Rank truncated product of P-values, with application to genomewide association scans

Large exploratory studies are often characterized by a preponderance of true null hypotheses, with a small though multiple number of false hypotheses. Traditional multiple-test adjustments consider either each hypothesis separately, or all hypotheses simultaneously, but it may be more desirable to consider the combined evidence for subsets of hypotheses, in order to reduce the number of hypotheses to a manageable size. Previously, Zaykin et al. ([2002] Genet. Epidemiol. 22:170-185) proposed forming the product of all P-values at less than a preset threshold, in order to combine evidence from all significant tests. Here we consider a complementary strategy: form the product of the K most significant P-values. This has certain advantages for genomewide association scans: K can be chosen on the basis of a hypothesised disease model, and is independent of sample size. Furthermore, the alternative hypothesis corresponds more closely to the experimental situation where all loci have fixed effects. We give the distribution of the rank truncated product and suggest some methods to account for correlated tests in genomewide scans. We show that, under realistic scenarios, it provides increased power to detect genomewide association, while identifying a candidate set of good quality and fixed size for follow-up studies.