No counts, no variance: allowing for loss of degrees of freedom when assessing biological variability from RNA-seq data.

RNA sequencing (RNA-seq) is widely used to study gene expression changes associated with treatments or biological conditions. Many popular methods for detecting differential expression (DE) from RNA-seq data use generalized linear models (GLMs) fitted to the read counts across independent replicate samples for each gene. This article shows that the standard formula for the residual degrees of freedom (d.f.) in a linear model is overstated when the model contains fitted values that are exactly zero. Such fitted values occur whenever all the counts in a treatment group are zero as well as in more complex models such as those involving paired comparisons. This misspecification results in underestimation of the genewise variances and loss of type I error control. This article proposes a formula for the reduced residual d.f. that restores error control in simulated RNA-seq data and improves detection of DE genes in a real data analysis. The new approach is implemented in the quasi-likelihood framework of the edgeR software package. The results of this article also apply to RNA-seq analyses that apply linear models to log-transformed counts, such as those in the limma software package, and more generally to any count-based GLM where exactly zero fitted values are possible.