Bayesian Empirical Likelihood Regression for Semiparametric Estimation of Optimal Dynamic Treatment Regimes.

We propose a semiparametric approach to Bayesian modeling of dynamic treatment regimes that is built on a Bayesian likelihood-based regression estimation framework. Methods based on this framework exhibit a probabilistic coherence property that leads to accurate estimation of the optimal dynamic treatment regime. Unlike most Bayesian estimation methods, our proposed method avoids strong distributional assumptions for the intermediate and final outcomes by utilizing empirical likelihoods. Our proposed method allows for either linear, or more flexible forms of mean functions for the stagewise outcomes. A variational Bayes approximation is used for computation to avoid common pitfalls associated with Markov Chain Monte Carlo approaches coupled with empirical likelihood. Through simulations and analysis of the STAR*D sequential randomized trial data, our proposed method demonstrates superior accuracy over Q-learning and parametric Bayesian likelihood-based regression estimation, particularly when the parametric assumptions of regression error distributions may be potentially violated.