Last updated: 2020-04-13
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The number of reads observed for a given gene is proportional not just to the expression level of the gene but also to its gene transcript length and to the sequencing depth of the library. Dividing each read count by the corresponding library size (in millions) yields counts per million (cpm), a simple measure of read abundance that can be compared across libraries of different sizes. Standardizing further by transcript length (in kilobases) gives rise to reads per kilobase per million (rpkm).
Differences in log-cpm between samples can be interpreted as log-fold-changes of expression. The counts are augmented by a small positive value (a half of one read) to avoid taking the logarithm of zero. This ensures no missing log-cpm values and reduces the variability at low count values.
Let \(r_{gi}\) denote the read count of gene \(g\) in sample \(i\), and \(y_{gi} = \log_2 (\frac{r_{gi}+0.5}{R_i+1}*10^6)\), where \(R_i = \sum_gr_{gi}\). Voom assumes mean-variance relationship of \(r\) being \(var(r) = \lambda+\phi\lambda^2\), where \(\lambda=E(r)\).
library(edgeR)
counts = read.delim('https://raw.githubusercontent.com/ucdavis-bioinformatics-training/2018-June-RNA-Seq-Workshop/master/thursday/all_counts.txt')
head(counts)
d0 <- DGEList(counts)
d0 <- calcNormFactors(d0)
cutoff <- 1
drop <- which(apply(cpm(d0), 1, max) < cutoff)
d <- d0[-drop,]
dim(d) # number of genes left
snames <- colnames(counts) # Sample names
cultivar <- substr(snames, 1, nchar(snames) - 2)
time <- substr(snames, nchar(snames) - 1, nchar(snames) - 1)
group <- interaction(cultivar, time)
mm <- model.matrix(~0 + group)
y <- voom(d, mm, plot = T)
# lmFit fits a linear model using weighted least squares for each gene:
fit <- lmFit(y, mm)
head(coef(fit))
dim(coef(fit))
contr <- makeContrasts(groupI5.9 - groupI5.6, levels = colnames(coef(fit)))
contr
sessionInfo()R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)
Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] workflowr_1.6.0 Rcpp_1.0.2 digest_0.6.18 later_0.7.5
[5] rprojroot_1.3-2 R6_2.3.0 backports_1.1.2 git2r_0.26.1
[9] magrittr_1.5 evaluate_0.12 stringi_1.2.4 fs_1.3.1
[13] promises_1.0.1 whisker_0.3-2 rmarkdown_1.10 tools_3.5.1
[17] stringr_1.3.1 glue_1.3.0 httpuv_1.4.5 yaml_2.2.0
[21] compiler_3.5.1 htmltools_0.3.6 knitr_1.20