Joint Confounder Selection for Causal Mediation Analysis in High Dimensions

The estimation of causal effects in observational research fundamentally relies on proper adjustment for confounding variables. While data-driven confounder selection is well-established for conventional exposure-outcome analyses, such methodologies remain underdeveloped in causal mediation analysis. This paper proposes a Bayesian nonparametric framework for confounder selection in mediation analysis using Bayesian Additive Regression Trees (BART). We introduce a shared sparsity-inducing prior across the exposure, mediator, and outcome models to identify the minimal sufficient adjustment set that satisfies the mediation disjunctive cause criterion. Importantly, we provide rigorous theoretical guarantees for the proposed method: we establish the posterior consistency of confounder selection even in high-dimensional regimes ($P \gg N$) and demonstrate that this selection consistency translates into the consistent estimation of natural direct and indirect effects. The proposed method demonstrates consistently strong performance across a range of simulation scenarios, offering a principled and practical approach for high-dimensional mediation analysis.