/or other diseases that are also in need of funding in Hong Kong. "],["pop-genetics.html", "Chapter 8 Population Genetics and Diseases 8.1 Case study 1: Heritability and human traits", " Chapter 8 Population Genetics and Diseases 8.1 Case study 1: Heritability and human traits 8.1.1 Part 1 Scenario: You are a researcher working on a twin study on cardiovascular traits to assess the genetic and environmental contribution relevant to metabolism and cardiovascular disease risk. You have recruited a cohort of volunteer adult twins of the same ancestry. The volunteers have undergone a series of baseline clinical evaluations and performed genotyping on a panel of single nucleotide polymorphisms that may be associated with the traits.! 8.1.1.1 Questions for Discussion Q1. Besides the clinical measurements, what data do you need to collect from the subjects? Answers: Sex Age Other confounding factors, e.g. BMI, blood pressure, smoking status, etc. Q2. How is genotype data represented for statistical genetic analysis? Answers: Allele: 0/1, 1/2, A/C, etc Genotype: 0 0, 0 1, 1 0, 1 1 Genotype probabilities: P(0/0)=0, P(0/1)=1, P(1/1)=0 Genotype dosage: 0/1/2, 0.678 (continuous from 0-1 or 0-2) Q3. How can you test for association between genotypes and phenotypes (binary and quantitative)? Answers: Allelic chi-square test Fisher’s exact test Linear/Logistic regression Linear mixed model 8.1.1.2 Hands-on exercise : Association test Now, you are given a dataset of the twin cohort with a cardiovascular phenotype and 5 quantitative trait loci (QTL). Data set and template notebook are available on Moodle (recommended) and also on this GitHub Repo. The information for columns: zygosity: 1 for monozygotic (MZ) and 2 for dizygotic (DZ) twin T1QTL_A[1-5] and T2QTL_A[1-5]: 5 quantitative loci (A1-A5) in additive coding for Twin 1 (T1) and Twin 2 (T2) respectively The same 5 QTL (D1-D5) in dominance coding for T1 and T2 Phenotype scores of T1 and T2 Download the data dataTwin.dat to your working directory. Start the RStudio program and set the working directory. dataTwin &lt;- read.table(&quot;dataTwin.dat&quot;,h=T) Exploratory analysis A1-5: The QTLs are biallelic with two alleles A and a. The genotypes aa, Aa, and AA are coded additively as 0 (aa), 1 (Aa) and 2 (AA). D1-5: The genotypes aa, Aa, and AA are coded as 0 (aa), 1 (Aa) and 0 (AA). Q1. How many MZ and DZ volunteers are there? Q2. How are the genotypes represented? Q3. Are the QTL independent of each other? Q4. Are there outliers in phenotypes? ?table # Write your codes here # Any outlier &gt;4SD? Q5. Compute the genotype frequencies for each variant. Compute the allele frequencies. # Write your codes here Test for association between variants and phenotype for T1 * Regress “phenoT1” on T1QTL_A1 to estimate the proportion of variance explained (R2). * Model: phenoT1 = b0 + b1* T1QTL_A1 + e * Calculate the conditonal mean of phenotype (i.e. phenotypic mean conditional genotype) If the relationship between the QTL and the phenotype is perfectly linear, the regression line should pass through the conditional means (c_means), and the differences between the conditional means should be about equal. Q6. What are the values of b0, b1? Is QTL1 significant associated with the phenotype at alpha&lt;0.01 (multiple testing of 5 loci)? Q7. What is the proportion of phenotypic variance explained? ?lm ?glm # Write your codes here # compute the conditional mean (c_means) # visualize the fitting To test this “linearity”, we can use the dominant coding of the QTL and add the dominance term to the regression model. * Model: phenoT1 = b0 + b1* T1QTL_A1 + b2* T1QTL_D1 + e * Repeat for the other 4 QTL and determine which QTL shows strongest association with the phenotype * Repeat for T2. Q8. Why can’t we analyse T1 and T2 together? Q9. Is there a dominance effect? # Write your codes here # visualize the fitting If the subjects with top 5% of the phenotype score are considered as cases, perform case-control association test for most significant SNP (from Q3) and interpret the result. Q10. What are the odds ratio, p-value, and 95% confidence interval? ?quantile ?seq # odds ratio # p-value # 95% confidence interval? 8.1.2 Part 2 Scenario: You are asked to estimate the additive and dominance genetic variance explained using regression-based method and a classical twin design. Given standardization of phenotype and the ADE model, we assume that the phenotypic variance equals \\(\\sigma^{2}_{P}\\) = \\(\\sigma^{2}_{A}\\) + \\(\\sigma^{2}_{D}\\) + \\(\\sigma^{2}_{E}\\), where \\(\\sigma^{2}_{P}\\) is the phenotypic variance, \\(\\sigma^{2}_{A}\\) is additive genetic variance, \\(\\sigma^{2}_{D}\\) is dominance genetic variance, and \\(\\sigma^{2}_{E}\\) is unshared environmental variance. cov(MZ) = cor(MZ) = rMZ= \\(\\sigma^{2}_{A}\\) + \\(\\sigma^{2}_{D}\\) cov(DZ) = cor(DZ) = rDZ = 0.5 * \\(\\sigma^{2}_{A}\\) + 0.25 * \\(\\sigma^{2}_{D}\\), where the coefficients 1/2 and 1/4 are based on quantitative genetic theory (Mather &amp; Jinks, 1971). By solving the unknowns, the Falconer’s equations for the ADE model: \\(\\sigma^{2}_{A}\\) = 4*rDZ - rMZ \\(\\sigma^{2}_{D}\\) = 2rMZ - 4rDZ \\(\\sigma^{2}_{E}\\) = 1 - \\(\\sigma^{2}_{A}\\) - \\(\\sigma^{2}_{D}\\) 8.1.2.1 Questions for discussions : Q1. What is missing heritability of common traits in the era of genome-wide association analysis (GWAS)? Q2. What are the potential sources of missing heritability? Suggested reading: Manolio TA, Collins FS, Cox NJ, et al. Finding the missing heritability of complex diseases. Nature. 2009 ;461(7265):747-753. doi:10.1038/nature08494 8.1.2.2 Hands-on exercise : variance explained Q1. What is the variance of the phenotype? Q2. Compute the explained variance attributable to the additive genetic component of the QTL with strongest association in Part 1. Q3. Compute the explained variance attributable to the dominance genetic component of the QTL with strongest association in Part 1. R2 from the regression represents the proportion of phenotypic variance explained; thus the raw explained variance component is R2 times the variance of the phenotype (var_pheno). Example for T1 on QTL1 The proportion of explained variance are 0.02732 (additive) and 0.03658 (total: additive + dominance). As the predictors are uncorrelated, the proportion of explained variance by dominance = 0.03658 - 0.02732 = 0.00926 Given the phenotypic variance of 15.102, then Total genetic: 0.03658*15.102 = 0.552 Additive genetic: 0.02732*15.102 = 0.412 Dominance genetic: 0.00926*15.102 = 0.140 var_pheno &lt;- var(dataTwin$phenoT1) # the variance of the phenotype var_pheno summary(linAD1)$r.squared # proportion of explained variance by total genetic component summary(linA1)$r.squared # proportion of explained variance by additive component summary(linAD1)$r.squared*var_pheno # (raw) variance component of total genetic component summary(linA1)$r.squared*var_pheno # (raw) variance component of additive genetic component (summary(linAD1)$r.squared-summary(linA1)$r.squared)*var_pheno # (raw) variance component of dominance genetic component Q4. Estimate the variance explained by all the QTL using linear regression. Based on our regression results, we have estimates of the total genetic variance as well as the A and D components. In practice, this is impossible as we do not know all the variants associated with any polygenic trait. Now, let’s estimate the A (additive genetic) and D (dominance) variance with the classical twin design using Falconer’s equations based on ADE model. Q5. Compute rMZ and rDZ. Q6. Estimate the additive and dominance genetic variances using the Falconer’s equations for the ADE model. "],["install.html", "Appendix A: Install R &amp; RStudio A.1 Install R A.2 Install RStudio A.3 Use R inside RStudio A4. Cloud computing", " Appendix A: Install R &amp; RStudio This manual covers the installation of both R and RStudio for three different operating systems: Windows, macOS and Ubuntu. You only need to follow the one that you are using on your computer. Differences between R and RStudio R is the backbone of R programming. Once R is installed, you can use it via its built-in R Console (self-contained), terminal or any third-party integrated development environment (IDE), e.g., RStudio. RStudio is a multi-faceted and user-friendly IDE that can make R programming and data analysis in one place and easy to manage. We recommend using RStudio and only demonstrate with it, while you are free to use any other alternative. Acknowledgements This manual is adapted and updated from the materials produced by Xiunan Fang and other team members in Dr Joshua Ho’s lab. A.1 Install R R on Windows Open an internet browser and go to https://cran.r-project.org/. Click on the Download R for Windows link at the top of the page. Choose the base and then Click on the Download R 4.3.1 for Windows link at the top of the page (or a new version if this manual is outdated). Once the download is finished, you will obtain a file named R-4.3.1-win.exe or similar depending on the version that you download. Most of the time, you will likely want to go with the defaults, so click the button Next until the process is complete. R on macOS Open an internet browser and go to https://cran.r-project.org/. Click on the Download R for macOS link at the top of the page. Click on the file containing the latest version of R under the Latest release. Save the R-4.3.1-**.pkg file, double-click it to open, and follow the installation instructions. Note, there are two versions of the .pkg installation file according to the CPU model: Intel Macs (Intel-based) or M1/M2 Macs (ARM-based). Please choose accordingly. R on Linux (Ubuntu) As commonly used in Ubuntu, prior to installing R, let us update the system package index and upgrade all our installed packages using the following two commands: sudo apt update sudo apt -y upgrade After that, all that you have to do is run the following in the command line to install base R. sudo apt -y install r-base A.2 Install RStudio Now that R is installed, you need to download and install RStudio. The installation of RStudio is more straightforward and very similar across the three Operating Systems. Go to https://posit.co/download/rstudio-desktop/#download. We are using `RStudio Desktop Free version. Click on the right file for your OS (e.g., .exe file for Windows or .dmg for MacOS) The installation process is very straightforward as the figure below. A.3 Use R inside RStudio R studio RStudio is a very powerful IDE and provides many useful tools through a four-pane workspace. By default, the four panels are placed as follows (you can also change the setting for your own preference): Top-left panel: Your scripts of the R codes, script is good to keep a record of your work and also convenient for command execution. You can create a new script by File –&gt; New –&gt; R Script Bottom-left panel: R console for R commands, where you actually run the R codes. Top-right panel: Workspace tab: All the data(more specifically, R objects) you have created in the Workspace and all previous commands you previously ran in the History. Bottom-right panel: Files in your working directory(you probably should also set your working directory) in Files, and the plots you have created in Plots. Set working directory Create a folder named “biof_Rdir” in your preferred directory Create a “data” folder in the “biof_Rdir” From RStudio, use the menu to change your working directory under Session &gt; Set Working Directory &gt; Choose Directory Choose the directory to “biof_Rdir” Or you can type in the console: setwd(&quot;/yourdirectory/biof_Rdir&quot;) For Windows, the command might look like : setwd(&quot;c:/yourdirectory/biof_Rdir&quot;) Some general knowledge R is case-sensitive Type enter to run R code in the console pane Ctrl-enter or Cmd-return if the code is in the scripts pane. Comments come after # will not be treated as codes R has some pre-loaded data sets, to see the list of pre-loaded data, type data() In R, a function is an object, a basic syntax of an R function looks like something below: function_name &lt;- function(arg_1, arg_2, ...) { actual function codes } For example: my_average &lt;- function(x){ sum(x)/length(x) } my_average(c(1, 4, 5, 7)) #&gt; [1] 4.25 R contains a lot of built-in functions, you can use ? or help() to see the documentation of a function, there are also a lot of external libraries with specific functions. To use a library, we do: install.packages(&#39;package_name&#39;) library(package_name) Install packages There are several packages used in this workshop, in the R console, type: install.packages(&#39;ggplot2&#39;) install.packages(&#39;pheatmap&#39;) install.packages(&#39;aod&#39;) A4. Cloud computing In case you have limited computing power, you can still use cloud computing to finish this course. There can be multiple options and here we mainly recommend RStudio cloud (https://posit.cloud; previously known as https://rstudio.cloud/). You can explore directly from their website. "],["references.html", "References", " References "]]
+[["index.html", "Biomedical Data Science - introduction with case studies Welcome", " Biomedical Data Science - introduction with case studies BIOF1001 teaching team 2024-08-29 Welcome Welcome to the book Biomedical Data Science - an introduction with case studies. Most contents are demonstrated with R programming language. This book is designed as a collection of R Markdown notebooks, as supplementary to the lecture notes for the course BIOF1001: Introduction to Biomedical Data Science, an undergraduate course (Year 1) at the University of Hong Kong. Note: Most contents may be only updated before or right after the lectures, so please refer to the updated version. GitHub Repository: you can find the source files on StatBiomed/BMDS-book and the way to re-build this book. "],["preface.html", "Preface Introduction for readers Other reference books Acknowledgements", " Preface This book is designed as the lecture notes and textbook for BIOF1001: Introduction to Biomedical Data Science, an undergraduate course (Year 1) at the University of Hong Kong. This book is not aimed to be a comprehensive textbook, but rather more Rmarkdown notebooks as supplementary to lecture notes so that students can reproduce the teaching contents more easily. Introduction for readers What you will learn from this course/book In part I, you will find a general introduction to data science (by Dr YH Huang): Basic programming and visualisation skills: R scripts for the quantitative methods and data visualisation. Quantitative methods: t-test, correlation analysis, clustering, linear regression, linear classification. Gain familiarity with common databases in the biomedical domain. Introduce ethical, legal, social and technological issues related to biomedical data sciences. Introduce good practice in managing a data science project and communicate results to key stakeholders. In part II, you will experience data types in four different biomedical topics, which will be illustrated with both introduction and cases that are suitable for problem-based learning format: Medical imaging and digital health, by Dr Joshua Ho and Dr Rachel Kwan Cancer genomics and epidemiology, by Dr David Shih and Dr Jason Wong Population genetics and diseases, by Dr Clara Tang and Dr Yuanhua Huang What we recommend you do while reading this book To enhance the knowledge and skills learned from this book, we recommend that readers Read the materials/slides provided in each module Practice quantitative skills by solving problems using R Other reference books Besides this online book as a collection of R materials for the teaching contents, we also recommend the following online books as reference: Introduction to Data Science: Data Wrangling and Visualization with R by Rafeal A. Irizarry Advanced Data Science: Statistics and Prediction Algorithms Through Case Studies by Rafeal A. Irizarry Acknowledgements We thank all teachers and student helpers contributing to this course across all years, including 2022: Dr Lequan Yu and Dr Carlos Wong 2022 &amp; 2023: Dr Asif Javed, Dr Tommy Lam, and Dr Kathy Leung Student helpers: Mr Mingze Gao, Ms Fangxin Cai, and Mr Hoi Man Chung. "],["introR.html", "Chapter 1 Introduction to R programming 1.1 Data types 1.2 Data structures 1.3 Read and write files (tables) 1.4 Functions and Packages 1.5 Flow Control 1.6 Plotting 1.7 Scientific computating 1.8 Exercises", " Chapter 1 Introduction to R programming This notebook collects the scripts used for teaching in BIOF1001 for Introduction to R (1 hour teaching). You can get this Rmd file on Moodle or here (right-click and “save link as” to download). R is a programming language, particularly popular for its power in statistical computing, elegant graphics, and also genomic data analysis. It is a free and open-source software, with active support and development from the community. Additionally, R is relatively easy to get started for scientific computing. Note To learn and practice R programming, you need to install R and RStudio on your computer. You can follow the instructions for installation in the Appendix A chapter. 1.1 Data types In R language setting (similar to some other programming languages), there are a few commonly used data types that are predefined in the built-in environment. You can use the class() and typeof() functions to check the class and data type of any variable. In total, R has five data types: Numeric Integers Complex Logical Characters 1.1.1 nemeric (or double) The numeric is for numeric values, as the most common and the default data type. The numeric datatype saves values in double precision (double number of bytes in memory), so the type is also double. x &lt;- c(1.0, 2.0, 5.0, 7.0) x #&gt; [1] 1 2 5 7 class(x) #&gt; [1] &quot;numeric&quot; typeof(x) #&gt; [1] &quot;double&quot; 1.1.2 integer The integer is another data type used for the set of all integers. You can use the capital ‘L’ notation as a suffix to specify a particular value as the integer data type. Also, you can convert a value into an integer type using the as.integer() function. y &lt;- c(1L, 2L, 5L, 7L) y #&gt; [1] 1 2 5 7 class(y) #&gt; [1] &quot;integer&quot; typeof(y) #&gt; [1] &quot;integer&quot; # Assign a integer value to y y = 5 # is y an integer? print(is.integer(y)) #&gt; [1] FALSE 1.1.3 logical In R, the logical data type takes either a value of true or false. A logical value is often generated when comparing variables. z &lt;- c(TRUE, TRUE, TRUE, FALSE) z #&gt; [1] TRUE TRUE TRUE FALSE typeof(z) #&gt; [1] &quot;logical&quot; 1.1.4 character In R, the character is a data type where you have all the alphabets and special characters. It stores character values or strings. Strings in R can contain alphabets, numbers, and symbols. The character type is usually denoted by wrapping the value inside single or double inverted commas. w &lt;- c(&quot;aa&quot;, &quot;bb&quot;, &quot;5&quot;, &quot;7&quot;) w #&gt; [1] &quot;aa&quot; &quot;bb&quot; &quot;5&quot; &quot;7&quot; typeof(w) #&gt; [1] &quot;character&quot; 1.1.5 Memeory usage Each data type is explicitly defined, especially the size of the memory. When initializing a certain data type, there are a few small bytes used to store basic information. Let’s look at the empty values. object.size(numeric()) #&gt; 48 bytes object.size(integer()) #&gt; 48 bytes object.size(logical()) #&gt; 48 bytes object.size(character()) #&gt; 48 bytes To illustrate, let’s use 1000 elements below to show the memory size usage for each data type. As we will see, integer and logical use 4 bytes per element, which is only half of the memory usage by double (numeric) and character of 8 bytes. object.size(rep(1, 1000)) #&gt; 8048 bytes object.size(rep(1L, 1000)) #&gt; 4048 bytes object.size(rep(TRUE, 1000)) #&gt; 4048 bytes object.size(rep(&quot;aa&quot;, 1000)) #&gt; 8104 bytes 1.2 Data structures Data structure is one of the most important features in programming. It involves how the data is organised and can be accessed and modified. Using an appropriate data structure may largely improve computing efficiency. 1.2.1 Vector Vector is a basic data structure in R. It contains elements in the same data type (no matter double, integer, character or others). You can check the data type by using typeof() function and the length of the vector by length() function. Since a vector has elements of the same type, this function will try and coerce elements to the same type, if they are different. Coercion is from lower to higher types, i.e., from logical to integer to double to a character. See more introduction here. x &lt;- c(1, 2, 5, 7) x #&gt; [1] 1 2 5 7 typeof(x) #&gt; [1] &quot;double&quot; x &lt;- rep(3, 5) x #&gt; [1] 3 3 3 3 3 typeof(x) #&gt; [1] &quot;double&quot; x &lt;- 1:12 # integer x #&gt; [1] 1 2 3 4 5 6 7 8 9 10 11 12 typeof(x) #&gt; [1] &quot;integer&quot; 1.2.2 Matrix Matrix is a two-dimensional data structure. It is in principle built based on vector but has more convenient built-in functions for computation. It has rows and columns, both of which can also have names. To check the dimensions, you can use the dim() function. See more introduction here. A &lt;- matrix(1:12, nrow=3) A #&gt; [,1] [,2] [,3] [,4] #&gt; [1,] 1 4 7 10 #&gt; [2,] 2 5 8 11 #&gt; [3,] 3 6 9 12 B &lt;- matrix(1:12, nrow=3, byrow=TRUE) B #&gt; [,1] [,2] [,3] [,4] #&gt; [1,] 1 2 3 4 #&gt; [2,] 5 6 7 8 #&gt; [3,] 9 10 11 12 colnames(A) &lt;- c(&quot;C1&quot;,&quot;C2&quot;,&quot;C3&quot;,&quot;C4&quot;) rownames(A) &lt;- c(&quot;R1&quot;,&quot;R2&quot;,&quot;R3&quot;) A #&gt; C1 C2 C3 C4 #&gt; R1 1 4 7 10 #&gt; R2 2 5 8 11 #&gt; R3 3 6 9 12 1.2.2.1 Index Vector and Matrix To index vector, you can use logical or integer, or the element name if it has. Note, when using an integer for indexing, the index starts from 1 in R, unlike most programming languages where the index starts from 0. We can also use negative integers to return all elements except those specified. But we cannot mix positive and negative integers while indexing and real numbers if used are truncated to integers. N.B., when using logical as the index, be careful if the index length is different from the vector. x &lt;- 1:12 x[3] #&gt; [1] 3 x[2:5] #&gt; [1] 2 3 4 5 x[c(2, 5, 6)] # index with integer #&gt; [1] 2 5 6 x[c(TRUE, FALSE, FALSE, TRUE)] # index with logical value #&gt; [1] 1 4 5 8 9 12 Now, let’s index a matrix. It is very similar to vector, but it has both rows and columns. A &lt;- matrix(1:12, nrow=3) colnames(A) &lt;- c(&quot;C1&quot;,&quot;C2&quot;,&quot;C3&quot;,&quot;C4&quot;) rownames(A) &lt;- c(&quot;R1&quot;,&quot;R2&quot;,&quot;R3&quot;) A #&gt; C1 C2 C3 C4 #&gt; R1 1 4 7 10 #&gt; R2 2 5 8 11 #&gt; R3 3 6 9 12 A[1, 2] #&gt; [1] 4 A[1, &quot;C2&quot;] #&gt; [1] 4 A[1, c(2, 3)] #&gt; C2 C3 #&gt; 4 7 A[1:2, c(2, 3)] #&gt; C2 C3 #&gt; R1 4 7 #&gt; R2 5 8 Single row or column matrix will become a vector, unless using drop=FALSE A[1, 2:4] #&gt; C2 C3 C4 #&gt; 4 7 10 dim(A[1, 2:4]) #&gt; NULL A[1, 2:4, drop=FALSE] #&gt; C2 C3 C4 #&gt; R1 4 7 10 dim(A[1, 2:4, drop=FALSE]) #&gt; [1] 1 3 1.2.2.2 Modify values A[1, 2:4] &lt;- c(-3, -5, 20) A #&gt; C1 C2 C3 C4 #&gt; R1 1 -3 -5 20 #&gt; R2 2 5 8 11 #&gt; R3 3 6 9 12 1.2.3 List Different from vector that has all elements in the same data type, the list data structure can have components of mixed data types. More broadly, a list can contain a list of any data structure: value, vector, matrix, etc. We can use str() function to view the structure of a list (or any object). x &lt;- list(2.5, TRUE, 1:3) x #&gt; [[1]] #&gt; [1] 2.5 #&gt; #&gt; [[2]] #&gt; [1] TRUE #&gt; #&gt; [[3]] #&gt; [1] 1 2 3 str(x) #&gt; List of 3 #&gt; $ : num 2.5 #&gt; $ : logi TRUE #&gt; $ : int [1:3] 1 2 3 We can also have a name for each element: x &lt;- list(&quot;a&quot; = 2.5, &quot;b&quot; = TRUE, &quot;c&quot; = 1:3) x #&gt; $a #&gt; [1] 2.5 #&gt; #&gt; $b #&gt; [1] TRUE #&gt; #&gt; $c #&gt; [1] 1 2 3 str(x) #&gt; List of 3 #&gt; $ a: num 2.5 #&gt; $ b: logi TRUE #&gt; $ c: int [1:3] 1 2 3 1.2.3.1 Indexing list Different from vector and matrix, for a list, you need to use double-layer square brackets, either by numeric index or name. Alternatively, you can also use $ symbol with the name. x[[3]] #&gt; [1] 1 2 3 x[[&quot;c&quot;]] #&gt; [1] 1 2 3 x$c #&gt; [1] 1 2 3 1.2.4 Data Frame Data frame is widely used for rectangular data, where each column has the same data type (vector) but different columns can have different data types (like Excel) As you guess, the data frame is a special type of list: A list of vectors with the same length. df &lt;- data.frame(&quot;SN&quot; = 1:2, &quot;Age&quot; = c(21,15), &quot;Name&quot; = c(&quot;John&quot;,&quot;Dora&quot;)) df #&gt; SN Age Name #&gt; 1 1 21 John #&gt; 2 2 15 Dora df$Age[2] #&gt; [1] 15 # View(df) 1.2.5 Factor vs vector For vector, if it only contains pre-defined values (which can have specified orders), you may consider using factor. Factor is a data structure used for fields that takes only predefined, finite number of values (categorical data) The order of predefined values can be specified, instead of alphabetic by default x = c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;) # vector x #&gt; [1] &quot;single&quot; &quot;married&quot; &quot;married&quot; &quot;single&quot; class(x) #&gt; [1] &quot;character&quot; typeof(x) #&gt; [1] &quot;character&quot; y = factor(c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;)) y #&gt; [1] single married married single #&gt; Levels: married single class(y) #&gt; [1] &quot;factor&quot; typeof(y) #&gt; [1] &quot;integer&quot; 1.2.5.1 Change the order of factor levels z &lt;- factor(c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;) , levels=c(&quot;single&quot;, &quot;married&quot;)) z #&gt; [1] single married married single #&gt; Levels: single married 1.2.5.2 Smaller memory as categorical data type x = c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;) # vector y = factor(c(&quot;single&quot;, &quot;married&quot;, &quot;married&quot;, &quot;single&quot;)) object.size(rep(x, 1000)) #&gt; 32160 bytes object.size(rep(y, 1000)) #&gt; 16560 bytes 1.3 Read and write files (tables) Besides operating in the R environment, we also want to read data from files or write results into files. For tables, R has convenient built-in function read.table() and write.table(). 1.3.1 Read file We can use read.table() function to read tables, e.g., in comma separated values (csv) or tab separated values (tsv) formats. See full manuals: help(read.table) or ?read.table or its online manual help(&quot;read.table&quot;) ?read.table Here, let’s read an example file. Data is available on Moodle and on the github repository df = read.table(&quot;./SRP029880.colData.tsv&quot;, sep=&quot;\\t&quot;) df #&gt; source_name group #&gt; CASE_1 metastasized cancer CASE #&gt; CASE_2 metastasized cancer CASE #&gt; CASE_3 metastasized cancer CASE #&gt; CASE_4 metastasized cancer CASE #&gt; CASE_5 metastasized cancer CASE #&gt; CTRL_1 normal colon CTRL #&gt; CTRL_2 normal colon CTRL #&gt; CTRL_3 normal colon CTRL #&gt; CTRL_4 normal colon CTRL #&gt; CTRL_5 normal colon CTRL 1.3.2 Write file The above file is loaded as a data frame. Here, let’s add an extra column to indicate if the sample is frozen or not, then save it into a file. df$frozen &lt;- c(1, 1, 0, 0, 0, 1, 1, 0, 0, 0) write.table(df, &quot;./SRP029880.colData.add_frozen.tsv&quot;, sep=&quot;\\t&quot;, quote=FALSE) 1.4 Functions and Packages As experienced above, we have used function multiple times, e.g., read.table and typeof. As one more example mean() is a function here and it is from the base package x &lt;- 4:10 mean(x) #&gt; [1] 7 base::mean(x) #&gt; [1] 7 Generally speaking, A function is a set of statements organized together to perform a specific task. Many lines of codes are packed into one function &amp; it’s reusable. A function can be written in the same R file and loaded, or it can be distributed as part of a package. For using such functions, we need to install the corresponding package and load it. 1.4.1 Install packages It depends on where the package is stored. Please refers to the documentation of the specific package you want to install and use. CRAN (the Comprehensive R Archive Network): main platform For example: install.packages(\"ggplot2\") Bioconductor: primarily for biology related packages For example: BiocManager::install(\"DESeq2\") As an example, we can install the powerful plotting package ggplot2 from CRAN. #install.packages(&quot;ggplot2&quot;) 1.4.2 Apply function repeatly We may often want to use a certain function for multiple times, e.g., calculate the sample mean for many genes. There are multiple ways to achieve it, e.g., via a for loop. Here, we will introduce apply and its variants for this purpose. See more introductions here. 1.4.2.1 apply, lapply, sapply and vapply In short, the apply() function and its variants apply a certain function to each element of a vector, a matrix, or a list. 1.4.2.1.1 apply for matrix The apply(X, MARGIN, FUN) function works for matrix (or array) for rows or columns. For example, calculating the median of each column: my.matrx &lt;- matrix(1:15, nrow = 5, ncol = 3) my.matrx #&gt; [,1] [,2] [,3] #&gt; [1,] 1 6 11 #&gt; [2,] 2 7 12 #&gt; [3,] 3 8 13 #&gt; [4,] 4 9 14 #&gt; [5,] 5 10 15 apply(my.matrx, 2, median) #&gt; [1] 3 8 13 1.4.2.1.2 lapply, sapply, and vapply for list or vector The above apply function requires MARGIN, hence won’t work for vector or list. There are a few variants to support lists or vectors for different purposes. From the manual, we can find out the arguments for these three functions: lapply(X, FUN, …) sapply(X, FUN, …, simplify = TRUE, USE.NAMES = TRUE) vapply(X, FUN, FUN.VALUE, …, USE.NAMES = TRUE) Let’s look at examples. The lapply works for vector and list and returns a list: A&lt;-c(1:9) B&lt;-c(1:12) C&lt;-c(1:15) my.lst&lt;-list(A,B,C) lapply(my.lst, median) #&gt; [[1]] #&gt; [1] 5 #&gt; #&gt; [[2]] #&gt; [1] 6.5 #&gt; #&gt; [[3]] #&gt; [1] 8 If you want the return as a vector, you can use sapply() for simplified output: sapply(my.lst, median) #&gt; [1] 5.0 6.5 8.0 If you want to check the data type of the return, you can further use the vapply function. An error will be raised if the data type does not match. Note, the FUN.VALUE argument takes the value as a template, so the use of numeric(1) or any numeric value, e.g., 3 is the same. vapply(my.lst, median, numeric(1)) #&gt; [1] 5.0 6.5 8.0 vapply(my.lst, median, 3) #&gt; [1] 5.0 6.5 8.0 # try this # vapply(my.lst, median, character(1)) 1.4.3 Pattern match Matching patterns between two vectors is a very common task, for example matching the gene names of two files or matching students IDs in two courses. Two commonly used functions for pattern match are match() and %in%, see the match() documentation: match returns a vector of the positions of (first) matches of its first argument in its second. %in% is a more intuitive interface as a binary operator, which returns a logical vector indicating if there is a match or not for its left operand. They work for any data type: numeric and character 1:6 %in% c(1,3,5,9) #&gt; [1] TRUE FALSE TRUE FALSE TRUE FALSE match(c(3, 4, 5), c(5, 3, 1, 9)) #&gt; [1] 2 NA 1 idx = match(c(3, 4, 5), c(5, 3, 1, 9)) c(5, 3, 1, 9)[idx] #&gt; [1] 3 NA 5 1.5 Flow Control 1.5.1 Logical operator The common logical operators are shown in the following table. Operator Description Associativity ! Logical NOT Left to right &amp; Element-wise logical AND Left to right &amp;&amp; Logical AND Left to right | Element-wise logical OR Left to right || Logical OR Left to right A few notes: Zero is considered FALSE and non-zero numbers are taken as TRUE. Operators &amp; and | perform element-wise operation, returning length of the longer operand. For operators &amp;&amp; and ||, it depends on the R version. In R&lt;=4.2.3, it examines only the first element of the operands, returning a single value, while in R=4.3.1, &amp;&amp; and || only compare single values and will return errors if input vectors. x &lt;- c(TRUE, FALSE, 0, 6) y &lt;- c(FALSE, TRUE, FALSE, TRUE) !x #&gt; [1] FALSE TRUE TRUE FALSE x &amp; y #&gt; [1] FALSE FALSE FALSE TRUE x | y #&gt; [1] TRUE TRUE FALSE TRUE # try it yourself # x &amp;&amp; y # x || y 1.5.2 if-else statements The if-else statement allows us to control when and how particular parts of our code are executed. # In Q10 in Section 1.8 we have x_mean and x_sd x_mean = 1.7 x_sd = 2.9 if ( (x_mean &gt; 0.1) &amp;&amp; (x_sd &lt; 2.0) ) { trend = &quot;increase&quot; } else{ trend = &quot;not_increase&quot; } print(trend) #&gt; [1] &quot;not_increase&quot; x_mean = 1.7 x_st = 2.9 trend = &quot;not_increase&quot; if ( (x_mean &gt; 0.1) &amp;&amp; (x_sd &lt; 2.0) ) { trend = &quot;increase&quot; } print(trend) #&gt; [1] &quot;not_increase&quot; 1.5.3 for-loop Loops, including for loop and while loop are used in programming to repeat a specific block of code, commonly with if-else statements. For example, calculate the sum from 1 to 10: sum_val = 0 for (val in seq(1, 10)) { # print(val) sum_val = sum_val + val } print(sum_val) #&gt; [1] 55 Or detect the differential expressed genes. Note, NA value may exist in the padj column: is_DE = rep(FALSE, nrow(df_DEG)) for (i in 1:nrow(df_DEG)) { if (df_DEG$padj[i] &lt;= 0.05) { is_DE[i] = TRUE } } print(sum(is_DE)) 1.6 Plotting 1.6.1 datasets Let’s use a built-in dataset for illustration: iris (4 flower features in 3 plants) head(iris) #&gt; Sepal.Length Sepal.Width Petal.Length Petal.Width Species #&gt; 1 5.1 3.5 1.4 0.2 setosa #&gt; 2 4.9 3.0 1.4 0.2 setosa #&gt; 3 4.7 3.2 1.3 0.2 setosa #&gt; 4 4.6 3.1 1.5 0.2 setosa #&gt; 5 5.0 3.6 1.4 0.2 setosa #&gt; 6 5.4 3.9 1.7 0.4 setosa summary(iris) #&gt; Sepal.Length Sepal.Width Petal.Length Petal.Width #&gt; Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100 #&gt; 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300 #&gt; Median :5.800 Median :3.000 Median :4.350 Median :1.300 #&gt; Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199 #&gt; 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800 #&gt; Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500 #&gt; Species #&gt; setosa :50 #&gt; versicolor:50 #&gt; virginica :50 #&gt; #&gt; #&gt; There are two common ways of plotting: the built-in plotting functions the ggplot format 1.6.2 Basic plotting 1.6.2.1 Histogram hist(iris$Sepal.Length) 1.6.2.2 Scatter plot plot(x=iris$Sepal.Length, y=iris$Sepal.Width) 1.6.2.3 boxplot x1 &lt;- iris$Sepal.Length[iris$Species == &quot;setosa&quot;] x2 &lt;- iris$Sepal.Length[iris$Species == &quot;versicolor&quot;] x3 &lt;- iris$Sepal.Length[iris$Species == &quot;virginica&quot;] boxplot(x1, x2, x3) 1.6.3 ggplot2 See more instructions: http://www.sthda.com/english/wiki/ggplot2-essentials 1.6.3.1 Install and load package if (!requireNamespace(&quot;ggplot2&quot;, quietly = TRUE)) install.packages(&quot;ggplot2&quot;) library(ggplot2) 1.6.3.2 Histogram ggplot(iris, aes(x=Sepal.Length)) + geom_histogram(bins = 8) 1.6.3.3 Scatter plot ggplot(iris, aes(x=Sepal.Length, y=Sepal.Width)) + geom_point() 1.6.3.4 Box plot ggplot(iris, aes(x=Species, y=Sepal.Length)) + geom_boxplot() 1.7 Scientific computating 1.7.1 Orders of operators See lecture slides. If you are not sure about a certain ordering, use brackets! 5 * 2 &gt; 4 #&gt; [1] TRUE 5 * (2 &gt; 4) #&gt; [1] 0 1.7.2 Functions for statistics More theory and practice to come in next session 1.7.3 Correlation cor(iris$Sepal.Length, iris$Petal.Length) #&gt; [1] 0.8717538 cor.test(iris$Sepal.Length, iris$Petal.Length) #&gt; #&gt; Pearson&#39;s product-moment correlation #&gt; #&gt; data: iris$Sepal.Length and iris$Petal.Length #&gt; t = 21.646, df = 148, p-value &lt; 2.2e-16 #&gt; alternative hypothesis: true correlation is not equal to 0 #&gt; 95 percent confidence interval: #&gt; 0.8270363 0.9055080 #&gt; sample estimates: #&gt; cor #&gt; 0.8717538 1.7.4 Hypothesis testing (t test) x1 &lt;- iris$Sepal.Length[iris$Species == &quot;setosa&quot;] x2 &lt;- iris$Sepal.Length[iris$Species == &quot;versicolor&quot;] x3 &lt;- iris$Sepal.Length[iris$Species == &quot;virginica&quot;] t.test(x2, x3) #&gt; #&gt; Welch Two Sample t-test #&gt; #&gt; data: x2 and x3 #&gt; t = -5.6292, df = 94.025, p-value = 1.866e-07 #&gt; alternative hypothesis: true difference in means is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.8819731 -0.4220269 #&gt; sample estimates: #&gt; mean of x mean of y #&gt; 5.936 6.588 1.7.5 Regression fit &lt;- lm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, data=iris) summary(fit) # show results #&gt; #&gt; Call: #&gt; lm(formula = Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width, #&gt; data = iris) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -0.82816 -0.21989 0.01875 0.19709 0.84570 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 1.85600 0.25078 7.401 9.85e-12 *** #&gt; Sepal.Width 0.65084 0.06665 9.765 &lt; 2e-16 *** #&gt; Petal.Length 0.70913 0.05672 12.502 &lt; 2e-16 *** #&gt; Petal.Width -0.55648 0.12755 -4.363 2.41e-05 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 0.3145 on 146 degrees of freedom #&gt; Multiple R-squared: 0.8586, Adjusted R-squared: 0.8557 #&gt; F-statistic: 295.5 on 3 and 146 DF, p-value: &lt; 2.2e-16 This means the fitted regression is: Sepal.Length ~ 1.856 + 0.65*Sepal.Width + 0.709*Petal.Length - 0.556*Petal.Width We can check how good the regression is by plotting it out y_pred &lt;- fit$coefficients[1] + fit$coefficients[2] * iris$Sepal.Width + fit$coefficients[3] * iris$Petal.Length + fit$coefficients[4] * iris$Petal.Width cor(iris$Sepal.Length, y_pred) #&gt; [1] 0.926613 plot(iris$Sepal.Length, y_pred) 1.7.6 Resource links This notebook adapts contents from these resources: https://www.datamentor.io/r-programming/ https://www.geeksforgeeks.org/r-data-types/ https://data-flair.training/blogs/r-data-types/ http://www.sthda.com/english/wiki/ggplot2-essentials 1.7.7 Coding styling Elegant styling is crucial for maintenance and collaboration. Here is a highly recommended guideline: http://adv-r.had.co.nz/Style.html 1.8 Exercises This list of exercises will serve as a 2-hour demonstration in the BIOF1001 course. For other learners, you can go through it as homework. The expected time is around two hours if you have read the R materials carefully together with trying them with your own R environment. Note, before you get started, please make sure that you are familiar with the panels in RStudio. You may watch this YouTube Video or check this RStudio cheatsheet. 1.8.1 Part 1. Basics (~40min) Q1: We have 25 students in BIOF1001, to store the final marks (0 to 100 with a precision of 0.1), what data type will we use? Q2: For the grades (A+ to F), what data type and data structure can be used to keep the memory minimal? Q3: Make a matrix with name my_matrix, shape of 5 rows and 2 columns and values from 3 to 12. The first row is 3 and 4. Hint: for making a vector from 3 to 12, you may use seq() or :. Q4: Based on Q3, add the row names to Day1 to Day5 and column names to Lunch and Dinner. Q5: Based on Q4, get a matrix with shape of 3x1 and values of 6, 8, 10 from the matrix my_matrix. Q6: What will you get for my_matrix[c(TRUE, FALSE, FALSE, TRUE), ]? Hint: think of recycling if the index length is different from the query dimension (Over-flexibility comes with a price of wrong use). Q7: If you have two vectors the BIOF1001 marks and grades and one character for teaching performance \"good\", and you want to store them into one variable, which data structure will you use? Q8: Now, on your Desktop folder, make a subfolder with name R_exercises and download this file of differentailly expressed genes results Diff_Expression_results.tsv to the folder. Check your current work directory by getwd() function and change the work directory to the folder you just created. Hint: you may use setwd() to change the work directory or use the Session button of RStudio. Q9: Related to Q8, use the read.table() function to load the file into a data frame with the variable name df_DEG. Hint: You may consider using the full path or just the file name if it’s in the same work directory. Please keep header=TRUE for the argument. Think how to find help page for a certain function. Q10: Can you calculate the mean and standard deviation of the log2FoldChange? If the mean &gt;0.1 and the standard deviation &lt; 3, set the trend variable as “increase”, otherwise “not_increase”. What will happen if you add this trend variable to the data frame, and why? Hint: use mean() and st() functions for calculating mean and standard deviation. 1.8.2 Part 2. Making plotting (~40min) Q11: Keep use the df_DEG from part 1 Q9. Now, make a histogram of the log2FoldChange with both basic plotting function hist() and ggplot2. Q12: Make a plot with x-axis of log10(baseMean) and y-axis of log2FoldChange. Please try both the basic plot() function and ggplot2. Q13: Now, manipulate the dataframe by adding two columns: Add a column log2FC_clip for clipping log2FoldChange to [-5, +5] Add a column is_DE for padj &lt; 0.05 Q14: Try the summary() function with the above df_DEG data frame, and also table() function for the is_DE column. Q15: Based on ggplot2, add the color by the newly added column is_DE. Q16: Set the colors to “red” and “grey”, and make it in the order of TRUE and FALSE. Hint: use factor and set the levels parameter. Q17: Save the generated figure into “My_DEG_results.pdf”. Use the ggsave() function. Please set width = 5, height = 4. You are expected a figure like this DEG figure If you want to change labels on x-axis or y-axis and font size, etc., you can simply Google and find examples. 1.8.3 Part 3. For loop and repeating processing (~40min) Q18: Load the following table from this file on GitHub and View it in RStudio. It contains expressoon of 619 transcription factors from 7 Nasopharyngeal carcinoma (NPC) samples and 3 nasopharyngeal lymphatic hyperplasia (NLH) samples. https://github.com/StatBiomed/NegabinGLM/blob/main/data/NPC_NLH-Tcell-donorX.tsv df_NPC = read.table(\"https://github.com/StatBiomed/NegabinGLM/raw/main/data/NPC_NLH-Tcell-donorX.tsv\", sep=\"\\t\", header=TRUE) Q19: Extract the column 5 (HES5) to 623 (LEK4) and make it into a matrix TF_mat Hint: how to index a data frame like index a matrix. Q20: perform normalization. Divide the TF_mat by the df_NPC$total_counts and multiply by 1000000, and assign it to a new matrix named TF_mat_norm. You may further consider transformation by log1p(), i.e., log(TF_mat_norm + 1). Q21: calculate the log fold change on the first gene TP73 in TF_mat_norm between NPC (row 1 to 7) and NLH (row 8 to 10) and perform t-test return the p value and log fold change. Q22: perform t-test on the all gene in TF_mat_norm between NPC (row 1 to 7) and NLH (row 8 to 10). Hint: think of for loop or apply() function. "],["introHypoTest.html", "Chapter 2 Introduction to Hypothesis testing 2.1 Hypothesis testing and p value 2.2 Permutation test 2.3 t test 2.4 GLM test 2.5 Multiple testing", " Chapter 2 Introduction to Hypothesis testing 2.1 Hypothesis testing and p value How surprising is my result? Calculating a p-value There are many circumstances where we simply want to check whether an observation looks like it is compatible with the null hypothesis, \\(H_{0}\\). Having decided on a significance level \\(\\alpha\\) and whether the situation warrants a one-tailed or a two-tailed test, we can use the cdf of the null distribution to calculate a p-value for the observation. Acknowledgement: examples are from Dr John Pinney link here 2.1.1 Example 1: probability of rolling a six? Your arch-nemesis Blofeld always seems to win at ludo, and you have started to suspect him of using a loaded die. You observe the following outcomes from 100 rolls of his die: data = c(6, 1, 5, 6, 2, 6, 4, 3, 4, 6, 1, 2, 5, 6, 6, 3, 6, 2, 6, 4, 6, 2, 5, 4, 2, 3, 3, 6, 6, 1, 2, 5, 6, 4, 6, 2, 1, 3, 6, 5, 4, 5, 6, 3, 6, 6, 1, 4, 6, 6, 6, 6, 6, 2, 3, 1, 6, 4, 3, 6, 2, 4, 6, 6, 6, 5, 6, 2, 1, 6, 6, 4, 3, 6, 5, 6, 6, 2, 6, 3, 6, 6, 1, 4, 6, 4, 2, 6, 6, 5, 2, 6, 6, 4, 3, 1, 6, 6, 5, 5) Do you have enough evidence to confront him? # We will work with the binomial distribution for the observed number of sixes # Write down the hypotheses # H0: p = 1/6 # H1: p &gt; 1/6 # choose a significance level # alpha = 0.01 # number of sixes # number of trials stat_k = sum(data == 6) trials = length(data) print(paste(&quot;number of sixes:&quot;, stat_k)) #&gt; [1] &quot;number of sixes: 43&quot; print(paste(&quot;number of trials:&quot;, trials)) #&gt; [1] &quot;number of trials: 100&quot; # test statistic: number of sixes out of 100 trials # null distribution: dbinom(x, size=100, prob=1/6) # calculate p value p_val = 1 - pbinom(stat_k - 1, size=trials, prob=1/6) print(paste(&quot;Observed statistic is&quot;, stat_k)) #&gt; [1] &quot;Observed statistic is 43&quot; print(paste(&quot;p value is&quot;, p_val)) #&gt; [1] &quot;p value is 5.43908695860296e-10&quot; 2.1.1.1 Visualize the null distribution and the test statistic # plot the probability mass function of null distribution x = seq(0, 101) pmf = dbinom(x, size=100, prob=1/6) df = data.frame(x=x, pmf=pmf, extreme=(x &gt;= stat_k)) library(ggplot2) ggplot(df, aes(x=x)) + geom_point(aes(y=pmf, color=extreme)) + scale_color_manual(values=c(&quot;black&quot;, &quot;red&quot;)) + xlab(&#39;Number of sixes&#39;) + ylab(&#39;Probability Mass Function&#39;) + ggtitle(&#39;Distribution of n_six under the null hypothesis&#39;) 2.2 Permutation test 2.2.1 Example 2: difference in birth weight The birth weights of babies (in kg) have been measured for a sample of mothers split into two categories: nonsmoking and heavy smoking. The two categories are measured independently from each other. Both come from normal distributions The two groups are assumed to have the same unknown variance. data_heavysmoking = c(3.18, 2.84, 2.90, 3.27, 3.85, 3.52, 3.23, 2.76, 3.60, 3.75, 3.59, 3.63, 2.38, 2.34, 2.44) data_nonsmoking = c(3.99, 3.79, 3.60, 3.73, 3.21, 3.60, 4.08, 3.61, 3.83, 3.31, 4.13, 3.26, 3.54) We want to know whether there is a significant difference in mean birth weight between the two categories. # Write down the hypotheses # H0: there is no difference in mean birth weight between groups: d == 0 # H1: there is a difference, d != 0 # choose a significance level # alpha = 0.05 # Define test statistic: difference of group mean stat_mu = mean(data_heavysmoking) - mean(data_nonsmoking) stat_mu #&gt; [1] -0.5156923 2.2.2 Null distribution approximated by resampling #&#39; Simple function to generate permutation distribution get_permutation_null &lt;- function(x1, x2, n_permute=1000) { n1 = length(x1) n2 = length(x2) # pool data sets x_pool = c(x1, x2) null_distr = rep(0, n_permute) for (i in seq(n_permute)) { # split idx = sample(n1 + n2, size=n1) x1_perm = x_pool[idx] x2_perm = x_pool[-idx] # calculate test statistic null_distr[i] = mean(x1_perm) - mean(x2_perm) } return(null_distr) } set.seed(1) perm_null = get_permutation_null(data_heavysmoking, data_nonsmoking) We can plot the histogram of the null distribution obtained by resampling. We can also add line(s) for the values as extreme as observed statistic mu, where we can consider one side or both side as extreme values. df_perm = data.frame(perm_null = perm_null) ggplot(df_perm, aes(x=perm_null)) + geom_histogram(bins=20) + geom_vline(xintercept=stat_mu, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + geom_vline(xintercept=-stat_mu, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + xlab(&#39;Difference of group mean&#39;) + ylab(&#39;Resampling frequency&#39;) + ggtitle(&#39;Distribution of mu under the null hypothesis&#39;) ## Two tailed p value p_two_tailed = mean(abs(perm_null) &gt;= abs(stat_mu)) p_one_tailed = mean(perm_null &lt; stat_mu) print(paste(&quot;Two tailed p value:&quot;, round(p_two_tailed, 5))) #&gt; [1] &quot;Two tailed p value: 0.003&quot; print(paste(&quot;One (left) tailed p value:&quot;, round(p_one_tailed, 5))) #&gt; [1] &quot;One (left) tailed p value: 0.002&quot; 2.3 t test 2.3.1 Derivation of t distribution Null distribution approximated by \\(t\\) distribution We use the t test to assess whether two samples taken from normal distributions have significantly different means. The test statistic follows a Student’s t-distribution, provided that the variances of the two groups are equal. Other variants of the t-test are applicable under different conditions. The test statistic is \\[ t = \\frac{\\bar{X}_{1} - \\bar{X}_{2}}{s_p \\cdot \\sqrt{\\frac{1}{n_{1}} + \\frac{1}{n_{2}}}} \\] where \\[ s_p = \\sqrt{\\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} \\] is an estimator of the pooled standard deviation. Under the null hypothesis of equal means, the statistic follows a Student’s t-distribution with \\((n_{1} + n_{2} - 2)\\) degrees of freedom. # Same test statistic: difference of group mean stat_t = mean(data_heavysmoking) - mean(data_nonsmoking) stat_t #&gt; [1] -0.5156923 Calculate parameters for approximate t distribution n_ns = length(data_nonsmoking) n_hs = length(data_heavysmoking) s_ns = sd(data_nonsmoking) # degree of freedom: n-1 s_hs = sd(data_heavysmoking) # the pooled standard deviation sp = sqrt(((n_ns - 1)*s_ns**2 + (n_hs - 1)*s_hs**2) / (n_ns + n_hs - 2)) print(paste0(&quot;Pooled standard deviation:&quot;, sp)) #&gt; [1] &quot;Pooled standard deviation:0.428057812829366&quot; my_std = sp * sqrt(1/n_ns + 1/n_hs) print(paste(&quot;Estimated standard error of mean difference:&quot;, my_std)) #&gt; [1] &quot;Estimated standard error of mean difference: 0.162204962956089&quot; stat_t_scaled = stat_t / my_std print(paste(&quot;Rescaled t statistic:&quot;, stat_t_scaled)) #&gt; [1] &quot;Rescaled t statistic: -3.17926343494134&quot; print(paste(&quot;degree of freedom&quot;, n_hs+n_ns-2)) #&gt; [1] &quot;degree of freedom 26&quot; Here, we focusing the standardized \\(t\\) distribution, namely the variance=1, so let’s re-scale the test statistic by dividing the standard error my_std. xx = seq(-4.5, 4.5, 0.05) xx_pdf = dt(xx, df=n_hs+n_ns-2) df_t_dist = data.frame(x=xx, pdf=xx_pdf) ggplot(df_t_dist, aes(x=x)) + geom_line(aes(y=pdf)) + geom_vline(xintercept=stat_t_scaled, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + geom_vline(xintercept=-stat_t_scaled, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + xlab(&#39;Difference of group mean&#39;) + ylab(&#39;PDF approximated by t distr.&#39;) + ggtitle(&#39;Distribution of t under the null hypothesis&#39;) # Note, we used multiply 2 just because the t distribution is symmetric, # otherwise, we need calculate both side and add them. pval_t_twoside = pt(stat_t_scaled, df=n_hs+n_ns-2) * 2 print(paste(&#39;t-test p value (two-tailed):&#39;, round(pval_t_twoside, 6))) #&gt; [1] &quot;t-test p value (two-tailed): 0.003793&quot; 2.3.2 Direct use of t.test() In course and most of your future analyses, you can directly use the built-in t.test() function. # Note, we assumed the variance in both groups are the same, # we so need to set var.equal = TRUE t.test(data_nonsmoking, data_heavysmoking, var.equal = TRUE) #&gt; #&gt; Two Sample t-test #&gt; #&gt; data: data_nonsmoking and data_heavysmoking #&gt; t = 3.1793, df = 26, p-value = 0.003793 #&gt; alternative hypothesis: true difference in means is not equal to 0 #&gt; 95 percent confidence interval: #&gt; 0.1822752 0.8491094 #&gt; sample estimates: #&gt; mean of x mean of y #&gt; 3.667692 3.152000 2.4 GLM test We can also perform t-test in a Generalised linear model (GLM) setting to test if a coefficient is zero or not. Here, we simply use the marketing dataset as an example. # Install datarium library if you haven&#39;t if (!requireNamespace(&quot;datarium&quot;, quietly = TRUE)) { install.packages(&quot;datarium&quot;) } library(datarium) # Load data: then we will have a data.frame with name marketing data(marketing) head(marketing) #&gt; youtube facebook newspaper sales #&gt; 1 276.12 45.36 83.04 26.52 #&gt; 2 53.40 47.16 54.12 12.48 #&gt; 3 20.64 55.08 83.16 11.16 #&gt; 4 181.80 49.56 70.20 22.20 #&gt; 5 216.96 12.96 70.08 15.48 #&gt; 6 10.44 58.68 90.00 8.64 ggplot(marketing, aes(x=newspaper, y=sales)) + geom_point() + geom_smooth(method=lm) #&gt; `geom_smooth()` using formula = &#39;y ~ x&#39; # Fit linear regression res.lm &lt;- lm(sales ~ newspaper, data = marketing) # We can check the test via the summary() function summary(res.lm) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ newspaper, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -13.473 -4.065 -1.007 4.207 15.330 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 14.82169 0.74570 19.88 &lt; 2e-16 *** #&gt; newspaper 0.05469 0.01658 3.30 0.00115 ** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 6.111 on 198 degrees of freedom #&gt; Multiple R-squared: 0.05212, Adjusted R-squared: 0.04733 #&gt; F-statistic: 10.89 on 1 and 198 DF, p-value: 0.001148 glm_t_val = summary(res.lm)$coefficients[&quot;newspaper&quot;, &quot;t value&quot;] xx = seq(-5, 5, 0.01) yy = dt(xx, 198) df_ttest &lt;- data.frame(x=xx, PDF=yy) ggplot(df_ttest, aes(x=x, y=PDF)) + geom_line() + geom_vline(xintercept = glm_t_val, linetype=&quot;dashed&quot;, color=&quot;tomato&quot;) + geom_vline(xintercept = -glm_t_val, linetype=&quot;dashed&quot;, color=&#39;tomato&#39;) 2.5 Multiple testing Hypothetical null distribution. Feel feel to try any null distribution, examples below ## Example null distributions # t, normal or anything. we use chi-squared distribution as an example x_random = rchisq(n=1000, df=3) any_null_dist = dchisq(x_random, df=3) pvals_null = 1 - pchisq(x_random, df=3) 2.5.1 Null distribution (of test statistic) # Null distribution of test statistic hist(x_random) 2.5.2 Null distribution of p value # Null distribution of test statistic hist(pvals_null) 2.5.3 Minimal p values in 10 tests # We use matrix to group 100 trials into a column # We then use apply() to calculate min value for each column pval_null_mtx = matrix(pvals_null, nrow=10) p_min_in10 = apply(pval_null_mtx, MARGIN=2, FUN=min) hist(p_min_in10) print(paste(&#39;Proportion of tests with min(p) &lt; 0.05:&#39;, mean(p_min_in10 &lt; 0.05))) #&gt; [1] &quot;Proportion of tests with min(p) &lt; 0.05: 0.43&quot; 2.5.4 Homework Make a simulation of score: group A and B B follows normal(mean=0, std=1); A follows normal(mean=0.1, std=1) Generate 100 samples for each group, and do a t test, is difference significant? Please use set.seed(0) beforehand. Try 3) again but general 3,00 samples this time, later 1,000 samples. What do you find? Think the relation between power and sample size. set.seed(0) n_sample = 100 # change this value to 1000 and 10000 xB = rnorm(n_sample) xA = rnorm(n_sample, mean=0.1) t.test(xA, xB, var.equal = TRUE) #&gt; #&gt; Two Sample t-test #&gt; #&gt; data: xA and xB #&gt; t = 0.24294, df = 198, p-value = 0.8083 #&gt; alternative hypothesis: true difference in means is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.2261882 0.2897482 #&gt; sample estimates: #&gt; mean of x mean of y #&gt; 0.05444844 0.02266845 "],["introLinearReg.html", "Chapter 3 Introduction to Linear Regression 3.1 Linear Regression Using Simulated Data 3.2 Least Squares Using Simulated Data 3.3 Diagnostic check of a fitted regression model 3.4 Simple Linear Regression with lm function 3.5 Multiple Regression with lm function", " Chapter 3 Introduction to Linear Regression Acknowledgements: this chapter is adapted and updated from the materials originally produced by STAT1005 teaching team, especially Prof. Jeff Yao. 3.1 Linear Regression Using Simulated Data Let’s first simulate some data and look at how the predicted values (Ye) differ from the actual value (Y). 3.1.1 Simulating data: For X, we generate 100 normally distributed random numbers with mean 1.5 and standard deviation 2.5. For predicted value Ye, we assume an intercept (α) of 2 and a slope (β) of 0.3 and we write \\(Y_e = 2 + 0.3 x\\) Later, we will estimate the values of α and β using the least squares method and see how that changes the efficacy of the model. Though we estimate \\(Y_e = \\alpha + \\beta X\\), in reality Y is rarely perfectly linear. It usually has an error component or residual: \\(Y = \\alpha + \\beta X + R\\), where R is a random variable and is assumed to be normally distributed. Therefore for the actual value Y, we add a residual term (res), a random variable distributed normally with mean 0 and a standard deviation of 0.5. The following cell shows the code snippet to generate these numbers and convert these three columns in a data frame. Read through the code carefully and run the cell to output a sample of our simulated data. # Fix seed: each run gives the same random numbers so the same outputs. # Commenting out this line would read similar but different outputs at each run. # Try it out! set.seed(0) # Generate data X = 2.5 * rnorm(100) + 1.5 # Array of 100 values with mean = 1.5, stddev = 2.5 ypred = 2 + 0.3 * X # Prediction of Y, assuming a = 2, b = 0.3 res = 0.5 * rnorm(100) # Generate 100 residual terms yact = 2 + 0.3 * X + res # Actual values of Y # Create dataframe to store our X, ypred, and yact values df = data.frame(&#39;X&#39; = X, &#39;ypred&#39; = ypred, &#39;yact&#39; = yact) # Show the first six rows of our dataframe head(df) #&gt; X ypred yact #&gt; 1 4.6573857 3.397216 3.788145 #&gt; 2 0.6844166 2.205325 1.816937 #&gt; 3 4.8244982 3.447349 3.139354 #&gt; 4 4.6810733 3.404322 3.427612 #&gt; 5 2.5366036 2.760981 2.195788 #&gt; 6 -2.3498751 1.295037 1.583397 Now let’s plot both the actual output (yact) and predicted output (ypred) against the input variable (X) to see what the difference between yact and ypred is, and therefore, to see how accurately the proposed equation (ypred = 2 + 0.3 * X) has been able to predict the value of the output: # You can use basic plotting functions # plot(x=df$X, y=df$yact, col=&quot;red&quot;) # lines(x=df$X, y=df$ypred, col=&quot;darkgreen&quot;) # But let&#39;s use ggplot2 for higher flexibility library(ggplot2) ggplot(df, aes(X)) + # basic graphical object geom_point(aes(y=yact), colour=&quot;black&quot;) + # first layer geom_line(aes(y=ypred), colour=&quot;darkgreen&quot;) + # second layer ggtitle(&#39;Actual vs Predicted values from the dummy dataset&#39;) 3.1.2 Model efficacy How do we know the values we calculate for α and β are giving us a good model? We can explain the total variability in our model with the Total Sum of Squares or SST: \\[SST = \\sum_{i=1}^n\\Bigl(\\text{yact}_i - \\text{yavg}\\Bigr)^2, \\qquad\\qquad \\text{yavg}=\\frac1n \\sum_{i=1}^n \\text{yact}_i\\] Mathematically, we have \\[ \\sum_{i=1}^n\\Bigl(\\text{yact}_i - \\text{yavg}\\Bigr)^2 = \\sum_{i=1}^n\\Bigl(\\text{ypred}_i -\\text{yavg} \\Bigr)^2 + \\sum_{i=1}^n\\Bigl(\\text{yact}_i - \\text{ypred}_i\\Bigr)^2\\] The identity reads as Sum of Squares Total = Sum of Squares Regression + Sum of Squares Error, or simply , SST = SSR + SSE. The Regression Sum of Squares or SSR measures the variation of the regression/predicted values, and the Sum of Squares Error SSE the variation between the actual and the predicted values. An alternative saying is that SSR is the difference explained by the model, SSE is the difference not explained by the model and is random, and SST is the total error. Note, we often use SSE (Sum of Squares Error) and SSD (Sum of Squares Difference) interchangeably. 3.1.3 R-Squared The higher the ratio of SSR to SST, the better the model is. This ratio is quantified by the coefficient of determination (also known as R2 or R-squared): \\[ R^2= \\frac{SSR}{SST}\\] Since \\(SST= SSR+SSE\\), \\(\\qquad 0\\le R^2\\le 1\\). The closer it is to 1, the better the model. Note that there are many other factors that we need to analyse before we can conclude a linear regression model is effective, but a high \\(R^2\\) is a pretty good indicator. Let’s see what the value of \\(R^2\\) is for our simulated dataset. # Calculate the mean of Y ymean = mean(df$yact) print(paste(&#39;Mean of Y =&#39;, ymean)) # paste brings a white space by default #&gt; [1] &quot;Mean of Y = 2.44422555811815&quot; # Calculate SSR and SST df[&#39;SSR&#39;] = (df[&#39;ypred&#39;] - ymean)**2 df[&#39;SST&#39;] = (df[&#39;yact&#39;] - ymean)**2 SSR = sum(df[&#39;SSR&#39;]) SST = sum(df[&#39;SST&#39;]) # Calculate R-squared R2 = SSR / SST print(paste(&#39;R2 =&#39;, R2)) #&gt; [1] &quot;R2 = 0.583160943681119&quot; The value of \\(R^2=0.583\\) suggests that ypred provides a decent prediction of the yact. We have randomly assumed some values for \\(\\alpha\\) and \\(\\beta\\), but these may or may not be the best values. In the next step, we will use the least sum of square method to calculate the optimum value for \\(\\alpha\\) and \\(\\beta\\) to see if there is an improvement in \\(R^2\\). To get started on the next step, open the notebook called 02-linearReg-02.Rmd. 3.2 Least Squares Using Simulated Data Now, using our simulated data from the previous step, let’s estimate the optimum values of our variable coefficients, \\(\\alpha\\) and \\(\\beta\\). Using the predictor variable, X, and the output variable, yact, we will calculate the values of \\(\\alpha\\) and \\(\\beta\\) using the Least Squares method described in the lecture. The cell below creates the same dataframe as previously. Run the cell to get started! set.seed(0) # Generate data X = 2.5 * rnorm(100) + 1.5 # Array of 100 values with mean = 1.5, stddev = 2.5 ypred = 2 + 0.3 * X # Prediction of Y, assuming a = 2, b = 0.3 res = 0.5 * rnorm(100) # Generate 100 residual terms yact = 2 + 0.3 * X + res # Actual values of Y # Create dataframe to store our X, ypred, and yact values df = data.frame(&#39;X&#39; = X, &#39;ypred&#39; = ypred, &#39;yact&#39; = yact) Just to reiterate, here are the formulas for \\(\\alpha\\) and \\(\\beta\\) again: \\[\\hat\\beta=\\frac{\\sum_{i=1}^n(X_i-\\bar X)(Y_i-\\bar Y)}{\\sum_{i=1}^n(X_i-\\bar X)^2}=\\frac{\\text{cov}(X,Y)}{\\text{var}(X)}\\] \\[\\hat\\alpha=\\bar Y-\\hat\\beta * \\bar X\\] To calculate these coefficients, we will create a few more columns in our df data frame. We need to calculate xmean and ymean to calculate the covariance of X and Y (xycov) and the variance of X (xvar) before we can work out the values for alpha and beta. # Calculate the mean of X and Y xmean = mean(X) ymean = mean(yact) # Calculate the terms needed for the numator and denominator of beta df[&#39;xycov&#39;] = (df[&#39;X&#39;] - xmean) * (df[&#39;yact&#39;] - ymean) df[&#39;xvar&#39;] = (df[&#39;X&#39;] - xmean)**2 # Calculate beta and alpha beta = sum(df[&#39;xycov&#39;]) / sum(df[&#39;xvar&#39;]) alpha = ymean - (beta * xmean) print(paste(&#39;alpha =&#39;, alpha, &#39;;&#39;, &#39;beta =&#39;, beta)) #&gt; [1] &quot;alpha = 1.93401265576322 ; beta = 0.327758955833308&quot; As we can see, the values are only a little different from what we had assumed earlier. Let’s see how the value of \\(R^2\\) changes if we use the new values of \\(\\alpha\\) and \\(\\beta\\). The equation for the new model can be written as: \\[ y=1.934 + 0.328 * x \\] Let’s create a new column in df to accommodate the values generated by this equation and call this ypred2, and calculate the new \\(R^2\\). # Create new column to store new predictions df[&#39;ypred2&#39;] = alpha + beta * df[&#39;X&#39;] # Calculate new SSR with new predictions of Y. # Note that SST remains the same since yact and ymean do not change. df[&#39;SSR2&#39;] = (df[&#39;ypred2&#39;] - ymean)**2 df[&#39;SST&#39;] = (df[&#39;yact&#39;] - ymean)**2 SSR2 = sum(df[&#39;SSR2&#39;]) SST = sum(df[&#39;SST&#39;]) # Calculate new R2 R2_2 = SSR2 / SST print(paste(&#39;New R2 =&#39;, R2_2)) #&gt; [1] &quot;New R2 = 0.69524214766491&quot; The new value of \\(R^2= 0.695\\) shows a slight improvement from the previous value of \\(R^2=0.583\\) (obtained with \\(\\alpha=2,~\\beta=0.3\\)). Let’s also plot our new prediction model against the actual values and our earlier assumed model, just to get a better visual understanding. library(ggplot2) # Put color into aes ggplot(df, aes(X)) + # basic graphical object geom_point(aes(y=yact), colour=&quot;black&quot;) + # first layer geom_line(aes(y=ypred, colour=&quot;Guess&quot;)) + # second layer geom_line(aes(y=ypred2, colour=&quot;OLS&quot;)) + # third layer scale_colour_manual(name=&quot;Models&quot;, values = c(&quot;Guess&quot;=&quot;darkgreen&quot;, &quot;OLS&quot;=&quot;red&quot;)) + ggtitle(&#39;Actual vs Predicted with guessed parameters vs Predicted with calculated parameters&#39;) As we can see, the ypred2 and ypred are more or less overlapping since the respective values of ɑ and β are not very different. Next, we will explore other methods of determining model efficacy by using the notebook called 02-linearReg-03.Rmd. 3.3 Diagnostic check of a fitted regression model Apart from the \\(R^2\\) statistic, there are other statistics and parameters that you need to look at in order to determine if the model is efficient. We will discuss some commonly used statistics – Residual Standard Errors, \\(p\\)-values, and \\(F\\)-statistics. 3.3.1 Residual Standard Errors (RSE) RSE is a common statistic used to calculate the accuracy of values predicted by a model. It is an estimate of the variance of the error term, res. For a simple linear regression model, RSE is defined as: \\[ RSE^2 = \\frac{SSE}{n-2} = \\frac1{n-2} \\sum_{i=1}^n \\Bigl(\\text{yact}_i - \\text{ypred}_i \\Bigr)^2. \\] In general, \\[ RSE^2 = \\frac{SSE}{n-p-1} = \\frac1{n-p-1} \\sum_{i=1}^n \\Bigl(\\text{yact}_i - \\text{ypred}_i \\Bigr)^2. \\] where \\(p\\) is the number of predictor variables in a model where we have more than one predictor variables. A multiple linear regression model is a linear regression model with multiple predictors, written as \\[ Y_e = \\alpha +\\beta_1 * X_1 +\\cdots +\\beta_p X_p. \\] As you see, the parameters and predictors are subscripted from 1 up to the number of predictors \\(p\\). In multiple regression, the value of RSE generally decreases as we add variables that are more significant predictors of the output variable. Using our simulated data from the previous steps, the following code snippet shows how the RSE for a model can be calculated: set.seed(0) # Generate data X = 2.5 * rnorm(100) + 1.5 # Array of 100 values with mean = 1.5, stddev = 2.5 res = 0.5 * rnorm(100) # Generate 100 residual terms yact = 2 + 0.3 * X + res # Actual values of Y # Create dataframe to store our X, ypred, and yact values df = data.frame(&#39;X&#39; = X, &#39;yact&#39; = yact) # Calculate the mean of X and Y xmean = mean(X) ymean = mean(yact) # Calculate the terms needed for the numator and denominator of beta df[&#39;xycov&#39;] = (df[&#39;X&#39;] - xmean) * (df[&#39;yact&#39;] - ymean) df[&#39;xvar&#39;] = (df[&#39;X&#39;] - xmean)**2 # Calculate beta and alpha beta = sum(df[&#39;xycov&#39;]) / sum(df[&#39;xvar&#39;]) alpha = ymean - (beta * xmean) print(paste(&#39;alpha =&#39;, alpha, &#39;;&#39;, &#39;beta =&#39;, beta)) #&gt; [1] &quot;alpha = 1.93401265576322 ; beta = 0.327758955833308&quot; # Store predictions as in previous step df[&#39;ypred&#39;] = alpha + beta * df[&#39;X&#39;] # Show first five rows of dataframe head(df) #&gt; X yact xycov xvar ypred #&gt; 1 4.6573857 3.788145 4.1671116 9.6144310 3.460513 #&gt; 2 0.6844166 1.816937 0.5471556 0.7608280 2.158336 #&gt; 3 4.8244982 3.139354 2.2715611 10.6786935 3.515285 #&gt; 4 4.6810733 3.427612 3.0724952 9.7618890 3.468276 #&gt; 5 2.5366036 2.195788 -0.2434518 0.9602676 2.765407 #&gt; 6 -2.3498751 1.583397 3.3628671 15.2611034 1.163820 # Calculate SSE df[&#39;SSE&#39;] = (df[&#39;yact&#39;] - df[&#39;ypred&#39;])**2 SSE = sum(df[&#39;SSE&#39;]) # Calculate RSE RSE = sqrt(SSE / 98) # n = 100 print(paste(&#39;RSE =&#39;, RSE)) #&gt; [1] &quot;RSE = 0.481279277134956&quot; The value of RSE comes out to be 0.48. As you might have guessed, the smaller the residual standard errors, the better the model is. The benchmark to compare this to is the mean of the actual values, yact. As shown previously, this value is ymean = 2.54. In plain English, this means we observe an error of 0.48 over 2.44 - approximately 19.69%. error = RSE / ymean print(paste(&#39;Mean Y =&#39;, ymean)) #&gt; [1] &quot;Mean Y = 2.44422555811815&quot; print(paste(&#39;Error =&#39;, error)) #&gt; [1] &quot;Error = 0.196904608716023&quot; 3.3.2 p-values The calculation of \\(\\alpha\\) and \\(\\beta\\) are estimates, not exact calculations. Whether their values are significant or not needs to be tested using a hypothesis test. In the equation, \\(Y = \\alpha + \\beta X\\), if we set \\(\\beta=0\\), there will be no relation between \\(Y\\) and \\(X\\). Therefore, the hypothesis tests whether the value of \\(\\beta\\) is non-zero or not. \\[\\begin{align*} \\text{Null hypothesis}~ H_0~:~ \\beta=0, &amp; \\quad \\text{versus} \\\\ \\text{Alternative hypothesis}~ H_1~:~ \\beta\\ne 0.&amp; \\end{align*} \\] Whenever a regression task is performed and \\(\\beta\\) is calculated, there will be an accompanying p-value corresponding to this hypothesis test. We will not go through how this is calculated in this course (you can learn more here), since it is calculated automatically by ready-made methods in R. If the p-value is less than a chosen significance level (e.g. 0.05) then the null hypothesis that \\(\\beta = 0\\) is rejected and \\(\\beta\\) is said to be significant and non-zero. In the case of multiple linear regression, the p-value associated with each \\(\\beta_k\\) can be used to weed out insignificant predictors from the model. The higher the p-value for \\(\\beta_k\\), the less significant \\(X_k\\) is to the model. 3.3.3 F-statistics In a multiple regression model, apart from testing the significance of individual variables by checking the p-values, it is also necessary to check whether, as a group all the predictors are significant. This can be done using the following hypothesis: \\[\\begin{align*} \\text{Null hypothesis}~ H_0~:~ &amp; \\beta_1=\\beta_2=\\cdots=\\beta_p=0, \\quad \\text{versus} \\\\ \\text{Alternative hypothesis}~ H_1~:~&amp; \\text{at least one of the} ~\\beta_k&#39;s ~ \\text{is non zero}. \\end{align*} \\] The statistic that is used to test this hypothesis is called the F-statistic and is defined as follows: \\[ F\\text{-statistic} = \\text{Fisher statistic}= \\frac{ (SST-SSE)/p}{ SSE/(n-p-1)} \\] where \\(n\\) = number of rows (sample points) in the dataset and \\(p\\) = number of predictor variables in the model. There is a \\(p\\)-value that is associated with this \\(F\\)-statistic. If the \\(p\\)-value is smaller than the chosen significance level, the null hypothesis can be rejected. It is important to look at the F-statistic because: p-values are about individual relationships between predictors and the outcome variable. However, one predictor’s relationship with the output might be impacted by the presence of other variables. When the number of predictors in the model is very large and all the \\(\\beta_i\\) are very close to zero, the individual p-values associated with the predictors might give very small values so we might incorrectly conclude that there is a relationship between the predictors and the outcome. 3.4 Simple Linear Regression with lm function There are a few R packages, e.g., the built-in stat package have a lm (linear model) function to fit linear regression very easy - much easier than implementing from scratch like we did in the last lesson. See more details in the lm manual. We will start with the datarium library which contain the advertising data. # Install datarium library if you haven&#39;t if (!requireNamespace(&quot;datarium&quot;, quietly = TRUE)) { install.packages(&quot;datarium&quot;) } library(datarium) # Load data: then we will have a data.frame with name marketing data(marketing) head(marketing) #&gt; youtube facebook newspaper sales #&gt; 1 276.12 45.36 83.04 26.52 #&gt; 2 53.40 47.16 54.12 12.48 #&gt; 3 20.64 55.08 83.16 11.16 #&gt; 4 181.80 49.56 70.20 22.20 #&gt; 5 216.96 12.96 70.08 15.48 #&gt; 6 10.44 58.68 90.00 8.64 We can also check summary statistics of each column summary(marketing) #&gt; youtube facebook newspaper sales #&gt; Min. : 0.84 Min. : 0.00 Min. : 0.36 Min. : 1.92 #&gt; 1st Qu.: 89.25 1st Qu.:11.97 1st Qu.: 15.30 1st Qu.:12.45 #&gt; Median :179.70 Median :27.48 Median : 30.90 Median :15.48 #&gt; Mean :176.45 Mean :27.92 Mean : 36.66 Mean :16.83 #&gt; 3rd Qu.:262.59 3rd Qu.:43.83 3rd Qu.: 54.12 3rd Qu.:20.88 #&gt; Max. :355.68 Max. :59.52 Max. :136.80 Max. :32.40 This dataset contains data about the advertising budget spent on YouTub, Radio, and Newspapers for a particular product and the resulting sales. We expect a positive correlation between such advertising costs and sales. Let’s start with YouTub advertising costs to create a simple linear regression model. First let’s plot the variables to get a better sense of their relationship: # Create scatter plot library(ggplot2) ggplot(marketing, aes(x=youtube, y=sales)) + geom_point(colour=&quot;black&quot;) + ggtitle(&#39;YouTube vs Sales&#39;) As YouTube advertisement cost increases, sales also increase – they are positively correlated! Now with the linear model lm function, let’s create a line of best fit using the least sum of square method. # Fit linear regression # By default it include an incepter, so it is equvialent to add &quot;+ 1&quot; # res.lm &lt;- lm(sales ~ youtube + 1, data = marketing) res.lm &lt;- lm(sales ~ youtube, data = marketing) In the above code, we used lm to fit our simple linear regression model. This takes the formula y ~ X, where X is the predictor variable (YouTube advertising costs) and y is the output variable (Sales). Then, this function will return fitted model via a ordinary least squares (OLS) method. The res.lm is a list, you can get the it attributes by e.g., res.lm$coefficients res.lm$coefficients #&gt; (Intercept) youtube #&gt; 8.43911226 0.04753664 In the notation that we have been using, \\(\\alpha\\) is the intercept and \\(\\beta\\) is the slope i.e.: \\(\\alpha = 8.439, \\quad \\beta = 0.048\\) Thus, the equation for the model will be: \\(\\text{Sales} = 8.439 + 0.048*\\text{YouTube}\\) Let’s also check an indicator of the model efficacy, R2. Luckily, summary function can calculate it from the lm output and gives us a ready-made method for doing this so we don’t need to code all the math ourselves: res_summary = summary(res.lm) # Again, res_summary is also a list res_summary$r.squared #&gt; [1] 0.6118751 We can also take a look at the model summary by writing this snippet: # Print out the summary summary(res.lm) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ youtube, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -10.0632 -2.3454 -0.2295 2.4805 8.6548 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 8.439112 0.549412 15.36 &lt;2e-16 *** #&gt; youtube 0.047537 0.002691 17.67 &lt;2e-16 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.91 on 198 degrees of freedom #&gt; Multiple R-squared: 0.6119, Adjusted R-squared: 0.6099 #&gt; F-statistic: 312.1 on 1 and 198 DF, p-value: &lt; 2.2e-16 There is a lot here. Of these results, we have discussed: R-squared F-statistic Prob (F-statistic) - this is the p-value of the F-statistic Intercept coef - this is alpha YouTub coef - this is beta for predictor YouTub P&gt;|t| - this is the p-value for our coefficients Now that we’ve fit a simple regression model, we can try to predict the values of sales based on the equation we just derived! sales_pred = predict(res.lm, newdata = marketing[c(&#39;youtube&#39;)]) marketing[&#39;sales_pred&#39;] = sales_pred The predict fucntion predicts sales value for each row based on the model equation using YouTub costs. This is the equivalent of manually typing out our equation: sales_pred = 8.439 + 0.048*(advert['youtube']). We can visualise our regression model by plotting sales_pred against the YouTube advertising costs to find the line of best fit: library(ggplot2) ggplot(marketing, aes(x=youtube)) + geom_point(aes(y=sales), colour=&quot;black&quot;) + geom_line(aes(y=sales_pred), colour=&quot;red&quot;) + ggtitle(&#39;YouTube vs Sales&#39;) In the next step, we will add more features as predictors and see whether it improves our model. Go to the the notebook called 02-linearReg-05.Rmd. 3.5 Multiple Regression with lm function A multiple linear regression is simply a linear regression that involves more than one predictor variable. It is represented as: \\[\\qquad Y_e = \\alpha + \\beta_1*X_1 + \\beta_2*X_2 + \\dots + \\beta_p*X_p\\] Each βi will be estimated using the least sum of squares method. The data set is \\[ \\begin{array} {~~} Y_1, &amp; X_1^{(1)}, &amp; \\ldots, &amp; X_p^{(1)} \\\\ Y_2, &amp; X_1^{(2)}, &amp; \\ldots, &amp; X_p^{(2)} \\\\ \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\ Y_n, &amp; X_1^{(n)}, &amp; \\ldots, &amp; X_p^{(n)} \\end{array} \\] For each sample \\(i\\), the predicted value by the model is: \\(\\qquad Y_{i,e} = \\alpha + \\beta_1*X_1^{(i)} + \\beta_2*X_2^{(i)} + \\dots + \\beta_p*X_p^{(i)}\\) Define the sum of squares \\[ S(\\alpha,\\beta_1,\\ldots,\\beta_p) = \\sum_{i=1}^n \\left\\{ Y_i -Y_{i,e}\\right\\}^2 =\\sum_{i=1}^n \\left\\{ Y_i -\\left( \\alpha + \\beta_1*X_1^{(i)} + \\beta_2*X_2^{(i)} + \\dots + \\beta_p*X_p^{(i)}\\right)\\right\\}^2 \\] Least squares estimators: solve \\[ \\frac{\\partial S(\\alpha,\\beta_1,\\ldots,\\beta_p)}{\\partial \\alpha}=0,\\quad \\frac{\\partial S (\\alpha,\\beta_1,\\ldots,\\beta_p)}{\\partial \\beta_1}=0,\\quad \\ldots,\\quad \\frac{\\partial S (\\alpha,\\beta_1,\\ldots,\\beta_p)}{\\partial \\beta_p}=0. \\] to obtain the least squares estimators of the parameters \\[ \\hat\\alpha, \\hat\\beta_1,\\ldots,\\hat\\beta_p. \\] Note that be definition, \\[ SSE = S(\\hat\\alpha, \\hat\\beta_1,\\ldots,\\hat\\beta_p). \\] In other words, the fitted SSE (sum of squares error) is the minimized value of the sum squares with the estimated values of the parameters. The more varibles, the smaller the \\(R^2\\) Consider two regression models \\(\\quad ~ Y_e = \\alpha + \\beta_1*X_1\\) \\(\\quad \\tilde Y_e = \\alpha + \\beta_1*X_1 + \\beta_2*X_2\\) The model (II) has one more input variable \\(X_2\\). The \\(SSE_I\\) of Model (I) is the minimum of \\[ S_I(\\alpha,\\beta_1) = \\sum_{i=1}^n \\left\\{ Y_i -\\left( \\alpha + \\beta_1*X_1^{(i)} \\right)\\right\\}^2 \\] over all possible values of \\((\\alpha,\\beta_1)\\). The \\(SSE_{II}\\) of Model (II) is the minimum of \\[ S_{II}(\\alpha,\\beta_1,\\beta_2) = \\sum_{i=1}^n \\left\\{ Y_i -\\left( \\alpha + \\beta_1*X_1^{(i)} +\\beta_2*X_2^{(i)} \\right)\\right\\}^2. \\] over all possible values of \\((\\alpha,\\beta_1,\\beta_2)\\). Because \\(\\quad S_I(\\alpha,\\beta_1) = S_{II}(\\alpha,\\beta_1,\\beta_2=0 )\\), we find that \\(SSE_{II}\\le SSE_I\\), so \\[ R^2_{II} = SST - SSE_{II} \\ge SST - SSE_{I} = R^2_{I}. \\] With this simple dataset of three predictor variables, there can be seven possible models: Sales ~ YouTube Sales ~ Newspaper Sales ~ Facebook Sales ~ YouTube + Facebook Sales ~ YouTube + Newspaper Sales ~ Newspaper + Facebook Sales ~ YouTube + Facebook + Newspaper Generally, if there are p possible predictor variables, there can be (2p - 1) possible models – this can get large very quickly! Thankfully, there are a few guidelines to filter some of these and then navigate towards the most efficient one. Keep variables with low p-values and eliminate ones with high p-values Keep variables that increase the value of adjusted-R2 – this penalizes the model for adding insignificant variables and increases when we add significant variables. It is calculated by: \\[ R^2_{adj} = 1- (1-R^2) \\frac{n-1}{n-p-1}\\] Based on these guidelines, there are two approaches to select the predictor variables in the final model: Forward selection: start with a null model (no predictors), then add predictors one by one. If the p-value for the variable is small enough and the value of the adjusted-R2 goes up, the predictor is included in the model. Otherwise, it is not included. Backward selection: starts with a model that has all the possible predictors and discard some of them. If the p-value of a predictor variable is large and adjusted-R2 is lower when removed, it is discarded from the model. Otherwise, it remains a part of the model. Many statistical programs give us an option to select from these approaches while implementing multiple linear regression. For now, let’s manually add a few variables and see how it changes the model parameters and efficacy. First, add the newspaper variable to the model: library(datarium) data(marketing) head(marketing) #&gt; youtube facebook newspaper sales #&gt; 1 276.12 45.36 83.04 26.52 #&gt; 2 53.40 47.16 54.12 12.48 #&gt; 3 20.64 55.08 83.16 11.16 #&gt; 4 181.80 49.56 70.20 22.20 #&gt; 5 216.96 12.96 70.08 15.48 #&gt; 6 10.44 58.68 90.00 8.64 res_lm2 = lm(sales ~ youtube + newspaper, data=marketing) summary(res_lm2) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ youtube + newspaper, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -10.3477 -2.0815 -0.1138 2.2711 10.1415 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 6.929938 0.630405 10.993 &lt; 2e-16 *** #&gt; youtube 0.046901 0.002581 18.173 &lt; 2e-16 *** #&gt; newspaper 0.044219 0.010174 4.346 2.22e-05 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.745 on 197 degrees of freedom #&gt; Multiple R-squared: 0.6458, Adjusted R-squared: 0.6422 #&gt; F-statistic: 179.6 on 2 and 197 DF, p-value: &lt; 2.2e-16 As you see, the p-values for the coefficients are very small, suggesting that all the estimates are significant. The equation for this model will be: \\[ \\text{Sales} = 6.93+0.046* \\text{YouTube} + 0.044 * \\text{Newspaper}\\] The values of R2 and adjusted R2 are 0.646 and 0.642, which is just a minor improvement from before (0.612 and 0.610, respectively). Similarly for RSE (3.745). Only a small decrease in RSE and error… Let’s take a closer look at the summary above. The Adj-R2 increases slightly, but the F-statistic decreases (from 312.1 to 179.6), as does the associated p-value. This suggests that adding newspaper didn’t improve the model significantly. Let’s try adding facebook instead: # Initialise and fit new model with TV and Radio as predictors # model3 = smf.ols(&#39;Sales ~ TV + Radio&#39;, data=advert).fit() # print(model3.summary()) res_lm3 = lm(sales ~ youtube + facebook, data=marketing) summary(res_lm3) #&gt; #&gt; Call: #&gt; lm(formula = sales ~ youtube + facebook, data = marketing) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -10.5572 -1.0502 0.2906 1.4049 3.3994 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 3.50532 0.35339 9.919 &lt;2e-16 *** #&gt; youtube 0.04575 0.00139 32.909 &lt;2e-16 *** #&gt; facebook 0.18799 0.00804 23.382 &lt;2e-16 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 2.018 on 197 degrees of freedom #&gt; Multiple R-squared: 0.8972, Adjusted R-squared: 0.8962 #&gt; F-statistic: 859.6 on 2 and 197 DF, p-value: &lt; 2.2e-16 This gives us the model: \\[ \\text{Sales} = 3.51+0.046* \\text{YouTube} + 0.188 * \\text{Facebook}\\] The adjusted R2 value has improved considerably, as did the RSE and F-statistic, indicating an efficient model. Thus, we can conclude that facebook is a great addition to the model. YouTube and facebook advertising costs together are able to predict sales well. But, can we improve it a bit further by combining all three predictor variables? Try it out: see if you can figure out how to do this on your own! # Initialise and fit new model with TV, Newspaper, and Radio as predictors # Print summary of regression results # Calculate RSE - don&#39;t forget that the number of predictors p is now 3 You should get the equation: \\[ \\text{Sales} = 3.53+0.046*\\text{YouTube} -0.001*\\text{Newspaper} +0.188*\\text{Facebook}\\] You should also find that: RSE increases slightly, the coefficient for newspaper is negative, and the F-statistic decreases considerably from 859.6 to 570.3. All these suggest that the model actually became less efficient on addition of newspaper. Why? This step shows clearly that adding one more input variable Newspaper in Model 3 does not lead to any improvement. "],["introClassifier.html", "Chapter 4 Introduction to Classification 4.1 Visualise logistic and logit functions 4.2 Logistic regression on Diabetes 4.3 Cross-validation 4.4 More assessment metrics", " Chapter 4 Introduction to Classification 4.1 Visualise logistic and logit functions In this chapter, we will focus on logistic regression for classification. Let’s first look at what logistic and logit function look like. 4.1.1 Logistic function Let’s write our first function logestic() as follows. # Write your first function logistic &lt;- function(y) { exp(y) / (1 + exp(y)) } # Try it with different values: logistic(0.1) #&gt; [1] 0.5249792 logistic(c(-3, -2, 0.5, 3, 5)) #&gt; [1] 0.04742587 0.11920292 0.62245933 0.95257413 0.99330715 This is the equivalent to the built-in plogis() function in the stat package for the logistic distribution: plogis(0.1) #&gt; [1] 0.5249792 plogis(c(-3, -2, 0.5, 3, 5)) #&gt; [1] 0.04742587 0.11920292 0.62245933 0.95257413 0.99330715 4.1.2 Logit function Now, let look at the logistic’s inverse function logit(), and let’s define it manually. Note, this function only support input between 0 and 1. # Write your first function logit &lt;- function(x) { log(x / (1 - x)) } # Try it with different values: logit(0.4) #&gt; [1] -0.4054651 logit(c(0.2, 0.3, 0.5, 0.7, 0.9)) #&gt; [1] -1.3862944 -0.8472979 0.0000000 0.8472979 2.1972246 logit(c(-1, 2, 0.4)) #&gt; Warning in log(x/(1 - x)): NaNs produced #&gt; [1] NaN NaN -0.4054651 Again, the built-in stat package’s logistic distribution has an equivalent function qlogis(), though with a different name. qlogis(0.4) #&gt; [1] -0.4054651 qlogis(c(0.2, 0.3, 0.5, 0.7, 0.9)) #&gt; [1] -1.3862944 -0.8472979 0.0000000 0.8472979 2.1972246 qlogis(c(-1, 2, 0.4)) #&gt; Warning in qlogis(c(-1, 2, 0.4)): NaNs produced #&gt; [1] NaN NaN -0.4054651 4.1.3 Visualise the distribution Logisitc function # You can use seq() function to generate a vector # Check how to use it by help(seq) or ?seq x = seq(-7, 7, 0.3) df = data.frame(&#39;x&#39;=x, &#39;logistic&#39;=plogis(x)) # You can plot by plot function # plot(x=df$x, y=df$logistic, type=&#39;o&#39;) # Or ggplot2 library(ggplot2) ggplot(df, aes(x=x, y=logistic)) + geom_point() + geom_line() Logit function x = seq(0.001, 0.999, 0.01) df = data.frame(&#39;x&#39;=x, &#39;logit&#39;=qlogis(x)) ggplot(df, aes(x=x, y=logit)) + geom_point() + geom_line() 4.2 Logistic regression on Diabetes 4.2.1 Load Pima Indians Diabetes Database This dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. The objective of the dataset is to diagnostically predict whether or not a patient has diabetes, based on certain diagnostic measurements included in the dataset. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage. The datasets consist of several medical predictor (independent) variables and one target (dependent) variable, Outcome. Independent variables include the number of pregnancies the patient has had, their BMI, insulin level, age, and so on. Acknowledgement: This notebook is adapted and updated from STAT1005. # Install the mlbench library for loading the datasets if (!requireNamespace(&quot;mlbench&quot;, quietly = TRUE)) { install.packages(&quot;mlbench&quot;) } # Load data library(mlbench) data(PimaIndiansDiabetes) # Check the first few lines dim(PimaIndiansDiabetes) #&gt; [1] 768 9 head(PimaIndiansDiabetes) #&gt; pregnant glucose pressure triceps insulin mass pedigree age diabetes #&gt; 1 6 148 72 35 0 33.6 0.627 50 pos #&gt; 2 1 85 66 29 0 26.6 0.351 31 neg #&gt; 3 8 183 64 0 0 23.3 0.672 32 pos #&gt; 4 1 89 66 23 94 28.1 0.167 21 neg #&gt; 5 0 137 40 35 168 43.1 2.288 33 pos #&gt; 6 5 116 74 0 0 25.6 0.201 30 neg Now, let’s check two potential features: glucose and age, colored by the diabetes labels. library(ggplot2) ggplot(data=PimaIndiansDiabetes, aes(x=glucose, y=age)) + geom_point(aes(color=diabetes)) Before we start fit models, let’s split the data into training and test sets in a 4:1 ratio. Let define it manually, though there are functions to do it automatically. set.seed(0) idx_train = sample(nrow(PimaIndiansDiabetes), size=0.75*nrow(PimaIndiansDiabetes), replace = FALSE) df_train = PimaIndiansDiabetes[idx_train, ] df_test = PimaIndiansDiabetes[-idx_train, ] # recall the meaning of negative symbol 4.2.2 Fit logistic regression In logistic regression, the predicted probability to be class 1 is: \\[P(y=1|X, W) = \\sigma(w_0, x_1 * w_1 + ... + x_p * w_p)\\] where the \\(\\sigma()\\) denotes the logistic function. In R, the built-in package stats already have functions to fit generalised linear model (GLM), including logistic regression, a type of GML. Here, let’s start with the whole dataset to fit a logistic regression. Note, we will specify the model family as binomial, as the likelihood we are using in logistic regression is a Bernoulli likelihood, a special case of binomial likelihood when the total trial n=1. # Define formula in different ways # my_formula = as.formula(diabetes ~ glucose + age) # my_formula = as.formula(paste(colnames(PimaIndiansDiabetes)[1:8], collapse= &quot; + &quot;)) # my_formula = as.formula(diabetes ~ .) # Fit logistic regression glm_res &lt;- glm(diabetes ~ ., data=df_train, family = binomial) # We can use the logLik() function to obtain the log likelihood logLik(glm_res) #&gt; &#39;log Lik.&#39; -281.9041 (df=9) We can use summary() function to see more details about the model fitting. summary(glm_res) #&gt; #&gt; Call: #&gt; glm(formula = diabetes ~ ., family = binomial, data = df_train) #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error z value Pr(&gt;|z|) #&gt; (Intercept) -8.044602 0.826981 -9.728 &lt; 2e-16 *** #&gt; pregnant 0.130418 0.036080 3.615 0.000301 *** #&gt; glucose 0.032196 0.004021 8.007 1.18e-15 *** #&gt; pressure -0.017158 0.006103 -2.811 0.004934 ** #&gt; triceps -0.003425 0.007659 -0.447 0.654752 #&gt; insulin -0.001238 0.001060 -1.169 0.242599 #&gt; mass 0.104029 0.018119 5.741 9.39e-09 *** #&gt; pedigree 0.911030 0.344362 2.646 0.008156 ** #&gt; age 0.012980 0.010497 1.237 0.216267 #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; (Dispersion parameter for binomial family taken to be 1) #&gt; #&gt; Null deviance: 756.83 on 575 degrees of freedom #&gt; Residual deviance: 563.81 on 567 degrees of freedom #&gt; AIC: 581.81 #&gt; #&gt; Number of Fisher Scoring iterations: 5 4.2.3 Assess on test data Now, we can evaluate the accuracy of the model on the 25% test data. # Train the full model on the training data glm_train &lt;- glm(diabetes ~ ., data=df_train, family = binomial) # Predict the probability of being diabeties on test data # We can also set a threshold, e.g., 0.5 for the predicted label pred_prob = predict(glm_train, df_test, type = &quot;response&quot;) pred_label = pred_prob &gt;= 0.5 # Observed label obse_label = df_test$diabetes == &#39;pos&#39; # Calculate the accuracy on test data # think how accuracy is defined # we can use (TN + TP) / (TN + TP + FN + FP) # we can also directly compare the proportion of correctness accuracy = mean(pred_label == obse_label) print(paste(&quot;Accuracy on test set:&quot;, accuracy)) #&gt; [1] &quot;Accuracy on test set: 0.796875&quot; 4.2.4 Model selection and diagnosis 4.2.4.1 Model2: New feature set by removing triceps # Train the full model on the training data glm_mod2 &lt;- glm(diabetes ~ pregnant + glucose + pressure + insulin + mass + pedigree + age, data=df_train, family = binomial) logLik(glm_mod2) #&gt; &#39;log Lik.&#39; -282.0038 (df=8) summary(glm_mod2) #&gt; #&gt; Call: #&gt; glm(formula = diabetes ~ pregnant + glucose + pressure + insulin + #&gt; mass + pedigree + age, family = binomial, data = df_train) #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error z value Pr(&gt;|z|) #&gt; (Intercept) -8.0317567 0.8251403 -9.734 &lt; 2e-16 *** #&gt; pregnant 0.1308094 0.0361230 3.621 0.000293 *** #&gt; glucose 0.0324606 0.0039854 8.145 3.80e-16 *** #&gt; pressure -0.0175651 0.0060269 -2.914 0.003563 ** #&gt; insulin -0.0014402 0.0009593 -1.501 0.133291 #&gt; mass 0.1018155 0.0173811 5.858 4.69e-09 *** #&gt; pedigree 0.9000134 0.3428652 2.625 0.008665 ** #&gt; age 0.0131238 0.0105147 1.248 0.211982 #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; (Dispersion parameter for binomial family taken to be 1) #&gt; #&gt; Null deviance: 756.83 on 575 degrees of freedom #&gt; Residual deviance: 564.01 on 568 degrees of freedom #&gt; AIC: 580.01 #&gt; #&gt; Number of Fisher Scoring iterations: 5 # Predict the probability of being diabeties on test data # We can also set a threshold, e.g., 0.5 for the predicted label pred_prob2 = predict(glm_mod2, df_test, type = &quot;response&quot;) pred_label2 = pred_prob2 &gt;= 0.5 accuracy2 = mean(pred_label2 == obse_label) print(paste(&quot;Accuracy on test set with model2:&quot;, accuracy2)) #&gt; [1] &quot;Accuracy on test set with model2: 0.807291666666667&quot; 4.2.4.2 Model3: New feature set by removing triceps and insulin # Train the full model on the training data glm_mod3 &lt;- glm(diabetes ~ pregnant + glucose + pressure + mass + pedigree + age, data=df_train, family = binomial) logLik(glm_mod3) #&gt; &#39;log Lik.&#39; -283.1342 (df=7) summary(glm_mod3) #&gt; #&gt; Call: #&gt; glm(formula = diabetes ~ pregnant + glucose + pressure + mass + #&gt; pedigree + age, family = binomial, data = df_train) #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error z value Pr(&gt;|z|) #&gt; (Intercept) -7.797803 0.802287 -9.719 &lt; 2e-16 *** #&gt; pregnant 0.130990 0.035957 3.643 0.00027 *** #&gt; glucose 0.030661 0.003755 8.164 3.23e-16 *** #&gt; pressure -0.017847 0.005953 -2.998 0.00272 ** #&gt; mass 0.097356 0.016969 5.737 9.61e-09 *** #&gt; pedigree 0.824150 0.338299 2.436 0.01484 * #&gt; age 0.015134 0.010426 1.452 0.14663 #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; (Dispersion parameter for binomial family taken to be 1) #&gt; #&gt; Null deviance: 756.83 on 575 degrees of freedom #&gt; Residual deviance: 566.27 on 569 degrees of freedom #&gt; AIC: 580.27 #&gt; #&gt; Number of Fisher Scoring iterations: 5 # Predict the probability of being diabeties on test data # We can also set a threshold, e.g., 0.5 for the predicted label pred_prob3 = predict(glm_mod3, df_test, type = &quot;response&quot;) pred_label3 = pred_prob3 &gt;= 0.5 accuracy3 = mean(pred_label3 == obse_label) print(paste(&quot;Accuracy on test set with model3:&quot;, accuracy3)) #&gt; [1] &quot;Accuracy on test set with model3: 0.786458333333333&quot; 4.3 Cross-validation In last section, we split the whole dataset into 75% for training and 25% for testing. However, when the dataset is small, the test set may not be big enough and introduce high variance on the assessment. One way to reduce this variance in assessment is performing cross-validation, where we split the data into K folds and use K-1 folds for training and the remaining fold for testing. This procedure will be repeated for fold 1 to fold K as testing fold and all folds will be aggregated for joint assessment. K is usually taken 3, 5 or 10. In extreme case that K=n_sample, we call it leave-one-out cross-validation (LOOCV). Let’s load the dataset (again) first. # Load data library(mlbench) data(PimaIndiansDiabetes) Besides implement the cross-validation from scratch, there are packages supporting it well, including caret package. We will install it and use it for cross-validation here. # Install the caret library for cross-validation if (!requireNamespace(&quot;caret&quot;, quietly = TRUE)) { install.packages(&quot;caret&quot;) } library(caret) # Define training control # We also want to have savePredictions=TRUE &amp; classProbs=TRUE set.seed(0) my_trControl &lt;- trainControl(method = &quot;cv&quot;, number = 5, classProbs = TRUE, savePredictions = TRUE) # Train the model cv_model &lt;- train(diabetes ~ ., data = PimaIndiansDiabetes, method = &quot;glm&quot;, family=binomial(), trControl = my_trControl) # Summarize the results print(cv_model) #&gt; Generalized Linear Model #&gt; #&gt; 768 samples #&gt; 8 predictor #&gt; 2 classes: &#39;neg&#39;, &#39;pos&#39; #&gt; #&gt; No pre-processing #&gt; Resampling: Cross-Validated (5 fold) #&gt; Summary of sample sizes: 615, 614, 615, 614, 614 #&gt; Resampling results: #&gt; #&gt; Accuracy Kappa #&gt; 0.7708344 0.4695353 We can also access to detailed prediction results after concatenating the K folds: head(cv_model$pred) #&gt; pred obs neg pos rowIndex parameter Resample #&gt; 1 neg neg 0.9656694 0.03433058 4 none Fold1 #&gt; 2 neg neg 0.8581071 0.14189290 6 none Fold1 #&gt; 3 neg pos 0.9508306 0.04916940 7 none Fold1 #&gt; 4 neg pos 0.6541361 0.34586388 17 none Fold1 #&gt; 5 neg pos 0.7675666 0.23243342 20 none Fold1 #&gt; 6 neg pos 0.6132685 0.38673152 26 none Fold1 We can double check the accuracy: CV_acc = mean(cv_model$pred$pred == cv_model$pred$obs) print(paste(&quot;Accuracy via 5-fold cross-validation&quot;, CV_acc)) #&gt; [1] &quot;Accuracy via 5-fold cross-validation 0.770833333333333&quot; 4.4 More assessment metrics 4.4.1 Two types of error In the above sections, we used the accuracy to perform model diagnosis, either only on one testing dataset or aggregating cross multiple folds in cross- validation. Accuracy is a widely used metric for model evaluation, on the averaged error rate. However, this metric still have limitations when assessing the model performance, especially the following two: When the samples are highly imbalance, high accuracy may not mean a good model. For example, for a sample with 990 negative samples and 10 positive samples, a simple model by predicting for all sample as negative will give an accuracy of 0.99. Thus, for highly imbalanced samples, we should be careful when interpreting the accuracy. In many scenarios, our tolerance on false positive errors and false negative errors may be different and we want to know both for a certain model. They are often called as type I and II errors: Type I error: false positive (rate) Type II error: false negative (rate) - a joke way to remember what type II mean Negative has two stripes. Here, we use the diabetes dataset and their cross-validation results above to illustrate the two types of errors and the corresponding model performance evaluation. # Let&#39;s start to define the values for the confusion matrix first # Recall what the difference between &amp; vs &amp;&amp; # Read more: https://stat.ethz.ch/R-manual/R-devel/library/base/html/Logic.html TP = sum((cv_model$pred$obs == &#39;pos&#39;) &amp; (cv_model$pred$pred == &#39;pos&#39;)) FN = sum((cv_model$pred$obs == &#39;pos&#39;) &amp; (cv_model$pred$pred == &#39;neg&#39;)) FP = sum((cv_model$pred$obs == &#39;neg&#39;) &amp; (cv_model$pred$pred == &#39;pos&#39;)) TN = sum((cv_model$pred$obs == &#39;neg&#39;) &amp; (cv_model$pred$pred == &#39;neg&#39;)) print(paste(&#39;TP, FN, FP, TN:&#39;, TP, FN, FP, TN)) #&gt; [1] &quot;TP, FN, FP, TN: 151 117 59 441&quot; We can also use the table() function to get the whole confusion matrix. Read more about the table function for counting the frequency of each element. A similar way is the confusionMatrix() in caret package. # Calculate confusion matrix confusion_mtx = table(cv_model$pred[, c(&quot;obs&quot;, &quot;pred&quot;)]) confusion_mtx #&gt; pred #&gt; obs neg pos #&gt; neg 441 59 #&gt; pos 117 151 # similar function confusionMatrix # conf_mat = confusionMatrix(cv_model$pred$pred, cv_model$pred$obs) # conf_mat$table We can also plot out the confusion matrix # Change to data.frame before using ggplot confusion_df = as.data.frame(confusion_mtx) ggplot(confusion_df, aes(pred, obs, fill= Freq)) + geom_tile() + geom_text(aes(label=Freq)) + scale_fill_gradient(low=&quot;white&quot;, high=&quot;darkgreen&quot;) Also the false positive rate, false negative rate and true negative rate. Note, the denominator is always the number of observed samples with the same label, namely they are a constant for a specific dataset. FPR = FP / sum(cv_model$pred$obs == &#39;neg&#39;) FNR = FN / sum(cv_model$pred$obs == &#39;pos&#39;) TPR = TP / sum(cv_model$pred$obs == &#39;pos&#39;) print(paste(&quot;False positive rate:&quot;, FPR)) #&gt; [1] &quot;False positive rate: 0.118&quot; print(paste(&quot;False negative rate:&quot;, FNR)) #&gt; [1] &quot;False negative rate: 0.436567164179104&quot; print(paste(&quot;True positive rate:&quot;, TPR)) #&gt; [1] &quot;True positive rate: 0.563432835820896&quot; 4.4.2 ROC curve In the above assessment, we only used \\(P&gt;0.5\\) to denote predicted label as positive. We can imagine if we a lower cutoff lower, we will have more false positives and fewer false negatives. Indeed, in different scenarios, people may choose different level of cutoff for their tolerance of different types of errors. Let’s try cutoff \\(P&gt;0.4\\). Think what will you expect. # Original confusion matrix table(cv_model$pred[, c(&quot;obs&quot;, &quot;pred&quot;)]) #&gt; pred #&gt; obs neg pos #&gt; neg 441 59 #&gt; pos 117 151 # New confusion matrix with cutoff 0.4 cv_model$pred$pred_new = as.integer(cv_model$pred$pos &gt;= 0.4) table(cv_model$pred[, c(&quot;obs&quot;, &quot;pred_new&quot;)]) #&gt; pred_new #&gt; obs 0 1 #&gt; neg 408 92 #&gt; pos 89 179 Therefore, we may want to assess the model performance by varying the cutoffs and obtain a more systematic assessment. Actually, the Receiver operating characteristic (ROC) curve is what you need. It presents the TPR (sensitivity) vs the FPR (i.e., 1 - TNR or 1 - specificity) when varying the cutoffs. In order to achieve this, we can calculate FPR and TPR manually by varying the cutoff through a for loop. Read more about for loop and you may try write your own and here is an example from the cardelino package. For simplicity, let use an existing tool implemented in the plotROC package: plotROC::geom_roc() that is compatible with ggplot2. # Install the plotROC library for plotting ROC curve if (!requireNamespace(&quot;plotROC&quot;, quietly = TRUE)) { install.packages(&quot;plotROC&quot;) } library(ggplot2) library(plotROC) # You can set the n.cuts to show the cutoffs on the curve g = ggplot(cv_model$pred, aes(m = pos, d = as.integer(obs==&#39;pos&#39;))) + geom_roc(n.cuts=7, hjust = -0.4, vjust = 1.5) + coord_equal() + ggtitle(&quot;ROC curve&quot;) # Calculate AUC from the graph AUC_val = calc_auc(g)$AUC #&gt; Warning: The following aesthetics were dropped during statistical transformation: m, d #&gt; ℹ This can happen when ggplot fails to infer the correct grouping structure in #&gt; the data. #&gt; ℹ Did you forget to specify a `group` aesthetic or to convert a numerical #&gt; variable into a factor? # Display the plot g + annotate(&quot;text&quot;, x=0.8, y=0.1, label=paste(&quot;AUC =&quot;, round(AUC_val, 4))) #&gt; Warning: The following aesthetics were dropped during statistical transformation: m, d #&gt; ℹ This can happen when ggplot fails to infer the correct grouping structure in #&gt; the data. #&gt; ℹ Did you forget to specify a `group` aesthetic or to convert a numerical #&gt; variable into a factor? 4.4.3 Homework Now, try another model with removing triceps and plot the ROC curve and calculate the AUC score. Is it higher or lower than using the full features? "],["image-digital.html", "Chapter 5 Medical Image and Digital Health", " Chapter 5 Medical Image and Digital Health Contents to be added. "],["cancer.html", "Chapter 6 Cancer genomics and epidemiology 6.1 Case study 1: analysis of cBioportal mutation data 6.2 Case study 2: Cancer Epidemiology 6.3 1. Scenario 6.4 2. Hong Kong population 6.5 3. Cancer registry data 6.6 4. Existing cancer funding and publication data 6.7 5. Open disucssion", " Chapter 6 Cancer genomics and epidemiology 6.1 Case study 1: analysis of cBioportal mutation data Non-small cell lung cancer is a deadly disease, and we would like to identify mutations in genes that drive its formation and progression. George et al. (2015) has sequenced 120 small cell lung cancer samples and this data is available from cBioportal. The original data is in the MAF, and we have selected a subset of the columns, normalized the column names, and made the data available as an RDS file. In this exercise, we will explore the mutation data and examine genes that are frequently mutated in non-small cell lung cancer samples. We will implement a simple method for identifying candidate tumour suppressors based on loss-of-function mutations. 6.1.1 Exploratory analysis Q1. Load the data named mutations_sclc_ucologne_2015.rds into R. Examine it using head. In this data.frame, each row is a mutation detected in a particular gene from a particular sample in the study. For more information on the columns, see the MAF specification. ?readRDS ?head Q2. Identify the top 10 most frequently mutated genes. # calculate count frequencies using table ?table # freqs &lt;- ??? # sort the frequency vector in decreasing order ?sort # freqs &lt;- ??? # select the first 10 genes in the freqs # freqs.top &lt;- ??? # obtain the gene names # genes &lt;- names(freqs.top); # print(freqs.top) Q3. Tabulate the count frequencies of variant_class. What proportion of variants are Silent or inside an Intron? ?table Q4. A variant class value frame_shift_del appears to be misspelt due to case sensitivity. Correct this error. # x$variant_class[x$variant_class == &quot;frame_shift_del&quot;] &lt;- ???; Q5. To help us simplify the variant classes into loss-of-function or neutral, let us import the mutation_effects.tsv data. ?read.table # Hint: You need to set the `header` and `sep` arguments Q6. Define a new column in x that converts the variant classes to effects. ?match Q7. Create a subset of the data for the most frequently mutated genes, and tabulate the mutation count frequencies of variant classes for each gene. # x.sub &lt;- x[???, ] # order the factor levels based on `genes`, # which was previously sorted in decreasing order of frequency # x.sub$gene &lt;- factor(x.sub$gene, levels=genes); ?table Q8. Determine the number of mutations in each effect category, across all genes. Save the result in a variable named overall.counts. # overall.counts &lt;- table(???); # overall.counts Q9. Tabulate the mutation count frequencies for each gene and effect. Save the results in a variable named gene.counts. Look up the frequently mutated genes in this matrix. # gene.counts &lt;- table(???, ???); # gene.counts[???, ] 6.1.2 Statistical analysis Here, we implemented a simple statistical test for assessing whether a gene is significantly frequently targeted by loss-of-function mutations, based on the Fisher’s exact test. # Test whether a query gene has significantly more loss-of-function # mutations compared with other genes. # Requires global variables `gene.counts` and `overall.counts` lof_test &lt;- function(gene) { # Construct the following contingency table: # neutral lof # other genes a b # query gene c d cols &lt;- c(&quot;neutral&quot;, &quot;loss_of_function&quot;); gene.counts.sel &lt;- gene.counts[gene, cols]; ct &lt;- matrix( c( overall.counts[cols] - gene.counts.sel, gene.counts.sel ), byrow=TRUE, ncol=2 ); # Test whether the lof mutations are greater in frequency compared # to neutral mutations in the query gene, in comparison to all other genes fisher.test(ct, alternative=&quot;greater&quot;) } Q10. Subset the gene.counts table for the TP53 gene. Run lof_test on this gene. # gene.counts[???, ] # lof_test(???) Q11. Now, test to see if TTN and MUC16 are significantly frequently targeted by loss-of-function mutations. # similar to above Q12. Apply the loss-of-function test to all frequently mutated genes. ?lapply Q13. Extract odds ratio and p-values from the test results. # odds.ratios &lt;- vapply(hs, function(h) h$estimate, 0); # ps &lt;- vapply(hs, function(h) ???, 0); Q14. Since we tested many genes, we need to adjust for multiple hypothesis testing so that we can control the false discovery rate. So, adjust the p-values to obtain q-values. ?p.adjust Q15. Construct a results data.frame with gene names, odds ratio, p-values, and q-values that summarize the loss-of-function test results. # res &lt;- data.frame( # gene = ???, # odds_ratio = ???, # p = ???, # q = ??? # ); ?order #res &lt;- res[order(???), ]; Q16. Identify the significant genes from the results data.frame at a false discovery rate of 5% (i.e. q-value threshold of 0.05). Q17. Look up the significant genes in the gene.counts matrix. 6.1.3 Literature search Q18. Do the significant genes appear to be involved in cancer? What general roles do they play? Q19. How do these genes contribute specifically to the formation or progression of small cell lung cancer? Q20. What are some possible ways of identifying oncogenes that are activated by mutations or other genomic alterations? 6.2 Case study 2: Cancer Epidemiology by Dr Jason Wong Date: 6-11-2023 The RMarkdown notebook to run your own code can be downloaded here 6.3 1. Scenario You are a grants officer working for the Hong Kong Health Bureau. The HK government has recently announced new special funding in cancer research to be administered by the Bureau. You are tasked with coming up with a proposal for distribution of funding to specific cancer types that are in most need of research. Discussion points: What is important to consider when selecting a cancer type in need of research? What type of data is required? 6.4 2. Hong Kong population You are aware that generally cancer is disease that affects the elderly more than the young. You decide to first take a closer look at the structure of the population of Hong Kong. Historic population of Hong Kong can be obtained from the Census and Statistics Department. An abridged version of the full historic population of Hong Kong is provided here containing the population of Hong Kong from 1965, 1975, 1985, 1995, 2005, 2015 and 2022 categorised by sex and age (0-19, 20-44, 45-64, 65+). Discussion points: What is the trend in Hong Kong’s population over the past ~60 years? What is the best way to visualise this data? 6.4.1 Download population data HKPop&lt;- read.table(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HK_population_1965-2022.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = FALSE) HKPop #&gt; Sex Age 1965 1975 1985 1995 2005 2015 2022 #&gt; 1 male 0-19 901.9 989.7 909.0 835.6 719.0 613.8 530.6 #&gt; 2 male 20-44 607.4 795.6 1210.2 1363.7 1263.7 1146.9 1039.2 #&gt; 3 male 45-64 266.5 414.3 525.9 615.7 896.6 1084.9 1046.2 #&gt; 4 male 65+ 42.2 84.6 170.5 269.3 384.7 520.0 713.6 #&gt; 5 female 0-19 865.6 938.8 840.3 780.7 684.1 575.0 502.1 #&gt; 6 female 20-44 539.3 685.6 1093.7 1423.6 1530.4 1531.8 1338.7 #&gt; 7 female 45-64 286.3 400.7 470.7 535.0 884.7 1224.3 1314.7 #&gt; 8 female 65+ 88.7 152.3 235.9 332.5 450.0 594.6 806.5 6.4.2 Format data for plotting Here we convert the original dataframe into simplified format for ggplot2. male&lt;-data.frame(year = as.numeric(colnames(HKPop[1,3:9])), `0-19` = as.numeric(HKPop[1,3:9]), `20-44` = as.numeric(HKPop[2,3:9]), `45-64` = as.numeric(HKPop[3,3:9]), `65+` = as.numeric(HKPop[4,3:9]), check.names = FALSE) female&lt;-data.frame(year = as.numeric(colnames(HKPop[1,3:9])), `0-19` = as.numeric(HKPop[5,3:9]), `20-44` = as.numeric(HKPop[6,3:9]), `45-64` = as.numeric(HKPop[7,3:9]), `65+` = as.numeric(HKPop[8,3:9]), check.names = FALSE) if (!require(&quot;tidyverse&quot;)) install.packages(&quot;tidyverse&quot;) male&lt;-as_tibble(male) %&gt;% select(year,`0-19`,`20-44`,`45-64`,`65+`) %&gt;% gather (key=&quot;age&quot;,value=&quot;population (&#39;000s)&quot;,-year) female&lt;-as_tibble(female) %&gt;% select(year,`0-19`,`20-44`,`45-64`,`65+`) %&gt;% gather (key=&quot;age&quot;,value=&quot;population (&#39;000s)&quot;,-year) male #&gt; # A tibble: 28 × 3 #&gt; year age `population (&#39;000s)` #&gt; &lt;dbl&gt; &lt;chr&gt; &lt;dbl&gt; #&gt; 1 1965 0-19 902. #&gt; 2 1975 0-19 990. #&gt; 3 1985 0-19 909 #&gt; 4 1995 0-19 836. #&gt; 5 2005 0-19 719 #&gt; 6 2015 0-19 614. #&gt; 7 2022 0-19 531. #&gt; 8 1965 20-44 607. #&gt; 9 1975 20-44 796. #&gt; 10 1985 20-44 1210. #&gt; # ℹ 18 more rows female #&gt; # A tibble: 28 × 3 #&gt; year age `population (&#39;000s)` #&gt; &lt;dbl&gt; &lt;chr&gt; &lt;dbl&gt; #&gt; 1 1965 0-19 866. #&gt; 2 1975 0-19 939. #&gt; 3 1985 0-19 840. #&gt; 4 1995 0-19 781. #&gt; 5 2005 0-19 684. #&gt; 6 2015 0-19 575 #&gt; 7 2022 0-19 502. #&gt; 8 1965 20-44 539. #&gt; 9 1975 20-44 686. #&gt; 10 1985 20-44 1094. #&gt; # ℹ 18 more rows 6.4.3 Plotting population data Uses ggplot2 and gridExtra to make line plot of male and female population data side-by-side. if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) library(ggplot2) library(gridExtra) #Import the necessary packages and libraries pmale&lt;-ggplot(male,aes(x=year,y=`population (&#39;000s)`,group=age))+ geom_line(aes(color=age))+ geom_point(aes(color=age))+ scale_color_brewer(palette=&quot;Spectral&quot;)+ theme_classic()+ ylim(0,1600)+ theme(legend.position=&quot;none&quot;)+ scale_x_continuous(breaks = seq(1965, 2022, by = 10))+ ggtitle(&quot;male&quot;) pfemale&lt;-ggplot(female,aes(x=year,y=`population (&#39;000s)`,group=age))+ geom_line(aes(color=age))+ geom_point(aes(color=age))+ scale_color_brewer(palette=&quot;Spectral&quot;)+ theme_classic()+ ylim(0,1600)+ theme(legend.position=&quot;right&quot;,axis.title.y = element_blank())+ scale_x_continuous(breaks = seq(1965, 2022, by = 10))+ ggtitle(&quot;female&quot;) grid.arrange(pmale,pfemale,ncol=2,widths=c(3,3.75)) 6.5 3. Cancer registry data It is clear that Hong Kong has an aging population, thus cancer incidence would also likely increase. To examine cancer incidence and mortality in Hong Kong you obtain data from the Hong Kong Cancer Registry, which is maintained by the Hospital Authority. Cancer incidence data was summarised for the last three decades (1990-1999, 2000-2009 and 2010-2019). Discussion points: Has incidence been increasing for most cancers? How about mortality? How has cancer risk and mortality rate changed in the past 3 decades? Has the incidence-to-mortality ratio been decreasing generally? Is it statistically significant? Which cancer type has the highest incidence in children (0-19) when compared with the elderly (65+). Is this statistically significantly different to incidence of children versus elderly cancers in general? 6.5.1 Download cancer registry data HKCancer&lt;- read.table(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HK_cancer_incidence_mortality_1990-2020.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE) HKCancer #&gt; Type Sex Age Year Biliary Bladder Brain Breast Cervix #&gt; 1 incidence male 0-19 1990-1999 0 6 212 0 0 #&gt; 2 incidence male 20-44 1990-1999 36 165 368 6 0 #&gt; 3 incidence male 45-64 1990-1999 322 1266 393 28 0 #&gt; 4 incidence male 65+ 1990-1999 830 2920 318 35 0 #&gt; 5 incidence male 0-19 2000-2009 0 2 206 0 0 #&gt; 6 incidence male 20-44 2000-2009 31 103 267 9 0 #&gt; 7 incidence male 45-64 2000-2009 297 900 372 52 0 #&gt; 8 incidence male 65+ 2000-2009 1134 3103 299 96 0 #&gt; 9 incidence male 0-19 2010-2019 0 2 155 0 0 #&gt; 10 incidence male 20-44 2010-2019 28 18 276 14 0 #&gt; 11 incidence male 45-64 2010-2019 530 648 511 72 0 #&gt; 12 incidence male 65+ 2010-2019 1568 2399 380 107 0 #&gt; 13 incidence female 0-19 1990-1999 0 2 149 6 0 #&gt; 14 incidence female 20-44 1990-1999 52 62 283 4228 1263 #&gt; 15 incidence female 45-64 1990-1999 246 246 238 5311 1839 #&gt; 16 incidence female 65+ 1990-1999 909 1199 284 4122 1574 #&gt; 17 incidence female 0-19 2000-2009 0 0 132 4 4 #&gt; 18 incidence female 20-44 2000-2009 34 39 223 5887 1204 #&gt; 19 incidence female 45-64 2000-2009 287 179 265 11833 1676 #&gt; 20 incidence female 65+ 2000-2009 1190 1090 237 5774 1329 #&gt; 21 incidence female 0-19 2010-2019 0 2 119 1 0 #&gt; 22 incidence female 20-44 2010-2019 36 17 223 6658 1294 #&gt; 23 incidence female 45-64 2010-2019 452 188 394 22096 2288 #&gt; 24 incidence female 65+ 2010-2019 1500 872 283 10337 1269 #&gt; 25 mortality male 0-19 1990-1999 0 0 76 0 0 #&gt; Colorectum Eye Hodgkin.lymphoma Kaposi Kidney Larynx Leukaemia Liver Lung #&gt; 1 15 29 35 0 24 1 356 58 6 #&gt; 2 1087 8 64 0 141 86 509 1741 1036 #&gt; 3 4644 9 47 0 530 824 453 5702 8420 #&gt; 4 8058 21 41 0 721 1265 623 4806 15152 #&gt; 5 5 38 32 0 20 0 329 33 3 #&gt; 6 957 8 119 9 221 37 437 1116 772 #&gt; 7 6418 18 77 4 1071 658 642 6015 7909 #&gt; 8 13352 13 77 8 1275 1125 864 5808 18870 #&gt; 9 6 26 53 0 31 0 338 24 2 #&gt; 10 1005 10 163 25 293 29 401 659 541 #&gt; 11 10034 28 87 18 1978 684 1033 6500 9523 #&gt; 12 18003 15 114 12 1977 1043 1381 6716 20588 #&gt; 13 2 33 10 0 25 0 296 37 7 #&gt; 14 932 11 61 0 98 13 393 353 597 #&gt; 15 3166 9 19 0 256 59 312 1093 2629 #&gt; 16 7728 16 33 0 503 130 534 2244 8428 #&gt; 17 5 14 30 0 15 0 219 13 5 #&gt; 18 938 12 122 2 120 5 405 212 625 #&gt; 19 4430 10 33 0 482 37 469 1041 3397 #&gt; 20 10810 8 35 0 830 85 723 2637 9517 #&gt; 21 5 14 32 0 19 0 237 21 0 #&gt; 22 1057 9 174 0 135 7 443 168 647 #&gt; 23 7200 16 58 4 887 47 786 1168 6312 #&gt; 24 13119 20 58 5 1203 84 913 3007 10872 #&gt; 25 10 3 0 0 2 0 120 36 1 #&gt; Melanoma Mesothelioma Multiple.myeloma Nasal Nasopharynx #&gt; 1 3 0 1 4 33 #&gt; 2 50 0 43 53 3049 #&gt; 3 82 0 210 109 3724 #&gt; 4 107 0 421 120 1212 #&gt; 5 1 0 1 7 16 #&gt; 6 41 5 38 38 2114 #&gt; 7 98 34 326 161 3750 #&gt; 8 137 77 674 137 1177 #&gt; 9 0 0 0 3 21 #&gt; 10 47 4 26 41 1339 #&gt; 11 186 51 525 174 3653 #&gt; 12 195 154 910 154 1207 #&gt; 13 2 0 1 1 13 #&gt; 14 44 0 19 31 1380 #&gt; 15 58 0 150 57 1157 #&gt; 16 102 0 417 93 536 #&gt; 17 2 0 0 5 6 #&gt; 18 41 8 21 36 942 #&gt; 19 102 12 185 74 1187 #&gt; 20 118 14 559 92 465 #&gt; 21 3 0 0 6 6 #&gt; 22 70 10 24 37 583 #&gt; 23 128 34 399 105 1145 #&gt; 24 179 24 636 102 389 #&gt; 25 2 0 0 0 6 #&gt; Non.Hodgkin.lymphoma Non.melanoma.skin Oesophagus Oral Ovary Pancreas Penis #&gt; 1 137 8 0 18 0 4 2 #&gt; 2 596 211 158 324 0 106 19 #&gt; 3 997 613 1873 1165 0 514 78 #&gt; 4 1210 968 2203 1055 0 887 184 #&gt; 5 111 4 0 6 0 1 0 #&gt; 6 454 220 82 312 0 71 18 #&gt; 7 1216 917 1528 1354 0 780 71 #&gt; 8 1756 1835 2126 1416 0 1440 199 #&gt; 9 106 1 0 9 0 1 0 #&gt; 10 487 291 54 304 0 109 21 #&gt; 11 1910 1782 1321 1941 0 1402 154 #&gt; 12 2633 2975 1982 1813 0 2302 279 #&gt; 13 75 2 0 21 77 2 0 #&gt; 14 444 156 48 241 854 60 0 #&gt; 15 594 374 254 364 970 290 0 #&gt; 16 1120 1249 761 485 776 875 0 #&gt; 17 43 4 1 20 108 0 0 #&gt; 18 461 182 13 254 1299 62 0 #&gt; 19 888 580 190 454 1846 461 0 #&gt; 20 1409 2476 725 768 891 1329 0 #&gt; 21 57 4 0 9 84 3 0 #&gt; 22 475 303 16 259 1466 92 0 #&gt; 23 1561 1168 174 920 3166 923 0 #&gt; 24 1883 3268 624 1091 1128 2101 0 #&gt; 25 25 0 0 1 0 3 0 #&gt; Placenta Prostate Sarcoma Small.intestine Stomach Testis Thymus Thyroid #&gt; 1 0 0 137 0 5 61 12 22 #&gt; 2 0 10 320 31 429 275 71 250 #&gt; 3 0 481 281 102 1990 80 70 288 #&gt; 4 0 3073 261 131 3634 129 59 194 #&gt; 5 0 0 118 0 6 57 16 21 #&gt; 6 0 6 307 34 331 395 96 333 #&gt; 7 0 1588 367 113 1954 65 137 447 #&gt; 8 0 8676 316 163 4256 44 94 278 #&gt; 9 0 1 110 1 2 53 23 17 #&gt; 10 0 18 299 46 192 587 68 496 #&gt; 11 0 4128 527 293 2158 100 137 834 #&gt; 12 0 14703 507 336 4720 15 85 424 #&gt; 13 1 0 128 1 1 0 3 80 #&gt; 14 13 0 283 22 492 0 38 1294 #&gt; 15 0 0 232 53 826 0 38 788 #&gt; 16 0 0 232 116 2319 0 38 479 #&gt; 17 0 0 105 0 2 0 1 81 #&gt; 18 8 0 322 24 379 0 64 1659 #&gt; 19 3 0 300 80 971 0 116 1570 #&gt; 20 0 0 247 153 2512 0 65 595 #&gt; 21 0 0 86 1 0 0 5 103 #&gt; 22 12 0 330 38 318 0 30 2291 #&gt; 23 3 0 509 221 1653 0 81 3200 #&gt; 24 0 0 351 251 2809 0 67 940 #&gt; 25 0 0 41 1 0 2 7 1 #&gt; Uterus Vulva #&gt; 1 0 0 #&gt; 2 0 0 #&gt; 3 0 0 #&gt; 4 0 0 #&gt; 5 0 0 #&gt; 6 0 0 #&gt; 7 0 0 #&gt; 8 0 0 #&gt; 9 0 0 #&gt; 10 0 0 #&gt; 11 0 0 #&gt; 12 0 0 #&gt; 13 2 1 #&gt; 14 478 49 #&gt; 15 1362 96 #&gt; 16 729 235 #&gt; 17 2 2 #&gt; 18 821 44 #&gt; 19 3071 147 #&gt; 20 1130 336 #&gt; 21 3 1 #&gt; 22 1165 57 #&gt; 23 6582 235 #&gt; 24 1864 486 #&gt; 25 0 0 #&gt; [ reached &#39;max&#39; / getOption(&quot;max.print&quot;) -- omitted 23 rows ] 6.5.2 3a. Visualise changes in incidence and mortality # first plot incidence for each cancer type #Import the necessary packages and libraries if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) if (!require(&quot;ggpubr&quot;)) install.packages(&quot;ggpubr&quot;) library(ggplot2) library(gridExtra) library(ggpubr) HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] p&lt;-list() for (i in 1:(ncol(HKCancer_inc)-4)){ p[[i]]&lt;-ggplot(HKCancer_inc,aes_string(fill=names(HKCancer_inc)[3],x=names(HKCancer_inc)[4], y=names(HKCancer_inc)[i+4],group=names(HKCancer_inc)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;Incidence&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) # now plot mortality for each cancer type #Import the necessary packages and libraries if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) if (!require(&quot;ggpubr&quot;)) install.packages(&quot;ggpubr&quot;) if (!require(&quot;dplyr&quot;)) install.packages(&quot;dplyr&quot;) library(ggplot2) library(gridExtra) library(ggpubr) library(dplyr) HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] p&lt;-list() #(ncol(HKCancer_inc)-4) for (i in 1:(ncol(HKCancer_mort)-4)){ p[[i]]&lt;-ggplot(HKCancer_mort,aes_string(fill=names(HKCancer_mort)[3],x=names(HKCancer_mort)[4], y=names(HKCancer_mort)[i+4],group=names(HKCancer_mort)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_mort)[i+4])+ ylab(&quot;Mortality&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) 6.5.3 3b. Calculate cancer risk and mortality rate To calculate disease risk we need to calculated the number of new cases over the number of persons at risk over a specific time period. We have the incidence for each decade and can estimate the number of persons at risk based on the population in 1995, 2005 and 2015. # cancer risk calculation HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_inc_risk &lt;- HKCancer_inc[,1:5] risk &lt;- function(x,age,sex,year){ if (is.integer(x)){ pop_n &lt;- HKPop %&gt;% filter(Sex==sex &amp; Age==age) if (year == &quot;1990-1999&quot;){ return (as.double(x)/as.double(pop_n$`1995`)) } else if (year == &quot;2000-2009&quot;) {return (as.double(x)/as.double(pop_n$`2005`))} else { return (as.double(x)/as.double(pop_n$`2015`)) } } return (x) } for (i in 5:ncol(HKCancer_inc)){ HKCancer_inc_risk[names(HKCancer_inc)[i]] &lt;- mapply(risk,HKCancer_inc[,i],HKCancer_inc[,3],HKCancer_inc[,2],HKCancer_inc[,4]) } #visualise cancer risk p&lt;-list() for (i in 1:(ncol(HKCancer_inc_risk)-4)){ p[[i]]&lt;-ggplot(HKCancer_inc_risk,aes_string(fill=names(HKCancer_inc_risk)[3],x=names(HKCancer_inc_risk)[4], y=names(HKCancer_inc_risk)[i+4],group=names(HKCancer_inc_risk)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;incidence per 1000&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) # mortality rate calculation HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] HKCancer_mort_risk &lt;- HKCancer_mort[,1:5] risk &lt;- function(x,age,sex,year){ if (is.integer(x)){ pop_n &lt;- HKPop %&gt;% filter(Sex==sex &amp; Age==age) if (year == &quot;1990-1999&quot;){ return (as.double(x)/as.double(pop_n$`1995`)) } else if (year == &quot;2000-2009&quot;) {return (as.double(x)/as.double(pop_n$`2005`))} else { return (as.double(x)/as.double(pop_n$`2015`)) } } return (x) } for (i in 5:ncol(HKCancer_mort)){ HKCancer_mort_risk[names(HKCancer_mort)[i]] &lt;- mapply(risk,HKCancer_mort[,i],HKCancer_mort[,3],HKCancer_mort[,2],HKCancer_mort[,4]) } #visualise mortality rate p&lt;-list() for (i in 1:(ncol(HKCancer_mort_risk)-4)){ p[[i]]&lt;-ggplot(HKCancer_mort_risk,aes_string(fill=names(HKCancer_mort_risk)[3],x=names(HKCancer_mort_risk)[4], y=names(HKCancer_mort_risk)[i+4],group=names(HKCancer_mort_risk)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;mortality per 1000&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) 6.5.4 3c. Mortality-incidence ratio Cancer research can be focused on improving cancer outcomes in a number of ways. For example cancer prevention research that seeks to reduce cancer incidence which would also ultimately reduce cancer mortality. Another area is cancer therapy which would not affect incidence but seeks to reduce mortality, or at least prolong survival. We don’t go into survival analysis in this tutorial, but a way to get an idea whether treatment is improving by looking at the mortality-incidence ratio. HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] HKCancer_mort_inc &lt;- HKCancer_mort[,1:5] risk &lt;- function(mort,inc){ if (inc == 0){ return (0) } return (as.double(mort)/as.double(inc)) } for (i in 5:ncol(HKCancer_mort)){ HKCancer_mort_inc[names(HKCancer_mort)[i]] &lt;- mapply(risk,HKCancer_mort[,i],HKCancer_inc[,i]) } #visualise mortality incidence ratio p&lt;-list() for (i in 1:(ncol(HKCancer_mort_inc)-4)){ p[[i]]&lt;-ggplot(HKCancer_mort_inc,aes_string(fill=names(HKCancer_mort_inc)[3],x=names(HKCancer_mort_inc)[4], y=names(HKCancer_mort_inc)[i+4],group=names(HKCancer_mort_inc)[3]))+ geom_bar(position=&quot;dodge&quot;,stat=&quot;identity&quot;)+ facet_wrap(~Sex) + theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ theme(text = element_text(size = 10))+ ggtitle(names(HKCancer_inc)[i+4])+ ylab(&quot;mortality-incidence ratio&quot;) } do.call(&#39;grid.arrange&#39;,c(p,ncol=3,nrow=12)) 6.5.5 3d. Paired t-test on mortality-incidence ratio change In general, across the different cancer types is cancer treatment improving? We can use a paired t-test comparing the mortality-incidence ratio of cancers from the 1990-1999 period with the 2010-2019 period. #First sum up all incidence and mortality data for each cancer type across age and sex HKCancer_inc_sum &lt;- aggregate(HKCancer_inc[,-(1:4)],list(HKCancer_inc$Year),FUN=sum) HKCancer_mort_sum &lt;- aggregate(HKCancer_mort[,-(1:4)],list(HKCancer_mort$Year),FUN=sum) HKCancer_mort_inc_year &lt;- data.frame(Year=HKCancer_mort_sum[,1]) risk &lt;- function(mort,inc){ return (as.double(mort)/as.double(inc)) } for (i in 2:ncol(HKCancer_mort_sum)){ HKCancer_mort_inc_year[names(HKCancer_mort_sum)[i]] &lt;- mapply(risk,HKCancer_mort_sum[,i],HKCancer_inc_sum[,i]) } HKCancer_mort_inc_year_m &lt;-data.frame(`1990-1999` = as.numeric(HKCancer_mort_inc_year[1,2:37]), `2000-2009` = as.numeric(HKCancer_mort_inc_year[2,2:37]), `2010-2019` = as.numeric(HKCancer_mort_inc_year[3,2:37]), check.names = FALSE) HKCancer_mort_inc_year_m$Cancer &lt;- names(HKCancer_mort_inc_year)[-1] HKCancer_mort_inc_year_t&lt;-as_tibble(HKCancer_mort_inc_year_m) %&gt;% select(`Cancer`,`1990-1999`,`2000-2009`,`2010-2019`)%&gt;% gather (key=&quot;Year&quot;,value=&quot;MIR&quot;,-Cancer) plot&lt;-ggplot(HKCancer_mort_inc_year_t,aes(x=Year,y=MIR, color=Year))+ geom_boxplot(na.rm=T) + theme_classic()+ scale_color_brewer(palette=&quot;Dark2&quot;)+ geom_jitter(shape=16, position=position_jitter(0.2),na.rm=T)+ ylab(&quot;mortality-incidence ratio&quot;)+ ylim(0,1.2) + geom_signif(comparisons = list(c(&quot;1990-1999&quot;, &quot;2010-2019&quot;)), map_signif_level=F, test= &quot;t.test&quot;,test.args = list(paired = TRUE), na.rm = T, y_position = c(1.1, 1.3)) + geom_signif(comparisons = list(c(&quot;1990-1999&quot;, &quot;2000-2009&quot;)), map_signif_level=F, test= &quot;t.test&quot;,test.args = list(paired = TRUE), na.rm = T) + geom_signif(comparisons = list(c(&quot;2000-2009&quot;, &quot;2010-2019&quot;)), map_signif_level=F, test= &quot;t.test&quot;,test.args = list(paired = TRUE), na.rm = T) plot p&lt;-list() p[[1]]&lt;-t.test(HKCancer_mort_inc_year_m$`1990-1999`,HKCancer_mort_inc_year_m$`2000-2009`,paired=TRUE,alternative_m = &quot;two.sided&quot;) p[[2]]&lt;-t.test(HKCancer_mort_inc_year_m$`1990-1999`,HKCancer_mort_inc_year_m$`2010-2019`,paired=TRUE,alternative_m = &quot;two.sided&quot;) p[[3]]&lt;-t.test(HKCancer_mort_inc_year_m$`2000-2009`,HKCancer_mort_inc_year_m$`2010-2019`,paired=TRUE,alternative_m = &quot;two.sided&quot;) p #&gt; [[1]] #&gt; #&gt; Paired t-test #&gt; #&gt; data: HKCancer_mort_inc_year_m$`1990-1999` and HKCancer_mort_inc_year_m$`2000-2009` #&gt; t = 0.79695, df = 33, p-value = 0.4312 #&gt; alternative hypothesis: true mean difference is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.01415536 0.03238636 #&gt; sample estimates: #&gt; mean difference #&gt; 0.009115498 #&gt; #&gt; #&gt; [[2]] #&gt; #&gt; Paired t-test #&gt; #&gt; data: HKCancer_mort_inc_year_m$`1990-1999` and HKCancer_mort_inc_year_m$`2010-2019` #&gt; t = 2.1861, df = 33, p-value = 0.036 #&gt; alternative hypothesis: true mean difference is not equal to 0 #&gt; 95 percent confidence interval: #&gt; 0.002055217 0.057209924 #&gt; sample estimates: #&gt; mean difference #&gt; 0.02963257 #&gt; #&gt; #&gt; [[3]] #&gt; #&gt; Paired t-test #&gt; #&gt; data: HKCancer_mort_inc_year_m$`2000-2009` and HKCancer_mort_inc_year_m$`2010-2019` #&gt; t = 1.5413, df = 35, p-value = 0.1322 #&gt; alternative hypothesis: true mean difference is not equal to 0 #&gt; 95 percent confidence interval: #&gt; -0.005438019 0.039734021 #&gt; sample estimates: #&gt; mean difference #&gt; 0.017148 6.5.6 3e. Childhood versus elderly cancers Although it is clear that the incidence of cancer is typically higher in the elderly, some cancers affect children as well. What cancer types disproportionate affect children? For each cancer type, compare the proportion of 0-19 versus 65+ incidence against the 0-19 versus 65+ incidence for all other cancer types. # Examine the proportion of childhood HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_inc_age_sum &lt;- aggregate(HKCancer_inc[,-(1:4)],list(HKCancer_inc$Age),FUN=sum) HKCancer_inc_age_sum$Total&lt;- rowSums(HKCancer_inc_age_sum[,-1]) HKCancer_inc_age_sum_csq &lt;- data.frame(cancer=names(HKCancer_inc_age_sum[,2:ncol(HKCancer_inc_age_sum)])) pval &lt;- list() ratio &lt;- list() for (i in 2:(ncol(HKCancer_inc_age_sum))){ val = Map(&#39;-&#39;,HKCancer_inc_age_sum$Total,HKCancer_inc_age_sum[,i]) dat &lt;- data.frame(cancer=HKCancer_inc_age_sum[c(1,4),i], other =c(val[[1]],val[[2]])) pval &lt;- append(pval,fisher.test(dat)$p.val) ratio&lt;- append(ratio,log(as.double(dat[1,1]+0.1)/as.double(dat[2,1]+0.1))) } HKCancer_inc_age_sum_csq$pval &lt;- pval HKCancer_inc_age_sum_csq$ratio &lt;- ratio plot_child&lt;-ggplot(HKCancer_inc_age_sum_csq[-37,],aes(x=reorder(cancer,-as.numeric(ratio)),y=as.numeric(ratio)),fill=cancer)+ geom_bar(stat=&quot;identity&quot;,fill=&quot;red&quot;)+ geom_hline(yintercept=-4.12132318942113, linetype=&quot;dashed&quot;, color = &quot;black&quot;, linewidth=0.5)+ theme_classic()+ scale_fill_brewer(palette=&quot;Spectral&quot;)+ theme(legend.position=&quot;none&quot;)+ #theme(text = element_text(size = 10))+ theme(axis.title.x=element_blank())+ theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) + ylab(&quot;log((child+0.1)/(elderly+0.1)&quot;) plot_child HKCancer_inc_age_sum_csq #&gt; cancer pval ratio #&gt; 1 Biliary 1.21618e-216 -11.17481 #&gt; 2 Bladder 9.601084e-314 -6.711128 #&gt; 3 Brain 0 -0.615666 #&gt; 4 Breast 0 -7.519824 #&gt; 5 Cervix 1.635299e-126 -6.925188 #&gt; 6 Colorectum 0 -7.531208 #&gt; 7 Eye 2.085337e-112 0.5039276 #&gt; 8 Hodgkin.lymphoma 3.658856e-81 -0.6227962 #&gt; 9 Kaposi 0.41662 -5.525453 #&gt; 10 Kidney 1.560619e-71 -3.882371 #&gt; 11 Larynx 1.963055e-113 -8.129416 #&gt; 12 Leukaemia 0 -1.043172 #&gt; 13 Liver 0 -4.909033 #&gt; 14 Lung 0 -8.191896 #&gt; 15 Melanoma 6.246412e-15 -4.324192 #&gt; 16 Mesothelioma 5.396388e-09 -7.897668 #&gt; 17 Multiple.myeloma 6.126613e-106 -7.062026 #&gt; 18 Nasal 0.0001285609 -3.286427 #&gt; 19 Nasopharynx 4.628193e-74 -3.95948 #&gt; 20 Non.Hodgkin.lymphoma 4.513518e-11 -2.940272 #&gt; 21 Non.melanoma.skin 0 -6.315107 #&gt; 22 Oesophagus 1.377432e-251 -8.943186 #&gt; 23 Oral 5.100139e-108 -4.379029 #&gt; 24 Ovary 0.0002847234 -2.34054 #&gt; 25 Pancreas 3.11451e-246 -6.690686 #&gt; 26 Penis 3.023792e-18 -5.753479 #&gt; 27 Placenta 0.07013259 2.397895 #&gt; 28 Prostate 0 -10.08778 #&gt; 29 Sarcoma 9.774701e-213 -1.028899 #&gt; 30 Small.intestine 1.479593e-31 -5.916202 #&gt; 31 Stomach 0 -7.137096 #&gt; 32 Testis 1.871184e-97 -0.09472556 #&gt; 33 Thymus 6.748934e-06 -1.915502 #&gt; 34 Thyroid 7.821825e-09 -2.194891 #&gt; 35 Uterus 1.457974e-105 -6.262217 #&gt; 36 Vulva 1.521831e-27 -5.552298 #&gt; 37 Total 1 -4.121323 6.6 4. Existing cancer funding and publication data The Hong Kong government established in Health and Medical Research Fund (HMRF) in 2011 to specifically provide research funding for health and medical research in Hong Kong. Since 2016 over 370 projects in the category of Cancer has been funded for a total of ~$400 M dollars. A list of all funded projects can be found on the Health Bureau webpage. You would like to use this data to see if there is any association between previous project funding and the epidemiology of cancers in Hong Kong. We can also do a similar thing with publications and ask if the research publications in Hong Kong have been aligned with the incidence and mortality. We can obtain this data from PubMed using the following terms: (“Hong Kong”[Affiliation]) AND (neoplasms[MeSH Terms]) The data has been predownloaded as the Pubmed API via R is a bit slow. Discussion points: Why has research publications increased dramatically in recent years? Is there something unsual with the dataset? What are the main cancer types being researched in Hong Kong? Is there any correlation between funding and cancer incidence and mortality? 6.6.1 Download HMRF grants and Pubmed data HMRF&lt;- read.delim(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/HMRF_cancer_grants.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = TRUE) #HMRF pubmed&lt;- read.delim(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/pubmed__neoplasm_hongkong.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = TRUE) #pubmed hist(pubmed$Publication.Year) 6.6.2 Make word cloud for grants 6.6.3 Make compare grant funding with incidence and mortality if (!require(&quot;ggrepel&quot;)) install.packages(&quot;ggrepel&quot;) if (!require(&quot;ggplot2&quot;)) install.packages(&quot;gglot2&quot;) if (!require(&quot;gridExtra&quot;)) install.packages(&quot;gridExtra&quot;) library(ggrepel) library(ggplot2) library(gridExtra) grantpmsum&lt;- read.delim(&quot;https://github.com/StatBiomed/BMDS-book/raw/main/notebooks/module5-epidemi/Grants_pubmed_summary.txt&quot;, sep = &quot;\\t&quot;, header = TRUE, stringsAsFactor=FALSE, check.names = TRUE) grantpmsum #&gt; Cancer Grants Pubmed #&gt; 1 Biliary 0 72 #&gt; 2 Bladder 0 141 #&gt; 3 Brain 2 294 #&gt; 4 Breast 34 1147 #&gt; 5 Cervix 9 408 #&gt; 6 Colorectum 40 857 #&gt; 7 Eye 2 27 #&gt; 8 Hodgkin lymphoma 0 21 #&gt; 9 Kaposi 0 6 #&gt; 10 Kidney 0 133 #&gt; 11 Larynx 0 8 #&gt; 12 Leukaemia 18 515 #&gt; 13 Liver 97 2077 #&gt; 14 Lung 22 773 #&gt; 15 Melanoma 0 99 #&gt; 16 Mesothelioma 6 58 #&gt; 17 Multiple myeloma 0 104 #&gt; 18 Nasal 0 14 #&gt; 19 Nasopharynx 24 1113 #&gt; 20 Non-Hodgkin lymphoma 0 55 #&gt; 21 Skin 0 32 #&gt; 22 Oesophagus 7 404 #&gt; 23 Oral 5 229 #&gt; 24 Ovary 14 354 #&gt; 25 Pancreas 2 141 #&gt; 26 Penis 0 7 #&gt; 27 Placenta 0 9 #&gt; 28 Prostate 6 322 #&gt; 29 Sarcoma 2 216 #&gt; 30 Small intestine 0 11 #&gt; 31 Stomach 5 455 #&gt; 32 Testis 0 18 #&gt; 33 Thymus 0 3 #&gt; 34 Thyroid 2 231 #&gt; 35 Uterus 0 72 #&gt; 36 Vulva 0 8 HKCancer_inc &lt;- HKCancer[HKCancer$Type==&#39;incidence&#39;,] HKCancer_inc_sum &lt;- data.frame(incidence=colSums(HKCancer_inc[,-(1:4)])) HKCancer_mort &lt;- HKCancer[HKCancer$Type==&#39;mortality&#39;,] HKCancer_mort_sum &lt;- data.frame(mortality=colSums(HKCancer_inc[,-(1:4)])) HKCancer_compare &lt;-data.frame(cancer=grantpmsum$Cancer, grants=grantpmsum$Grants, pubmed=grantpmsum$Pubmed, incidence=colSums(HKCancer_inc[,-(1:4)]), mortality=colSums(HKCancer_mort[,-(1:4)])) gp&lt;-ggplot(HKCancer_compare, aes(y=grants, x=pubmed)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 45, box.padding = 0.4) + stat_cor(method = &quot;pearson&quot;, label.x = 3, label.y = 90) pinc&lt;-ggplot(HKCancer_compare, aes(y=pubmed, x=incidence)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 15, box.padding = 0.5)+ stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) pmor&lt;-ggplot(HKCancer_compare, aes(y=pubmed, x=mortality)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 15, box.padding = 0.5) + stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) ginc&lt;-ggplot(HKCancer_compare, aes(y=grants, x=incidence)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 40, box.padding = 0.4) + stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) gmor&lt;-ggplot(HKCancer_compare, aes(y=grants, x=mortality)) + geom_point() + scale_color_brewer(palette=&quot;Dark2&quot;) + theme_classic() + geom_label_repel(data=HKCancer_compare, aes(label=cancer), nudge_x = 2, size = 3.5,label.size = NA ,min.segment.length =unit(0, &#39;lines&#39;), max.overlaps = 40, box.padding = 0.4) + stat_cor(method = &quot;pearson&quot;, label.x = 40000, label.y = 0) grid.arrange(gp,ginc,gmor,pinc, pmor, ncol=3) 6.7 5. Open disucssion As a group discuss what cancer type would be most worthy of funding in Hong Kong. Statistics and figures should be used to support your decision. If possible also discuss other data/analyses that can be performed and/or other diseases that are also in need of funding in Hong Kong. "],["pop-genetics.html", "Chapter 7 Population Genetics and Diseases 7.1 Case study 1: Heritability and human traits", " Chapter 7 Population Genetics and Diseases 7.1 Case study 1: Heritability and human traits 7.1.1 Part 1 Scenario: You are a researcher working on a twin study on cardiovascular traits to assess the genetic and environmental contribution relevant to metabolism and cardiovascular disease risk. You have recruited a cohort of volunteer adult twins of the same ancestry. The volunteers have undergone a series of baseline clinical evaluations and performed genotyping on a panel of single nucleotide polymorphisms that may be associated with the traits. 7.1.1.1 Questions for Discussion Q1. Besides the clinical measurements, what data do you need to collect from the subjects? Answers: Sex Age Other confounding factors, e.g. BMI, blood pressure, smoking status, etc. Q2. How is genotype data represented for statistical genetic analysis? Answers: Allele: 0/1, 1/2, A/C, etc Genotype: 0 0, 0 1, 1 0, 1 1 Genotype probabilities: P(0/0)=0, P(0/1)=1, P(1/1)=0 Genotype dosage: 0/1/2, 0.678 (continuous from 0-1 or 0-2) Q3. How can you test for association between genotypes and phenotypes (binary and quantitative)? Answers: Allelic chi-square test Fisher’s exact test Linear/Logistic regression Linear mixed model 7.1.1.2 Hands-on exercise : Association test Now, you are given a dataset of age- and sex-matched twin cohort with two cardiovascular phenotypes and 5 quantitative trait loci (QTL). Data set and template notebook are available on Moodle (recommended) and also on this GitHub Repo. The information for columns: zygosity: 1 for monozygotic (MZ) and 2 for dizygotic (DZ) twin T1QTL_A[1-5] and T2QTL_A[1-5]: 5 quantitative loci (A1-A5) in additive coding for Twin 1 (T1) and Twin 2 (T2) respectively The same 5 QTL (D1-D5) in dominance coding for T1 and T2 Phenotype scores of T1 and T2 for the two quantitative cardiovascular traits Download the data dataTwin.dat to your working directory. Start the RStudio program and set the working directory. dataTwin &lt;- read.table(&quot;dataTwin2023.dat&quot;,h=T) Exploratory analysis A1-5: The QTLs are biallelic with two alleles A and a. The genotypes aa, Aa, and AA are coded additively as 0 (aa), 1 (Aa) and 2 (AA). D1-5: The genotypes aa, Aa, and AA are coded as 0 (aa), 1 (Aa) and 0 (AA). Q1. How many MZ and DZ volunteers are there? Answers: 1000 MZ and 1000 DZ Q2. How are the genotypes represented? Answers: Dosage/Count of non-reference allele : 0, 1, and 2 Q3. Are the QTL independent of each other? Answers: Yes. The pairwise correlations are low (&lt;0.2). Q4. Are there outliers in phenotypes? Answers: Yes. T2 individual 1303 has phenotype score (-4.21) being 4 SD below the mean. table(dataTwin$zygosity) # Q1: shows number of MZ and DZ twin pairs #&gt; #&gt; 1 2 #&gt; 1000 1000 table(dataTwin$T1QTL_A1) # Q2: shows the distribution of QTL_A1 #&gt; #&gt; 0 1 2 #&gt; 474 1021 505 table(dataTwin$T1QTL_D1) # Q2: shows the distribution of QTL_D1 #&gt; #&gt; 0 1 #&gt; 979 1021 table(dataTwin$T1QTL_A1, dataTwin$T1QTL_D1) # Q2: shows the distribution of QTL_A1 in relation to QTL_D1 #&gt; #&gt; 0 1 #&gt; 0 474 0 #&gt; 1 0 1021 #&gt; 2 505 0 cor(dataTwin[,2:11]) # Q3: shows the correlation between QTL_As #&gt; T1QTL_A1 T1QTL_A2 T1QTL_A3 T1QTL_A4 T1QTL_A5 #&gt; T1QTL_A1 1.00000000 -0.005470340 0.021705688 0.01940408 0.016278190 #&gt; T1QTL_A2 -0.00547034 1.000000000 0.017344822 -0.01421677 -0.008678746 #&gt; T1QTL_A3 0.02170569 0.017344822 1.000000000 0.01335711 -0.036751338 #&gt; T1QTL_A4 0.01940408 -0.014216767 0.013357109 1.00000000 0.074899996 #&gt; T1QTL_A5 0.01627819 -0.008678746 -0.036751338 0.07490000 1.000000000 #&gt; T2QTL_A1 0.53243815 0.004201635 -0.013909013 0.03252724 0.020081970 #&gt; T2QTL_A2 -0.04561174 0.464131160 -0.005044127 0.01324172 -0.003012277 #&gt; T2QTL_A3 0.03316574 -0.003552831 0.521253656 0.02045423 0.009081830 #&gt; T2QTL_A4 0.03271254 -0.033419904 0.020422583 0.48641289 0.019247531 #&gt; T2QTL_A5 -0.01285323 0.030413269 -0.045121964 0.08288145 0.457962222 #&gt; T2QTL_A1 T2QTL_A2 T2QTL_A3 T2QTL_A4 T2QTL_A5 #&gt; T1QTL_A1 0.532438150 -0.045611740 0.033165736 0.032712539 -0.01285323 #&gt; T1QTL_A2 0.004201635 0.464131160 -0.003552831 -0.033419904 0.03041327 #&gt; T1QTL_A3 -0.013909013 -0.005044127 0.521253656 0.020422583 -0.04512196 #&gt; T1QTL_A4 0.032527239 0.013241725 0.020454234 0.486412895 0.08288145 #&gt; T1QTL_A5 0.020081970 -0.003012277 0.009081830 0.019247531 0.45796222 #&gt; T2QTL_A1 1.000000000 0.006179257 -0.013129314 0.048294183 -0.01325839 #&gt; T2QTL_A2 0.006179257 1.000000000 -0.020860987 0.002164782 -0.01131418 #&gt; T2QTL_A3 -0.013129314 -0.020860987 1.000000000 -0.010583797 -0.02101270 #&gt; T2QTL_A4 0.048294183 0.002164782 -0.010583797 1.000000000 0.04350925 #&gt; T2QTL_A5 -0.013258394 -0.011314179 -0.021012699 0.043509251 1.00000000 cor(dataTwin[,2:11])&gt;0.2 #&gt; T1QTL_A1 T1QTL_A2 T1QTL_A3 T1QTL_A4 T1QTL_A5 T2QTL_A1 T2QTL_A2 #&gt; T1QTL_A1 TRUE FALSE FALSE FALSE FALSE TRUE FALSE #&gt; T1QTL_A2 FALSE TRUE FALSE FALSE FALSE FALSE TRUE #&gt; T1QTL_A3 FALSE FALSE TRUE FALSE FALSE FALSE FALSE #&gt; T1QTL_A4 FALSE FALSE FALSE TRUE FALSE FALSE FALSE #&gt; T1QTL_A5 FALSE FALSE FALSE FALSE TRUE FALSE FALSE #&gt; T2QTL_A1 TRUE FALSE FALSE FALSE FALSE TRUE FALSE #&gt; T2QTL_A2 FALSE TRUE FALSE FALSE FALSE FALSE TRUE #&gt; T2QTL_A3 FALSE FALSE TRUE FALSE FALSE FALSE FALSE #&gt; T2QTL_A4 FALSE FALSE FALSE TRUE FALSE FALSE FALSE #&gt; T2QTL_A5 FALSE FALSE FALSE FALSE TRUE FALSE FALSE #&gt; T2QTL_A3 T2QTL_A4 T2QTL_A5 #&gt; T1QTL_A1 FALSE FALSE FALSE #&gt; T1QTL_A2 FALSE FALSE FALSE #&gt; T1QTL_A3 TRUE FALSE FALSE #&gt; T1QTL_A4 FALSE TRUE FALSE #&gt; T1QTL_A5 FALSE FALSE TRUE #&gt; T2QTL_A1 FALSE FALSE FALSE #&gt; T2QTL_A2 FALSE FALSE FALSE #&gt; T2QTL_A3 TRUE FALSE FALSE #&gt; T2QTL_A4 FALSE TRUE FALSE #&gt; T2QTL_A5 FALSE FALSE TRUE apply(dataTwin[22:25],2,function(x){ any(x &lt; (mean(x) - 4*sd(x))) }) # Q4: any outlier &lt; 4 SD from the mean for the two quantitative phenotypes #&gt; pheno1_T1 pheno1_T2 pheno2_T1 pheno2_T2 #&gt; FALSE FALSE FALSE TRUE apply(dataTwin[22:25],2,function(x){ any(x &gt; (mean(x) + 4*sd(x))) }) # Q4: any outlier &gt; 4 SD from the mean for the two quantitative phenotypes #&gt; pheno1_T1 pheno1_T2 pheno2_T1 pheno2_T2 #&gt; FALSE FALSE FALSE FALSE # remove the phenotype score of the outlier (T2) for the phenotype 2 (pheno2_T2) outlier&lt;- which(dataTwin$pheno2_T2 &lt; (mean(dataTwin$pheno2_T2) - 4*sd(dataTwin$pheno2_T2) )) outlier #&gt; [1] 1303 dataTwin$pheno2_T2[outlier] #&gt; [1] -4.21 dataTwin$pheno2_T2[outlier] &lt;- NA Association test Test for association between QTL and pheno1 for T1 Regress pheno1_T1 on T1QTL_A1 to estimate the proportion of variance explained (R2). Model: pheno1_T1 = b0 + b1* T1QTL_A1 + e Calculate the conditional mean of phenotype (i.e. phenotypic mean conditional genotype) If the relationship between the QTL and the phenotype is perfectly linear, the regression line should pass through the conditional means (c_means), and the differences between the conditional means should be about equal. Q5. What are the values of b0, b1? Is QTL1 significant associated with the phenotype at alpha&lt;0.01 (multiple testing of 5 loci)? Answers: b0 = 4.1464 b1 = 0.9180 QTL1 is significantly associated with the phenotype with \\(P = 1.02\\times 10^{-13}\\) Q6. What is the proportion of phenotypic variance explained? Answers: Proportion of phenotypic variance explained = 0.027 linA1 &lt;- lm(pheno1_T1~T1QTL_A1, data=dataTwin) summary(linA1) #&gt; #&gt; Call: #&gt; lm(formula = pheno1_T1 ~ T1QTL_A1, data = dataTwin) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -15.1225 -2.4435 0.1105 2.7775 12.2555 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 4.1464 0.1511 27.438 &lt; 2e-16 *** #&gt; T1QTL_A1 0.9180 0.1226 7.491 1.02e-13 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.834 on 1998 degrees of freedom #&gt; Multiple R-squared: 0.02732, Adjusted R-squared: 0.02683 #&gt; F-statistic: 56.11 on 1 and 1998 DF, p-value: 1.022e-13 summary(linA1)$r.squared # proportion of explained variance by additive component #&gt; [1] 0.02731675 c_means &lt;- by(dataTwin$pheno1_T1,dataTwin$T1QTL_A1,mean) plot(dataTwin$pheno1_T1 ~ dataTwin$T1QTL_A1, col=&#39;grey&#39;, ylim=c(3,7)) lines(c(0,1,2), c_means, type=&quot;p&quot;, col=6, lwd=8) lines(sort(dataTwin$T1QTL_A1),sort(linA1$fitted.values), type=&#39;b&#39;, col=&quot;dark green&quot;, lwd=3) To test for the non-linearity, we can use the dominance coding of the QTL and add the dominance term to the regression model. Model: pheno1_T1 = b0 + b1* T1QTL_A1 + b2* T1QTL_D1 + e Repeat for T2. Q7. Why can’t we analyse T1 and T2 together? Answers: As T1 and T2 are biologically related as MZ or DZ twins, the genotypes of the QTLs are not independent. Treating the genotypes of T1 and T2 as independent observations will introduce bias. Q8. Is there a dominance effect? Answers: Yes. The model with dominance provides a better goodness of fit (lower p-value) linAD1 &lt;- lm(pheno1_T1 ~ T1QTL_A1 + T1QTL_D1, data=dataTwin) summary(linAD1) # results lm(phenoT1~T1QTL_A1+T1QTL_D1) #&gt; #&gt; Call: #&gt; lm(formula = pheno1_T1 ~ T1QTL_A1 + T1QTL_D1, data = dataTwin) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -14.7524 -2.5131 0.0586 2.8215 11.8894 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 3.7522 0.1753 21.405 &lt; 2e-16 *** #&gt; T1QTL_A1 0.9301 0.1220 7.622 3.83e-14 *** #&gt; T1QTL_D1 0.7483 0.1708 4.382 1.24e-05 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.816 on 1997 degrees of freedom #&gt; Multiple R-squared: 0.03658, Adjusted R-squared: 0.03562 #&gt; F-statistic: 37.91 on 2 and 1997 DF, p-value: &lt; 2.2e-16 plot(dataTwin$pheno1_T1 ~ dataTwin$T1QTL_A1, col=&#39;grey&#39;, ylim=c(3,7)) abline(linA1, lwd=3) lines(c(0,1,2), c_means, type=&#39;p&#39;, col=6, lwd=8) lines(sort(dataTwin$T1QTL_A1),sort(linA1$fitted.values), type=&#39;b&#39;, col=&quot;dark green&quot;, lwd=3) lines(sort(dataTwin$T1QTL_A1),sort(linAD1$fitted.values), type=&#39;b&#39;, col=&quot;blue&quot;, lwd=3) Q9. Repeat for the other 4 QTL and determine which QTL shows strongest association with the phenotype T1 Answers: QTL3 with \\(P = 7.77 \\times 10^{-25}\\) for model with dominance allQTL_A_T1 &lt;- 2:6 cpheno1_T1 &lt;- which(colnames(dataTwin)==&quot;pheno1_T1&quot;) ## Additive cbind(lapply(allQTL_A_T1,function(x){ fstat&lt;- summary(lm(pheno1_T1 ~ ., data=dataTwin[,c(x,cpheno1_T1)]))$fstatistic; pf(fstat[1],fstat[2],fstat[3],lower.tail = F) })) #&gt; [,1] #&gt; [1,] 1.021942e-13 #&gt; [2,] 8.329416e-15 #&gt; [3,] 1.007527e-13 #&gt; [4,] 4.523758e-18 #&gt; [5,] 8.207842e-13 ## Dominance cbind(lapply(allQTL_A_T1,function(x){ fstat&lt;- summary(lm(pheno1_T1 ~ ., data=dataTwin[,c(x,x+10,cpheno1_T1)]))$fstatistic; pf(fstat[1],fstat[2],fstat[3],lower.tail = F) })) #&gt; [,1] #&gt; [1,] 6.907834e-17 #&gt; [2,] 2.166957e-22 #&gt; [3,] 7.771588e-25 #&gt; [4,] 8.124437e-25 #&gt; [5,] 4.312127e-21 #Q9: QTL3 shows the strongest association with P=7.771588e-25 linAD3 &lt;- lm(pheno1_T1 ~ T1QTL_A3 + T1QTL_D3, data=dataTwin) summary(linAD3) # results lm(phenoT1~T1QTL_A1+T1QTL_D1) #&gt; #&gt; Call: #&gt; lm(formula = pheno1_T1 ~ T1QTL_A3 + T1QTL_D3, data = dataTwin) #&gt; #&gt; Residuals: #&gt; Min 1Q Median 3Q Max #&gt; -14.4988 -2.5701 0.1843 2.6991 11.5974 #&gt; #&gt; Coefficients: #&gt; Estimate Std. Error t value Pr(&gt;|t|) #&gt; (Intercept) 3.5437 0.1684 21.038 &lt; 2e-16 *** #&gt; T1QTL_A3 0.9076 0.1181 7.683 2.43e-14 *** #&gt; T1QTL_D3 1.2714 0.1692 7.515 8.55e-14 *** #&gt; --- #&gt; Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1 #&gt; #&gt; Residual standard error: 3.782 on 1997 degrees of freedom #&gt; Multiple R-squared: 0.05408, Adjusted R-squared: 0.05313 #&gt; F-statistic: 57.09 on 2 and 1997 DF, p-value: &lt; 2.2e-16 If the subjects with top 5% of the phenotype score are considered as cases, perform case-control association test for most significant SNP (from Q9) and interpret the result. Q10. What are the odds ratio, p-value, and 95% confidence interval (CI)? Answers: Odds ratio is 3.40 and the 95% CI is (1.65, 7.03) quant05 &lt;- quantile(c(dataTwin$pheno1_T1,dataTwin$pheno1_T2),seq(0,1,0.05)) dataTwin$CaseT1 &lt;- as.numeric(dataTwin$pheno1_T1&gt;quant05[20]) dataTwin$CaseT2 &lt;- as.numeric(dataTwin$pheno1_T2&gt;quant05[20]) logisticAD1 &lt;- summary(glm(CaseT1 ~ T1QTL_A3 + T1QTL_D3, data=dataTwin, family=&quot;binomial&quot;)) exp(logisticAD1$coefficients[2,1]) # odds ratio #&gt; [1] 3.404757 exp(logisticAD1$coefficients[2,1]-1.96*logisticAD1$coefficients[2,2]) # lower 95% confidence interval #&gt; [1] 1.648816 exp(logisticAD1$coefficients[2,1]+1.96*logisticAD1$coefficients[2,2]) # upper 95% confidence interval #&gt; [1] 7.030723 7.1.2 Part 2 Scenario: You are asked to estimate the additive genetic variance, dominance genetic variance and/or shared environmental variance using regression-based method and a classical twin design. \\[\\begin{align*} \\text{For ADE model : }~ &amp; \\sigma^{2}_{P} = \\sigma^{2}_{A} + \\sigma^{2}_{D} + \\sigma^{2}_{E}\\\\ \\text{For ACE model : }~ &amp; \\sigma^{2}_{P} = \\sigma^{2}_{A} + \\sigma^{2}_{C} + \\sigma^{2}_{E}, \\quad \\text{where} \\\\ \\sigma^{2}_{P} &amp; \\text{ is the phenotypic variance}, \\\\ \\sigma^{2}_{A} &amp; \\text{ is additive genetic variance}, \\\\ \\sigma^{2}_{D} &amp; \\text{ is dominance genetic variance}, \\\\ \\sigma^{2}_{C} &amp; \\text{ is shared environmental variance, and} \\\\ \\sigma^{2}_{E} &amp; \\text{ is unshared environmental variance.} \\end{align*}\\] For ADE model, \\[\\begin{align*} cov(MZ) = cor(MZ) &amp; = rMZ = \\sigma^{2}_{A} + \\sigma^{2}_{D} \\\\ cov(DZ) = cor(DZ) &amp; = rDZ = 0.5 * \\sigma^{2}_{A} + 0.25 * \\sigma^{2}_{D} \\quad \\text{ , where} \\\\ \\end{align*}\\] the coefficients 1/2 and 1/4 are based on quantitative genetic theory (Mather &amp; Jinks, 1971). By solving the unknowns, the Falconer’s equations for the ADE model: \\[\\begin{align*} \\sigma^{2}_{A} &amp; = 4*rDZ - rMZ \\\\ \\sigma^{2}_{D} &amp; = 2*rMZ - 4*rDZ \\\\ \\sigma^{2}_{E} &amp; = 1 - \\sigma^{2}_{A} - \\sigma^{2}_{D} \\\\ \\end{align*}\\] For ACE model, \\[\\begin{align*} cov(MZ) = cor(MZ) &amp; = rMZ= \\sigma^{2}_{A} + \\sigma^{2}_{C} \\\\ cov(DZ) = cor(DZ) &amp; = rDZ = 0.5 * \\sigma^{2}_{A} + \\sigma^{2}_{C} \\quad \\text{ , where} \\\\ \\end{align*}\\] By solving the unknowns, the Falconer’s equations for the ACE model: \\[\\begin{align*} \\sigma^{2}_{A} &amp; = 2*(rMZ - rDZ) \\\\ \\sigma^{2}_{C} &amp; = 2*rDZ - rMZ \\\\ \\sigma^{2}_{E} &amp; = 1 - \\sigma^{2}_{A} - \\sigma^{2}_{C} = 1 - rMZ \\end{align*}\\] 7.1.2.1 Questions for discussions : Q1. What is missing heritability of common traits in the era of genome-wide association analysis (GWAS)? Answers: Missing heritability refers to the discrepancy between twin/family-estimated heritability and the amount of variance explained by disease/trait-associated loci identified in GWAS Q2. What are the potential sources of missing heritability? Answers: Large number of variants with small effect not reaching GWAS significance due to inadequate power of GWAS Poor detection of rarer disease/trait-associated variants by genotyping arrays Structural variants poorly captured by genotyping arrays Low power to detect gene–gene interactions Underestimation of shared environment among relatives in twin/family-based studies Suggested reading: Manolio TA, Collins FS, Cox NJ, et al. Nature. 2009 ;461(7265):747-753. doi:10.1038/nature08494 7.1.2.2 Hands-on exercise : variance explained using regression-based method Q1. What is the variance of the phenotype? Q2. Compute the explained variance attributable to the additive genetic component of the QTL with strongest association in Part 1. Q3. Compute the explained variance attributable to the dominance genetic component of the QTL with strongest association in Part 1. R2 from the regression represents the proportion of phenotypic variance explained; thus the raw explained variance component is R2 times the variance of the phenotype (var_pheno). Answers The proportion of explained variance are 0.0273 (additive) and 0.0541 (total: additive + dominance). As the predictors are uncorrelated, the proportion of explained variance by dominance = 0.0541 - 0.0273 = 0.0267 Given the phenotypic variance of 15.102, then Total genetic: 0.0541*15.102 = 0.8168 Additive genetic: 0.0273*15.102 = 0.4128 Dominance genetic: 0.0267*15.102 = 0.4040 var_pheno &lt;- var(dataTwin$pheno1_T1) # the variance of the phenotype var_pheno #&gt; [1] 15.10257 linAD3 &lt;- lm(pheno1_T1 ~ T1QTL_A3 + T1QTL_D3, data=dataTwin) linA3 &lt;- lm(pheno1_T1 ~ T1QTL_A3, data=dataTwin) summary(linAD3)$r.squared # proportion of explained variance by total genetic component #&gt; [1] 0.05408025 summary(linA3)$r.squared # proportion of explained variance by additive component #&gt; [1] 0.02733034 summary(linAD3)$r.squared*var_pheno # (raw) variance component of total genetic component #&gt; [1] 0.8167509 summary(linA3)$r.squared*var_pheno # (raw) variance component of additive genetic component #&gt; [1] 0.4127585 (summary(linAD3)$r.squared-summary(linA3)$r.squared)*var_pheno # (raw) variance component of dominance genetic component #&gt; [1] 0.4039924 Q4. Estimate the variance explained by all the QTL using linear regression. Answers Proportion of variance explained by all 5 QTLs with dominance = 0.23 and the total variance explained = 3.52. # compute for all 5 QTL linAD5=(lm(pheno1_T1 ~ T1QTL_A1 + T1QTL_A2 + T1QTL_A3 + T1QTL_A4 + T1QTL_A5 + T1QTL_D1 + T1QTL_D2 + T1QTL_D3 + T1QTL_D4 + T1QTL_D5, data=dataTwin)) summary(linAD5)$r.squared # proportion of explained variance by total genetic component #&gt; [1] 0.2330307 summary(linAD5)$r.squared*var_pheno # (raw) variance component of total genetic component #&gt; [1] 3.519363 7.1.2.3 Hands-on exercise : variance explained using a classical twin design. Based on our regression results, we have estimates of the total genetic variance as well as the A and D components for phenotype 1. In practice, it is impossible to know all the variants associated with any polygenic trait. Given rMZ &gt; 2*rDZ, we can use Falconer’s formula based on ADE model to estimate the A (additive genetic) and D (dominance) variance with the classical twin design for phenotype 1 without genotypes. Q5. Compute rMZ and rDZ. Answers rMZ = 0.5434 rDZ = 0.1904 Q6. Estimate the proportion of additive and dominance genetic variances using the Falconer’s equations for the ADE model. Answers \\(\\sigma^{2}_{A} = 0.2181\\) \\(\\sigma^{2}_{D} = 0.3253\\) \\(\\sigma^{2}_{E} = 0.4566\\) dataMZ = dataTwin[dataTwin$zygosity==1, c(&#39;pheno1_T1&#39;, &#39;pheno1_T2&#39;)] # MZ data frame dataDZ = dataTwin[dataTwin$zygosity==2, c(&#39;pheno1_T1&#39;, &#39;pheno1_T2&#39;)] # DZ data frame rMZ=cor(dataMZ)[2,1] # element 2,1 in the MZ correlation matrix rDZ=cor(dataDZ)[2,1] # element 2,1 in the DZ correlation matrix rMZ rDZ sA2 = 4*rDZ - rMZ sD2 = 2*rMZ - 4*rDZ sE2 = 1 - sA2 - sD2 print(c(sA2, sD2, sE2)) Similarly, for phenotype 2, we can estimate the proportion of additive and/or dominance genetic variances as well as shared environmental variance using the Falconer’s formula. Q7. Which model (ACE or ADE) should be considered for phenotype 2? Answers ACE as rMZ &lt; 2*rDZ Q8. Estimate the proportion of A, C/D and E variance components for phenotype 2. Answers \\(\\sigma^{2}_{A} = 0.3526\\) \\(\\sigma^{2}_{C} = 0.1610\\) \\(\\sigma^{2}_{E} = 0.4864\\) dataMZ = dataTwin[dataTwin$zygosity==1, c(&#39;pheno2_T1&#39;, &#39;pheno2_T2&#39;)] # MZ data frame dataDZ = dataTwin[dataTwin$zygosity==2, c(&#39;pheno2_T1&#39;, &#39;pheno2_T2&#39;)] # DZ data frame rMZ=cor(dataMZ, use=&quot;complete.obs&quot;)[2,1] # element 2,1 in the MZ correlation matrix rDZ=cor(dataDZ, use=&quot;complete.obs&quot;)[2,1] # element 2,1 in the DZ correlation matrix rMZ rDZ sA2 = 2*(rMZ - rDZ) sC2 = 2*rDZ - rMZ sE2 = 1 - rMZ print(c(sA2, sC2, sE2)) 7.1.3 References Evans DM, Gillespie NA, Martin NG. Biometrical genetics. Biol Psychol. 2002 Oct;61(1-2):33-51. doi: 10.1016/s0301-0511(02)00051-0. PMID: 12385668. [Review article] Falconer, D.S. and Mackay, T.F.C. (1996) Introduction to Quantitative Genetics. 4th Edition, Addison Wesley Longman, Harlow. [Most classical; a lot of online version] Neale, B., Ferreira, M., Medland, S., &amp; Posthuma, D. (Eds.). (2007). Statistical Genetics: Gene Mapping Through Linkage and Association (1st ed.). Taylor &amp; Francis. https://doi.org/10.1201/9780203967201 [chapter on biometrical genetics; can be borrowed from HKU lib] https://ibg.colorado.edu/cdrom2020/dolan/biometricalGenetics/biom_gen_2020.pdf [Course material of the Boulder IBG workshop co-organized by top statistical geneticists] "],["install.html", "Appendix A: Install R &amp; RStudio A.1 Install R (&gt;=4.3.1) A.2 Install RStudio A.3 Use R inside RStudio A4. Cloud computing", " Appendix A: Install R &amp; RStudio This manual covers the installation of both R and RStudio for three different operating systems: Windows, macOS and Ubuntu. You only need to follow the one that you are using on your computer. Differences between R and RStudio R is the backbone of R programming. Once R is installed, you can use it via its built-in R Console (self-contained), terminal or any third-party integrated development environment (IDE), e.g., RStudio. RStudio is a multi-faceted and user-friendly IDE that can make R programming and data analysis in one place and easy to manage. We recommend using RStudio and only demonstrate with it, while you are free to use any other alternative. Acknowledgements This manual is adapted and updated from the materials produced by Xiunan Fang and other team members in Dr Joshua Ho’s lab. A.1 Install R (&gt;=4.3.1) R on Windows Open an internet browser and go to https://cran.r-project.org/. Click on the Download R for Windows link at the top of the page. Choose the base and then Click on the Download R 4.4.1 for Windows link at the top of the page (or a new version if this manual is outdated). Once the download is finished, you will obtain a file named R-4.4.1-win.exe or similar depending on the version that you download. Most of the time, you will likely want to go with the defaults, so click the button Next until the process is complete. R on macOS Open an internet browser and go to https://cran.r-project.org/. Click on the Download R for macOS link at the top of the page. Click on the file containing the latest version of R under the Latest release. Save the R-4.4.1-**.pkg file, double-click it to open, and follow the installation instructions. Note, there are two versions of the .pkg installation file according to the CPU model: Intel Macs (Intel-based) or M1/M2 Macs (ARM-based). Please choose accordingly. R on Linux (Ubuntu) As commonly used in Ubuntu, prior to installing R, let us update the system package index and upgrade all our installed packages using the following two commands: sudo apt update sudo apt -y upgrade After that, all that you have to do is run the following in the command line to install base R. sudo apt -y install r-base A.2 Install RStudio Now that R is installed, you need to download and install RStudio. The installation of RStudio is more straightforward and very similar across the three Operating Systems. Go to https://posit.co/download/rstudio-desktop/#download. We are using `RStudio Desktop Free version. Click on the right file for your OS (e.g., .exe file for Windows or .dmg for MacOS) The installation process is very straightforward as the figure below. A.3 Use R inside RStudio R studio RStudio is a very powerful IDE and provides many useful tools through a four-pane workspace. By default, the four panels are placed as follows (you can also change the setting for your own preference): Top-left panel: Your scripts of the R codes, script is good to keep a record of your work and also convenient for command execution. You can create a new script by File –&gt; New –&gt; R Script Bottom-left panel: R console for R commands, where you actually run the R codes. Top-right panel: Workspace tab: All the data(more specifically, R objects) you have created in the Workspace and all previous commands you previously ran in the History. Bottom-right panel: Files in your working directory(you probably should also set your working directory) in Files, and the plots you have created in Plots. Set working directory Create a folder named “biof_Rdir” in your preferred directory Create a “data” folder in the “biof_Rdir” From RStudio, use the menu to change your working directory under Session &gt; Set Working Directory &gt; Choose Directory Choose the directory to “biof_Rdir” Or you can type in the console: setwd(&quot;/yourdirectory/biof_Rdir&quot;) For Windows, the command might look like : setwd(&quot;c:/yourdirectory/biof_Rdir&quot;) Some general knowledge R is case-sensitive Type enter to run R code in the console pane Ctrl-enter or Cmd-return if the code is in the scripts pane. Comments come after # will not be treated as codes R has some pre-loaded data sets, to see the list of pre-loaded data, type data() In R, a function is an object, a basic syntax of an R function looks like something below: function_name &lt;- function(arg_1, arg_2, ...) { actual function codes } For example: my_average &lt;- function(x){ sum(x)/length(x) } my_average(c(1, 4, 5, 7)) #&gt; [1] 4.25 R contains a lot of built-in functions, you can use ? or help() to see the documentation of a function, there are also a lot of external libraries with specific functions. To use a library, we do: install.packages(&#39;package_name&#39;) library(package_name) Install packages There are several packages used in this workshop, in the R console, type: install.packages(&#39;ggplot2&#39;) install.packages(&#39;pheatmap&#39;) install.packages(&#39;aod&#39;) A4. Cloud computing In case you have limited computing power, you can still use cloud computing to finish this course. There can be multiple options and here we mainly recommend RStudio cloud (https://posit.cloud; previously known as https://rstudio.cloud/). You can explore directly from their website. "],["references-1.html", "References", " References "]]