Ambiguous Dynamic Treatment Regimes: A Reinforcement Learning Approach (2112.04571v4)

Abstract: A main research goal in various studies is to use an observational data set and provide a new set of counterfactual guidelines that can yield causal improvements. Dynamic Treatment Regimes (DTRs) are widely studied to formalize this process. However, available methods in finding optimal DTRs often rely on assumptions that are violated in real-world applications (e.g., medical decision-making or public policy), especially when (a) the existence of unobserved confounders cannot be ignored, and (b) the unobserved confounders are time-varying (e.g., affected by previous actions). When such assumptions are violated, one often faces ambiguity regarding the underlying causal model. This ambiguity is inevitable, since the dynamics of unobserved confounders and their causal impact on the observed part of the data cannot be understood from the observed data. Motivated by a case study of finding superior treatment regimes for patients who underwent transplantation in our partner hospital and faced a medical condition known as New Onset Diabetes After Transplantation (NODAT), we extend DTRs to a new class termed Ambiguous Dynamic Treatment Regimes (ADTRs), in which the causal impact of treatment regimes is evaluated based on a "cloud" of causal models. We then connect ADTRs to Ambiguous Partially Observable Mark Decision Processes (APOMDPs) and develop Reinforcement Learning methods, which enable using the observed data to efficiently learn an optimal treatment regime. We establish theoretical results for these learning methods, including (weak) consistency and asymptotic normality. We further evaluate the performance of these learning methods both in our case study and in simulation experiments.