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# glmGamPoi
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[](https://github.com/const-ae/glmGamPoi)
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> Fit Small and Large Scale Gamma-Poisson Generalized Linear Models.
*Gamma-Poisson is just another name for the Negative Binomial model. It
however better emphasizes the overdispersed count nature of this model.*
The `glmGamPoi` R package provides an easy to use interface to fit
Gamma-Poisson models efficiently. It is designed to handle large scale
datasets with thousands of rows and columns as they are typically
encountered in modern high-throughput biology. It can automatically
determine the appropriate size factors to normalize for different sizes
across samples and infer the overdispersion for each row in the input
matrix. The package can handle in-memory datasets, but also on-disk
matrices with the `DelayedArray` package.
## Installation
You can install the development version of `glmGamPoi` from
[Github](https://github.com/const-ae/glmGamPoi):
``` r
# install.packages("devtools")
devtools::install_github("const-ae/glmGamPoi")
```
Please make sure that you are using at least version `3.6` of R and
`3.10` of BioConductor.
## Example
To fit a single Gamma-Poisson GLM do:
``` r
# overdispersion = 1/size
counts <- rnbinom(n = 10, mu = 5, size = 1/0.7)
# size_factors = FALSE, because only a single GLM is fitted
fit <- glmGamPoi::glm_gp(counts, design = ~ 1, size_factors = FALSE)
fit
#> glmGamPoiFit object:
#> The data had 1 rows and 10 columns.
#> A model with 1 coefficient was fitted.
# Internally fit is just a list:
c(fit)
#> $Beta_est
#> [,1]
#> [1,] 1.774952
#>
#> $overdispersions
#> [1] 1.143448
#>
#> $Mu_est
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,] 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9
#>
#> $size_factors
#> [1] 1 1 1 1 1 1 1 1 1 1
#>
#> $model_matrix
#> Intercept
#> [1,] 1
#> [2,] 1
#> [3,] 1
#> [4,] 1
#> [5,] 1
#> [6,] 1
#> [7,] 1
#> [8,] 1
#> [9,] 1
#> [10,] 1
#> attr(,"assign")
#> [1] 0
#>
#> $design_formula
#> ~1
```
The `glm_gp()` function returns a list with the results of the fit. Most
importantly, it contains the estimates for the coefficients β and the
overdispersion.
Fitting repeated Gamma-Poisson GLMs for each gene of a single cell
dataset is just as easy:
I will first load an example dataset using the `TENxPBMCData` package.
The dataset has 33,000 genes and 4340 cells
``` r
pbmcs <- TENxPBMCData::TENxPBMCData("pbmc4k")
#> snapshotDate(): 2019-04-29
#> see ?TENxPBMCData and browseVignettes('TENxPBMCData') for documentation
#> downloading 0 resources
#> loading from cache
#> 'EH1613 : 1613'
pbmcs
#> class: SingleCellExperiment
#> dim: 33694 4340
#> metadata(0):
#> assays(1): counts
#> rownames(33694): ENSG00000243485 ENSG00000237613 ...
#> ENSG00000277475 ENSG00000268674
#> rowData names(3): ENSEMBL_ID Symbol_TENx Symbol
#> colnames: NULL
#> colData names(11): Sample Barcode ... Individual Date_published
#> reducedDimNames(0):
#> spikeNames(0):
```
I call `glm_gp()` to fit one GLM model for each gene and force the
calculation to happen in memory.
``` r
# This takes ~1 minute
fit <- glmGamPoi::glm_gp(pbmcs, on_disk = FALSE)
```
Let’s look at the result:
``` r
# Overview of the fit:
summary(fit)
#> glmGamPoiFit object:
#> The data had 33694 rows and 4340 columns.
#> A model with 1 coefficient was fitted.
#> The design formula is: Y~1
#>
#> Beta_est:
#> Min 1st Qu. Median 3rd Qu. Max
#> [1,] -Inf -Inf -7.68 -3.62 5.37
#>
#> overdispersion:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0 0 0 0.228 10311
#>
#> size_factors:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0.743 0.968 1 1.03 2.06
#>
#> Mu_est:
#> Min 1st Qu. Median 3rd Qu. Max
#> 0 0 0.000488 0.0269 442
# Best_est = -Inf means that `all(counts == 0)` for that gene
# Make a plot of mean-overdispersion relation
library(ggplot2)
ggplot(data.frame(mean=fit$Mu[,1], overdispersion=fit$overdispersions),
aes(x=mean, y = overdispersion)) +
geom_point(size = 0.1, alpha = 0.1) +
scale_x_log10() + scale_y_log10() +
labs(title = "Overdispersion Trend Against the Mean Expression",
caption = "Note the large number of genes with overdispersion = 0 at the bottom of the plot")
```
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## Benchmark
For demonstration purposes, I create a sample benchmark with 300
non-empty genes from the `pbmc4k` dataset:
``` r
non_empty_rows <- which(DelayedMatrixStats::rowSums2(assay(pbmcs)) > 0)
pbmcs_subset <- as.matrix(SummarizedExperiment::assay(pbmcs)[sample(non_empty_rows, 300), ])
model_matrix <- matrix(1, nrow = ncol(pbmcs_subset))
dim(pbmcs_subset)
#> [1] 300 4340
```
I 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.
``` r
bench::mark(
glmGamPoi_in_memory = {
glmGamPoi::glm_gp(pbmcs_subset, design = model_matrix, on_disk = FALSE)
}, glmGamPoi_on_disk = {
glmGamPoi::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
)
#> # A tibble: 4 x 6
#> expression min median `itr/sec` mem_alloc `gc/sec`
#> <bch:expr> <bch:tm> <bch:tm> <dbl> <bch:byt> <dbl>
#> 1 glmGamPoi_in_memory 390.5ms 393.09ms 2.54 248.9MB 0
#> 2 glmGamPoi_on_disk 3.47s 3.47s 0.289 755.26MB 0.289
#> 3 DESeq2 20.07s 20.07s 0.0498 1.14GB 0.0498
#> 4 edgeR 5.21s 5.21s 0.192 978.54MB 0.192
```
Fitting the full `pbmc4k` dataset on a modern MacBook Pro in-memory
takes ~1 minute and on-disk ~4 minutes. Fitting the `pbmc68k` (17x the
size) takes ~73 minutes (17x the time) on-disk. Fitting that dataset
in-memory is not possible because it is just too big: the maximum
in-memory matrix size is `2^31-1 ≈ 2.1e9` is elements, the `pbmc68k`
dataset however has nearly 100 million elements more.
Comparing the results:
``` r
# Results with my method
fit <- glmGamPoi::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)
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)
```
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The inferred Beta coefficients and gene means agree well between the
methods, however the overdispersion differs quite a bit. `DESeq2` has
problems estimating some of the overdispersions and sets them to `1e-8`.
`edgeR` only approximates the overdispersions which explains the
variation around the overdispersions calculated with `glmGamPoi`.
