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Open Access Publications from the University of California

Shrinkage of dispersion parameters in the double exponential family of distributions, with applications to genomic sequencing

  • Author(s): Ruddy, Sean
  • Advisor(s): Purdom, Elizabeth
  • et al.

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 that of gene expression data, where the counts per gene are often modeled as some form of an overdispersed Poisson. In this case, shrinkage estimates of the per-gene dispersion parameter have lead to improved estimation of dispersion 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. Such a model can be useful for testing differential exon inclusion in mRNA-Seq experiments in addition to the typical differential gene expression analysis. In this setting, there are fewer such shrinkage methods for the dispersion parameter. We introduce a novel method that is developed by modeling the dispersion based on the double exponential family of distributions proposed by Efron (1986), also known as the exponential dispersion model (Jorgensen, 1987). Our methods (WEB-Seq and DEB-Seq) are empirical bayes strategies for producing a shrunken estimate of dispersion that can be applied to any double exponential dispersion family, though we focus on the binomial and poisson. These methods effectively detect differential proportional usage, and have close ties to the weighted likelihood strategy of edgeR developed for gene expression data (Robinson and Smyth, 2007; Robinson et al., 2010). We analyze their behavior on simulated data sets as well as real data for both differential exon usage and differential gene expression. In the exon usage case, we will demonstrate our methods' superior ability to control the FDR and detect truly different features compared to existing methods. In the gene expression setting, our methods fail to control the FDR; however, the rankings of the genes by p-value is among the top performers and proves to be robust to both changes in the probability distribution used to generate the counts and in low sample size situations. We provide implementation of our methods in the R package DoubleExpSeq available from the Comprehensive R Archive Network (CRAN).

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