Weighted False Discovery Rate Control in Large-scale Multiple Testing
Pallavi Basu, T. Tony Cai, Kiranmoy Das, and Wenguang Sun
The use of weights provides an effective strategy to incorporate prior domain knowledge in large-scale inference. This paper studies weighted multiple testing in a decision-theoretic framework. We develop oracle and data-driven procedures that aim to maximize the expected number of true positives subject to a constraint on the weighted false discovery rate. The asymptotic validity and optimality of the proposed methods are established. Our work shows that incorporating informative domain knowledge enhances the interpretability of results and precision of inference. Simulation studies are conducted to compare our method with existing methods. The results show that the proposed method controls the error rate at the nominal level, and the gain in power over existing methods is substantial in many settings. An application to genome-wide association study is discussed.