Shrinkage of dispersion parameters in the binomial family, with application to differential exon skipping

Abstract

The prevalence of sequencing experiments in genomics has led to an increased use of methods for count data in analyzing high-throughput genomic data to perform analyses. The importance of shrinkage methods in improving the performance of statistical methods remains. A common example is gene expression data, where the counts per gene are often modeled as some form of an overdispersed Poisson. Shrinkage estimates of the per-gene dispersion parameter have led to improved estimation of dispersion, particularly in the case of a small number of samples.

We address a different count setting introduced by the use of sequencing data: comparing differential proportional usage via an overdispersed binomial model. We are motivated by our interest in testing for differential exon skipping in mRNA-Seq experiments. We introduce a novel shrinkage method that models the overdispersion with the double binomial distribution proposed by Efron [J. Amer. Statist. Assoc. 81 (1986) 709–721].

Our method (WEB-Seq) is an empirical Bayes strategy for producing a shrunken estimate of dispersion and effectively detects differential proportional usage, and has close ties to the weighted-likelihood strategy of edgeR developed for gene expression data [Bioinformatics 23 (2007) 2881–2887, Bioinformatics (Oxford, England) 26 (2010) 139–140]. We analyze its behavior on simulated data sets as well as real data and show that our method is fast, powerful and gives accurate control of the FDR compared to alternative approaches. We provide implementation of our methods in the R package DoubleExpSeq available on CRAN.