Unified approach to false discovery rate control under dependence that incorporates null distribution and shrinkage estimation

Abstract

FDR-controlling procedures are less stringent but powerful multiple testing procedures for large-scale inference and are therefore the preferred error rate to control in such studies. But, the validity and accuracy of any FDR-controlling procedure is essentially determined by whether the chosen test statistic is optimal, the null distributions are correctly or conservatively specified, and whether the data are independent across tests. This study proposes two methods which provide asymptotic FDR control. The first method incorporates null distribution and shrinkage estimation into the original procedures of Benjamini and Hochberg (1995) and Benjamini et al. (2006). Extensive Monte Carlo simulations show that the proposed procedures are essentially more stable and as powerful or substantially more powerful than some procedures proposed in finite sample inferential problems, provided there are at least 30 observations in each group for a case-control experiment. The second part of the study proposes a step-down procedure that explicitly incorporates information about the dependence structure of the test statistic, thereby providing a gain in power. One main distinction of this approach from existing stepwise procedures is the null distribution used in place of the unknown distribution of the test statistics. This null distribution does not rely on the restrictive subset pivotality assumption of Westfall and Young (1993).