Fit Gamma-Poisson Generalized Linear Models Reliably.
Pronounciation:
dʒi əl əm ɡam ˈpwɑ
The core design aims of glmGamPoi are:
- Fit Gamma-Poisson models on arbitrarily large or small datasets
- Be faster than alternative methods, such as
DESeq2oredgeR - Calculate exact or approximate results based on user preference
- Support in-memory or on-disk data
- Follow established conventions around tools for RNA-seq analysis
- Present a simple user-interface
- Avoid unnecessary dependencies
- Make integration into other tools easy
You can install the release version of glmGamPoi from BioConductor:
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("glmGamPoi")For the latest developments, see the GitHub repo.
If you use this package in a scientific publication, please cite:
glmGamPoi: Fitting Gamma-Poisson Generalized Linear Models on Single Cell Count Data
Constantin Ahlmann-Eltze, Wolfgang Huber
Bioinformatics; 2020-12-09; doi: https://doi.org/10.1093/bioinformatics/btaa1009
Load the glmGamPoi package
library(glmGamPoi)To fit a single Gamma-Poisson GLM do:
# overdispersion = 1/size
counts <- rnbinom(n = 10, mu = 5, size = 1/0.7)
# design = ~ 1 means that an intercept-only model is fit
fit <- glm_gp(counts, design = ~ 1)
fit
#> glmGamPoiFit object:
#> The data had 1 rows and 10 columns.
#> A model with 1 coefficient was fitted.
# Internally fit is just a list:
as.list(fit)[1:2]
#> $Beta
#> Intercept
#> [1,] 1.504077
#>
#> $overdispersions
#> [1] 0.3792855The glm_gp() function returns a list with the results of the fit. Most
importantly, it contains the estimates for the coefficients β and the
overdispersion.
Fitting repeated Gamma-Poisson GLMs for each gene of a single cell dataset is just as easy:
I will first load an example dataset using the TENxPBMCData package.
The dataset has 33,000 genes and 4340 cells. It takes roughly 1.5
minutes to fit the Gamma-Poisson model on the full dataset. For
demonstration purposes, I will subset the dataset to 300 genes, but keep
the 4340 cells:
library(SummarizedExperiment)
library(DelayedMatrixStats)# The full dataset with 33,000 genes and 4340 cells
# The first time this is run, it will download the data
pbmcs <- TENxPBMCData::TENxPBMCData("pbmc4k")
#> snapshotDate(): 2022-10-31
#> see ?TENxPBMCData and browseVignettes('TENxPBMCData') for documentation
#> loading from cache
# I want genes where at least some counts are non-zero
non_empty_rows <- which(rowSums2(assay(pbmcs)) > 0)
pbmcs_subset <- pbmcs[sample(non_empty_rows, 300), ]
pbmcs_subset
#> class: SingleCellExperiment
#> dim: 300 4340
#> metadata(0):
#> assays(1): counts
#> rownames(300): ENSG00000126457 ENSG00000109832 ... ENSG00000143819
#> ENSG00000188243
#> rowData names(3): ENSEMBL_ID Symbol_TENx Symbol
#> colnames: NULL
#> colData names(11): Sample Barcode ... Individual Date_published
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):I call glm_gp() to fit one GLM model for each gene and force the
calculation to happen in memory.
fit <- glm_gp(pbmcs_subset, on_disk = FALSE)
summary(fit)
#> glmGamPoiFit object:
#> The data had 300 rows and 4340 columns.
#> A model with 1 coefficient was fitted.
#> The design formula is: Y~1
#>
#> Beta:
#> Min 1st Qu. Median 3rd Qu. Max
#> Intercept -8.51 -6.57 -3.91 -2.59 0.903
#>
#> deviance:
#> Min 1st Qu. Median 3rd Qu. Max
#> 14 86.8 657 1686 5507
#>
#> overdispersion:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0 1.65e-13 0.288 1.84 24687
#>
#> Shrunken quasi-likelihood overdispersion:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0.707 0.991 1 1.04 7.45
#>
#> size_factors:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0.117 0.738 1.01 1.32 14.5
#>
#> Mu:
#> Min 1st Qu. Median 3rd Qu. Max
#> 2.34e-05 0.00142 0.0185 0.0779 35.8I compare my method (in-memory and on-disk) with DESeq2 and edgeR. Both are classical methods for analyzing RNA-Seq datasets and have been around for almost 10 years. Note that both tools can do a lot more than just fitting the Gamma-Poisson model, so this benchmark only serves to give a general impression of the performance.
# Explicitly realize count matrix in memory so that it is a fair comparison
pbmcs_subset <- as.matrix(assay(pbmcs_subset))
model_matrix <- matrix(1, nrow = ncol(pbmcs_subset))
bench::mark(
glmGamPoi_in_memory = {
glm_gp(pbmcs_subset, design = model_matrix, on_disk = FALSE)
}, glmGamPoi_on_disk = {
glm_gp(pbmcs_subset, design = model_matrix, on_disk = TRUE)
}, DESeq2 = suppressMessages({
dds <- DESeq2::DESeqDataSetFromMatrix(pbmcs_subset,
colData = data.frame(name = seq_len(4340)),
design = ~ 1)
dds <- DESeq2::estimateSizeFactors(dds, "poscounts")
dds <- DESeq2::estimateDispersions(dds, quiet = TRUE)
dds <- DESeq2::nbinomWaldTest(dds, minmu = 1e-6)
}), edgeR = {
edgeR_data <- edgeR::DGEList(pbmcs_subset)
edgeR_data <- edgeR::calcNormFactors(edgeR_data)
edgeR_data <- edgeR::estimateDisp(edgeR_data, model_matrix)
edgeR_fit <- edgeR::glmFit(edgeR_data, design = model_matrix)
}, check = FALSE, min_iterations = 3
)
#> # A tibble: 4 × 6
#> expression min median `itr/sec` mem_alloc `gc/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl> <bch:byt> <dbl>
#> 1 glmGamPoi_in_memory 1.32s 1.36s 0.640 533.47MB 2.13
#> 2 glmGamPoi_on_disk 4.82s 5.03s 0.200 851.78MB 1.20
#> 3 DESeq2 22.07s 23s 0.0440 1.05GB 0.352
#> 4 edgeR 5.69s 5.81s 0.172 792.91MB 0.804On this dataset, glmGamPoi is more than 5 times faster than edgeR
and more than 18 times faster than DESeq2. glmGamPoi does not
use approximations to achieve this performance increase. The performance
comes from an optimized algorithm for inferring the overdispersion for
each gene. It is tuned for datasets typically encountered in single
RNA-seq with many samples and many small counts, by avoiding duplicate
calculations.
To demonstrate that the method does not sacrifice accuracy, I compare
the parameters that each method estimates. The means and β coefficients
are identical, but that the overdispersion estimates from glmGamPoi
are more reliable:
# Results with my method
fit <- glm_gp(pbmcs_subset, design = model_matrix, on_disk = FALSE)
# DESeq2
dds <- DESeq2::DESeqDataSetFromMatrix(pbmcs_subset,
colData = data.frame(name = seq_len(4340)),
design = ~ 1)
sizeFactors(dds) <- fit$size_factors
dds <- DESeq2::estimateDispersions(dds, quiet = TRUE)
dds <- DESeq2::nbinomWaldTest(dds, minmu = 1e-6)
#edgeR
edgeR_data <- edgeR::DGEList(pbmcs_subset, lib.size = fit$size_factors)
edgeR_data <- edgeR::estimateDisp(edgeR_data, model_matrix)
edgeR_fit <- edgeR::glmFit(edgeR_data, design = model_matrix)
I am comparing the gene-wise estimates of the coefficients from all
three methods. Points on the diagonal line are identical. The inferred
Beta coefficients and gene means agree well between the methods, however
the overdispersion differs quite a bit. DESeq2 has problems estimating
most of the overdispersions and sets them to 1e-8. edgeR only
approximates the overdispersions which explains the variation around the
overdispersions calculated with glmGamPoi.
The method scales linearly, with the number of rows and columns in the
dataset. For example: fitting the full pbmc4k dataset with subsampling
on a modern MacBook Pro in-memory takes ~1 minute and on-disk a little
over 4 minutes. Fitting the pbmc68k (17x the size) takes ~73 minutes
(17x the time) on-disk.
glmGamPoi provides an interface to do quasi-likelihood ratio testing
to identify differentially expressed genes. To demonstrate this feature,
we will use the data from Kang et al.
(2018) provided by the
MuscData package. This is a single cell dataset of 8 Lupus patients
for which 10x droplet-based scRNA-seq was performed before and after
treatment with interferon beta. The SingleCellExperiment object
conveniently provides the patient id (ind), treatment status (stim)
and cell type (cell):
sce <- muscData::Kang18_8vs8()
#> snapshotDate(): 2022-10-31
#> see ?muscData and browseVignettes('muscData') for documentation
#> loading from cache
colData(sce)
#> DataFrame with 29065 rows and 5 columns
#> ind stim cluster cell multiplets
#> <integer> <factor> <integer> <factor> <factor>
#> AAACATACAATGCC-1 107 ctrl 5 CD4 T cells doublet
#> AAACATACATTTCC-1 1016 ctrl 9 CD14+ Monocytes singlet
#> AAACATACCAGAAA-1 1256 ctrl 9 CD14+ Monocytes singlet
#> AAACATACCAGCTA-1 1256 ctrl 9 CD14+ Monocytes doublet
#> AAACATACCATGCA-1 1488 ctrl 3 CD4 T cells singlet
#> ... ... ... ... ... ...
#> TTTGCATGCTAAGC-1 107 stim 6 CD4 T cells singlet
#> TTTGCATGGGACGA-1 1488 stim 6 CD4 T cells singlet
#> TTTGCATGGTGAGG-1 1488 stim 6 CD4 T cells ambs
#> TTTGCATGGTTTGG-1 1244 stim 6 CD4 T cells ambs
#> TTTGCATGTCTTAC-1 1016 stim 5 CD4 T cells singletFor demonstration purpose, I will work on a subset of the genes and cells:
set.seed(1)
# Take highly expressed genes and proper cells:
sce_subset <- sce[rowSums(counts(sce)) > 100,
sample(which(sce$multiplets == "singlet" &
! is.na(sce$cell) &
sce$cell %in% c("CD4 T cells", "B cells", "NK cells")),
1000)]
# Convert counts to dense matrix
counts(sce_subset) <- as.matrix(counts(sce_subset))
# Remove empty levels because glm_gp() will complain otherwise
sce_subset$cell <- droplevels(sce_subset$cell)In the first step we will aggregate the counts of each patient, condition and cell type and form pseudobulk samples. This ensures that I get reliable p-value by treating each patient as a replicate and not each cell.
sce_reduced <- pseudobulk(sce_subset, group_by = vars(ind, stim, cell))
#> Aggregating assay 'counts' using 'rowSums2'.
#> Aggregating reducedDim 'TSNE' using 'rowMeans2'.We will identify which genes in CD4 positive T-cells are changed most by
the treatment. We will fit a full model including the interaction term
stim:cell. The interaction term will help us identify cell type
specific responses to the treatment:
fit <- glm_gp(sce_reduced, design = ~ cell + stim + stim:cell - 1,
reference_level = "NK cells")
summary(fit)
#> glmGamPoiFit object:
#> The data had 9727 rows and 47 columns.
#> A model with 6 coefficient was fitted.
#> The design formula is: Y~cell + stim + stim:cell - 1
#>
#> Beta:
#> Min 1st Qu. Median 3rd Qu. Max
#> cellNK cells -1e+08 -1.0e+08 -1.20 -0.107 6.94
#> cellB cells -1e+08 -1.0e+08 -1.36 -0.394 6.93
#> cellCD4 T cells -1e+08 -2.6e+00 -1.62 -0.523 6.97
#> ...
#>
#> deviance:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0 14.6 25.2 35.6 2567
#>
#> overdispersion:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0 1.86e-07 0.0882 0.532 60.8
#>
#> Shrunken quasi-likelihood overdispersion:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0.33 1.02 1.04 1.12 229
#>
#> size_factors:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0.0448 0.511 0.963 1.83 10.5
#>
#> Mu:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0 0 0.218 0.832 11003To see how the coefficient of our model are called, we look at the
colnames(fit$Beta):
colnames(fit$Beta)
#> [1] "cellNK cells" "cellB cells"
#> [3] "cellCD4 T cells" "stimstim"
#> [5] "cellB cells:stimstim" "cellCD4 T cells:stimstim"In our example, we want to find the genes that change specifically in T cells. Finding cell type specific responses to a treatment is a big advantage of single cell data over bulk data.
# The contrast argument specifies what we want to compare
# We test the expression difference of stimulated and control T-cells
de_res <- test_de(fit, contrast = cond(cell = "CD4 T cells", stim = "ctrl") - cond(cell = "CD4 T cells", stim = "stim"))
# Most different genes
head(de_res[order(de_res$pval), ])
#> name pval adj_pval f_statistic df1 df2 lfc
#> 189 IFI6 1.561865e-36 1.519226e-32 494.3754 1 82.25076 -5.295261
#> 5181 IFIT3 1.941621e-33 9.443076e-30 402.8278 1 82.25076 -6.754418
#> 5182 IFIT1 2.906395e-31 9.423503e-28 347.3425 1 82.25076 -5.530940
#> 5 ISG15 2.494256e-29 6.065408e-26 303.3882 1 82.25076 -4.799133
#> 4563 LY6E 3.606785e-27 6.454804e-24 259.5989 1 82.25076 -3.692098
#> 7218 ISG20 3.981580e-27 6.454804e-24 258.7812 1 82.25076 -2.892739The test is successful and we identify interesting genes that are differentially expressed in interferon-stimulated T cells: IFI6, IFIT3 and ISG15 literally stand for Interferon Induced/Stimulated Protein.
To get a more complete overview of the results, we can make a volcano plot that compares the log2-fold change (LFC) vs the logarithmized p-values.
library(ggplot2)
#>
#> Attaching package: 'ggplot2'
#> The following object is masked from 'package:glmGamPoi':
#>
#> vars
ggplot(de_res, aes(x = lfc, y = -log10(pval))) +
geom_point(size = 0.6, aes(color = adj_pval < 0.1)) +
ggtitle("Volcano Plot", "Genes that change most through interferon-beta treatment in T cells")
Another important task in single cell data analysis is the identification of marker genes for cell clusters. For this we can also use our Gamma-Poisson fit.
Let’s assume we want to find genes that differ between T cells and the B cells. We can directly compare the corresponding coefficients and find genes that differ in the control condition (this time not accounting for the pseudo-replication structure):
fit_full <- glm_gp(sce_subset, design = ~ cell + stim + stim:cell - 1,
reference_level = "NK cells")
marker_genes <- test_de(fit_full, `cellCD4 T cells` - `cellB cells`, sort_by = pval)
head(marker_genes)
#> name pval adj_pval f_statistic df1
#> 2873 CD74 9.414538e-198 9.157522e-194 1411.8278 1
#> 3150 HLA-DRA_ENSG00000204287 7.389637e-180 3.593950e-176 1228.0745 1
#> 3152 HLA-DRB1_ENSG00000196126 1.921033e-121 6.228630e-118 717.8697 1
#> 9116 CD79A_ENSG00000105369 2.307338e-74 5.610869e-71 390.5803 1
#> 3166 HLA-DPA1_ENSG00000231389 3.226069e-70 6.275995e-67 364.8244 1
#> 3167 HLA-DPB1_ENSG00000223865 2.257490e-64 3.659768e-61 329.2877 1
#> df2 lfc
#> 2873 1070.895 -5.052300
#> 3150 1070.895 -7.143245
#> 3152 1070.895 -6.993047
#> 9116 1070.895 -7.282279
#> 3166 1070.895 -5.004210
#> 3167 1070.895 -4.257008If we want find genes that differ in the stimulated condition, we just include the additional coefficients in the contrast:
marker_genes2 <- test_de(fit_full, (`cellCD4 T cells` + `cellCD4 T cells:stimstim`) -
(`cellB cells` + `cellB cells:stimstim`),
sort_by = pval)
head(marker_genes2)
#> name pval adj_pval f_statistic df1
#> 2873 CD74 8.764650e-187 8.525375e-183 1297.5198 1
#> 3150 HLA-DRA_ENSG00000204287 5.304332e-175 2.579762e-171 1180.6034 1
#> 3152 HLA-DRB1_ENSG00000196126 2.668295e-109 8.651501e-106 626.9933 1
#> 3166 HLA-DPA1_ENSG00000231389 2.972347e-85 7.228005e-82 460.4820 1
#> 3167 HLA-DPB1_ENSG00000223865 1.871362e-71 3.640548e-68 372.4584 1
#> 9116 CD79A_ENSG00000105369 1.327524e-58 2.152138e-55 295.0837 1
#> df2 lfc
#> 2873 1070.895 -4.753566
#> 3150 1070.895 -6.635859
#> 3152 1070.895 -5.969909
#> 3166 1070.895 -5.207105
#> 3167 1070.895 -5.086061
#> 9116 1070.895 -10.000000We identify many genes related to the human leukocyte antigen (HLA) system that is important for antigen presenting cells like B-cells, but are not expressed by T helper cells. The plot below shows the expression differences.
A note of caution: applying test_de() to single cell data without the
pseudobulk gives overly optimistic p-values. This is due to the fact
that cells from the same sample are not independent replicates! It can
still be fine to use the method for identifying marker genes, as long as
one is aware of the difficulties interpreting the results.
# Create a data.frame with the expression values, gene names, and cell types
tmp <- data.frame(gene = rep(marker_genes$name[1:6], times = ncol(sce_subset)),
expression = c(counts(sce_subset)[marker_genes$name[1:6], ]),
celltype = rep(sce_subset$cell, each = 6))
ggplot(tmp, aes(x = celltype, y = expression)) +
geom_jitter(height = 0.1) +
stat_summary(geom = "crossbar", fun = "mean", color = "red") +
facet_wrap(~ gene, scales = "free_y") +
ggtitle("Marker genes of B vs. T cells")
This work was supported by the EMBL International PhD Programme and the European Research Council Synergy grant DECODE under grant agreement No. 810296.
sessionInfo()
#> R version 4.2.1 RC (2022-06-17 r82503)
#> Platform: x86_64-apple-darwin17.0 (64-bit)
#> Running under: macOS Big Sur ... 10.16
#>
#> Matrix products: default
#> BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
#>
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] stats4 stats graphics grDevices utils datasets methods
#> [8] base
#>
#> other attached packages:
#> [1] ggplot2_3.4.0 muscData_1.12.0
#> [3] ExperimentHub_2.6.0 AnnotationHub_3.6.0
#> [5] BiocFileCache_2.6.0 dbplyr_2.3.0
#> [7] TENxPBMCData_1.16.0 HDF5Array_1.26.0
#> [9] rhdf5_2.42.0 SingleCellExperiment_1.20.0
#> [11] DelayedMatrixStats_1.20.0 DelayedArray_0.24.0
#> [13] Matrix_1.5-3 SummarizedExperiment_1.28.0
#> [15] Biobase_2.58.0 GenomicRanges_1.50.2
#> [17] GenomeInfoDb_1.34.9 IRanges_2.32.0
#> [19] S4Vectors_0.36.1 BiocGenerics_0.44.0
#> [21] MatrixGenerics_1.10.0 matrixStats_0.63.0
#> [23] glmGamPoi_1.11.4
#>
#> loaded via a namespace (and not attached):
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#> [3] RColorBrewer_1.1-3 filelock_1.0.2
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#> [7] utf8_1.2.3 R6_2.5.1
#> [9] colorspace_2.1-0 DBI_1.1.3
#> [11] rhdf5filters_1.10.0 withr_2.5.0
#> [13] tidyselect_1.2.0 DESeq2_1.38.3
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