  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
(FDR) 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. We investigate operating characteristics of the test as a
function of the total number of studies considered, the rank threshold within
each study, and the number of studies within which a gene must be recaptured to
be declared significant. We investigate the trade off between FDR control and
expected sensitivity (the expected proportion of true-positive genes identified
as significant). We give practical guidance on how to design a bioinformatic
list-intersection study with maximal expected sensitivity and prespecified
control of type I error (at the set level) and false discovery rate (at the
gene level). We show how optimal choice of parameters may depend on particular
alternative hypothesis which might hold. We illustrate our methods using
prostate cancer gene-expression datasets from the curated Oncomine database,
and discuss the effects of dependence between genes on the test.
