False Discovery Rate Control for Confounder Selection Using Mirror Statistics

Abstract: While data-driven confounder selection requires careful consideration, it is frequently employed in observational studies. Widely recognized criteria for confounder selection include the minimal-set approach, which involves selecting variables relevant to both treatment and outcome, and the union-set approach, which involves selecting variables associated with either treatment or outcome. These approaches are often implemented using heuristics and off-the-shelf statistical methods, where the degree of uncertainty may not be clear. In this paper, we focus on the false discovery rate (FDR) to measure uncertainty in confounder selection. We define the FDR specific to confounder selection and propose methods based on the mirror statistic, a recently developed approach for FDR control that does not rely on p-values. The proposed methods are p-value-free and require only the assumption of some symmetry in the distribution of the mirror statistic. It can be combined with sparse estimation and other methods that involve difficulties in deriving p-values. The properties of the proposed methods are investigated through exhaustive numerical experiments. Particularly in high-dimensional data scenarios, the proposed methods effectively control FDR and perform better than the p-value-based methods.