COARSE-TO-FINE MULTIPLE TESTING STRATEGIES.

Abstract

We consider a multiple testing scenario encountered in the biological sciences and elsewhere: there are a great many null hypotheses about the distribution of a high-dimensional random variable but only a very small fraction are false (or “active”); moreover, controlling the false positives rate through FWER or FDR is imperative. Not surprisingly, the usual methods applied to control the two former criteria are often too conservative and lead to a small number of true detections. Clearly, some additional assumptions or domain-specific knowledge are then necessary to improve power. Motivated by applications in genomics, particularly genome-wide association studies, we suppose the set indexing the hypotheses has a natural hierarchical structure, the simplest case being a partition into “cells.” In principle, it should then be possible to gain power if the active hypotheses tend to cluster within cells. We explore different coarse-to-fine, two-level multiple testing strategies, which control the FWER or the FDR and are designed to gain power relative to usual single level methods, in so far as clustering allows it. Simulations confirm a sharp improvement for in data models we consider.