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Estimating empirical null distributions for Chi-squared and Gamma statistics with application to multiple testing in RNA-seq

Genome and transcriptome studies using microarray and RNA-seq technologies often involve simultaneous hypothesis testing of thousands of genes or transcripts. A key step determining significant differential expression in such large-scale testing is obtaining the null distribution of the test statistics. We show by examples that the asymptotic null is often inappropriate for many of the χ tests in RNA-seq analysis. Instead we propose a Gamma mixture model and new methods based on maximum likelihood and characteristic functions to estimate an empirical null distribution in these settings. We show by simulations and applications that our proposed methods perform favorably compared with other existing methods.