Joint Mirror Procedure: Controlling False Discovery Rate for Identifying Simultaneous Signals

In many applications, identifying a single feature of interest requires testing the statistical significance of several hypotheses. Examples include mediation analysis which simultaneously examines the existence of the exposure-mediator and the mediator-outcome effects, and replicability analysis aiming to identify simultaneous signals that exhibit statistical significance across multiple independent experiments. In this work, we develop a novel procedure, named joint mirror (JM), to detect such features while controlling the false discovery rate (FDR) in finite samples. The JM procedure iteratively shrinks the rejection region based on partially revealed information until a conservative false discovery proportion (FDP) estimate is below the target FDR level. We propose an efficient algorithm to implement the method. Extensive simulations demonstrate that our procedure can control the modified FDR, a more stringent error measure than the conventional FDR, and provide power improvement in several settings. Our method is further illustrated through real-world applications in mediation and replicability analyses.