Abstract
Gene set analysis (GSA) remains a common step in genome-scale studies because it can reveal insights that are not apparent from results obtained for individual genes. Many different computational tools are applied for GSA, which may be sensitive to different types of signals; however, most methods implicitly test whether there are differences in the distribution of the effect of some experimental condition between genes in gene sets of interest. We have developed a unifying framework for GSA that first fits effect size distributions, and then tests for differences in these distributions between gene sets. These differences can be in the proportions of genes that are perturbed or in the sign or size of the effects. Inspired by statistical meta-analysis, we take into account the uncertainty in effect size estimates by reducing the influence of genes with greater uncertainty on the estimation of distribution parameters. We demonstrate, using simulation and by application to real data, that this approach provides significant gains in performance over existing methods. Furthermore, the statistical tests carried out are defined in terms of effect sizes, rather than the results of prior statistical tests measuring these changes, which leads to improved interpretability and greater robustness to variation in sample sizes.