Weighted False Discovery Rate Control in Large-Scale Multiple Testing

TL;DR

This paper introduces weighted multiple testing procedures that incorporate prior knowledge to improve detection power while controlling the false discovery rate in large-scale inference tasks.

Contribution

It develops oracle and data-driven methods with proven asymptotic validity and optimality, enhancing interpretability and precision in multiple testing.

Findings

Controls error rate at the nominal level in simulations

Significant power gains over existing methods

Effective in genome-wide association studies

Abstract

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. The results demonstrate that incorporating informative domain knowledge enhances the interpretability of results and precision of inference. Simulation studies 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.