Nonparametric false discovery rate control for identifying simultaneous signals

It is frequently of interest to jointly analyze multiple sequences of multiple tests in order to identify simultaneous signals, defined as features tested in two or more independent studies that are significant in each. For example, researchers often wish to discover genetic variants that are significantly associated with multiple traits. This paper proposes a false discovery rate control procedure for identifying simultaneous signals in two studies. A pair of test statistics is available for each feature, and the goal is to identify features for which both are non-null. Error control is difficult due to the composite nature of a non-discovery, as one of the tests in the pair can still be non-null. Very few existing methods have high power while still provably controlling the false discovery rate. This paper proposes a simple, fast, tuning parameter-free nonparametric procedure that can be shown to provide asymptotically conservative false discovery rate control. Surprisingly, the procedure does not require knowledge of either the null or the alternative distributions of the test statistics. In simulations, the proposed method had higher power and better error control than existing procedures. In an analysis of genome-wide association study results from five psychiatric disorders, it identified more pairs of disorders that share simultaneously significant genetic variants, as well as more variants themselves, compared to other methods. The proposed method is available in the R package ssa.