Learning Optimal Distributionally Robust Individualized Treatment Rules Integrating Multi-Source Data

Abstract: Integrative analysis of multiple datasets for estimating optimal individualized treatment rules (ITRs) can enhance decision efficiency. A central challenge is posterior shift, wherein the conditional distribution of potential outcomes given covariates differs between source and target populations. We propose a prior information-based distributionally robust ITR (PDRO-ITR) that maximizes the worst-case policy value over a covariate-dependent distributional uncertainty set, ensuring robust performance under posterior shift. The uncertainty set is constructed as an individualized combination of source distributions, with weights combining prior source-membership probabilities and deviation terms constrained to the probability simplex to accommodate posterior shift. We derive a closed-form solution for the PDRO-ITR and develop an adaptive procedure to tune the uncertainty level. We establish risk bounds for the PDRO-ITR estimator, which guarantees robust performance under the worst case. Extensive simulations and two real-data applications demonstrate that the proposed method achieves superior performance compared to existing approaches.