Two‐Stage Multiple Test Procedures Controlling False Discovery Rate With Auxiliary Variable and Their Application to Set4Δ Mutant Data

In this paper, we present novel methodologies that incorporate auxiliary variables for multiple hypotheses testing related to the main point of interest while effectively controlling the false discovery rate. When dealing with multiple tests concerning the primary variable of interest, researchers can use auxiliary variables to set preconditions for the significance of primary variables, thereby enhancing test efficacy. Depending on the auxiliary variable's role, we propose two approaches: one terminates testing of the primary variable if it does not meet predefined conditions, and the other adjusts the evaluation criteria based on the auxiliary variable. Employing the copula method, we elucidate the dependence between the auxiliary and primary variables by deriving their joint distribution from individual marginal distributions. Our numerical studies, compared with existing methods, demonstrate that the proposed methodologies effectively control the FDR and yield greater statistical power than previous approaches solely based on the primary variable. As an illustrative example, we apply our methods to the Set4 mutant data set. Our findings highlight the distinctions between our methodologies and traditional approaches, emphasizing the potential advantages of our methods in introducing the auxiliary variable for selecting more genes.