Directional False Discovery Rate Control in Large‐Scale Multiple Testing Under Data Dependence

Abstract

ABSTRACT Detecting directional signals in multiple testing is crucial to take targeted and effective measures. In this article, we consider the directional multiple testing under the dependence problem within a three‐group model. Given the assumption that the observed data are generated according to an underlying three‐state hidden Markov model, we develop oracle and data‐driven procedures to maximize the expected number of true discoveries (ETD) while controlling the false discovery rates (FDRs) of both alternative states at their nominal levels. It is shown theoretically that the proposed directional multiple testing procedures are valid and have certain optimality properties for directional FDR‐control. An extensive numerical study shows that our procedures are significantly more powerful than their competitors since the former can accommodate the dependence structure among hypotheses. The proposed procedures also exhibit high flexibility by allowing different nominal levels for the two alternative states, which is appealing in cases when the false discoveries of different alternative states are not equally important. As a demonstration, the proposed data‐driven procedure is applied to learn the transcriptomic characteristics of bronchoalveolar lavage fluid in COVID‐19 patients.