Exact statistical tests for the intersection of independent lists of genes

Public data repositories have enabled researchers to compare results across multiple genomic studies in order to replicate findings. A common approach is to first rank genes according to an hypothesis of interest within each study. Then, lists of the top-ranked genes within each study are compared across studies. Genes recaptured as highly ranked (usually above some threshold) in multiple studies are considered to be significant. However, this comparison strategy often remains informal, in that Type I error and false discovery rate are usually uncontrolled. In this paper, we formalize an inferential strategy for this kind of list-intersection discovery test. We show how to compute a p-value associated with a `recaptured' set of genes, using a closed-form Poisson approximation to the distribution of the size of the recaptured set. The distribution of the test statistic depends on the rank threshold and the number of studies within which a gene must be recaptured. We use a Poisson approximation to investigate operating characteristics of the test. We give practical guidance on how to design a bioinformatic list-intersection study with prespecified control of Type I error (at the set level) and false discovery rate (at the gene level). We show how choice of test parameters will affect the expected proportion of significant genes identified. We present a strategy for identifying optimal choice of parameters, depending on the particular alternative hypothesis which might hold. We illustrate our methods using prostate cancer gene-expression datasets from the curated Oncomine database.