  Next-generation sequencing technologies now constitute a method of choice to
measure gene expression. Data to analyze are read counts, commonly modeled
using Negative Binomial distributions. A relevant issue associated with this
probabilistic framework is the reliable estimation of the overdispersion
parameter, reinforced by the limited number of replicates generally observable
for each gene. Many strategies have been proposed to estimate this parameter,
but when differential analysis is the purpose, they often result in procedures
based on plug-in estimates, and we show here that this discrepancy between the
estimation framework and the testing framework can lead to uncontrolled type-I
errors. Instead we propose a mixture model that allows each gene to share
information with other genes that exhibit similar variability. Three consistent
statistical tests are developed for differential expression analysis. We show
that the proposed method improves the sensitivity of detecting differentially
expressed genes with respect to the common procedures, since it is the best one
in reaching the nominal value for the first-type error, while keeping elevate
power. The method is finally illustrated on prostate cancer RNA-seq data.
