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

TL;DR

This paper introduces a distributionally robust method for estimating individualized treatment rules that effectively handles differences between source and target populations by maximizing worst-case policy value, ensuring robust decision-making.

Contribution

The paper proposes a novel PDRO-ITR approach that incorporates prior information and constructs a covariate-dependent uncertainty set, with a closed-form solution and adaptive tuning for robust treatment rule estimation.

Findings

Outperforms existing methods in simulations and real data.

Provides theoretical risk bounds guaranteeing robustness.

Achieves superior decision accuracy under posterior shift.

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.