Statistical power of gene-set enrichment analysis is a function of gene set correlation structure

We develop an analytic statistical framework for examining a variety of gene-set enrichment analysis tests. Within this framework, we describe why statistical power for both self-contained and competitive gene set tests is a function of the correlation structure of co-expressed genes, and why this characteristic is undesireable for gene-set analyses. We additionally describe why past gene-set tests have su↵ered from inflated type 1 error, and how permutation-based methods have sought to address the issue with some success in the case of self-contained tests and with less success in the case of competitive tests. While the context of this investigation is microarray analysis, with particular focus on leading tests CAMERA, ROAST, SAFE, and GAGE, the observations are also relevant to recently proposed RNAseq gene-set tests, including MAST. The variable statistical power we describe as a function of gene correlation structure has not been studied. While type 1 error inflation has been well-studied and described previously for both self-contained and competitive tests, it has less often been done in an analytical framework and so it is useful to make assumptions explicit and examine parametric distributions.