Robust Bayesian Learning for Individualized Treatment Rules Under Unmeasured Confounding

Abstract

Data-driven personalized decision-making has become increasingly important in many scientific fields. Most existing methods rely on the assumption of no unmeasured confounding to establish causal inferences before proceeding with decision-making for identifying the optimal individualized treatment rule (ITR). However, this assumption is often violated in practice, especially in observational studies. While techniques like instrumental variables or proxy variables can help address unmeasured confounding, such additional data sources are not always available. Moreover, robustly learning the optimal ITR from observational data is challenging when data are unbalanced, where certain combinations of treatments and patient characteristics are underrepresented. In this paper, we develop a novel Bayesian approach to robustly learn the optimal ITR for continuous treatments under unmeasured confounding. For causal identification, we propose a Bayesian causal model that achieves unique identification under certain mild distributional assumptions, without requiring additional data sources. For policy optimization, we develop a practical algorithm that robustly learns the optimal ITR by identifying a conservative policy. Through simulations and an application to a large-scale kidney transplantation dataset, we demonstrate the proposed method’s identifiability, utility, and robustness, highlighting its value in advancing precision medicine.