School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia.
Stat Med. 2024 Dec 10;43(28):5461-5472. doi: 10.1002/sim.10251. Epub 2024 Oct 24.
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.
我们提出了一种基于贝叶斯似然回归估计框架的半参数方法，用于动态治疗方案的贝叶斯建模。基于该框架的方法具有概率一致性特性，可实现最优动态治疗方案的准确估计。与大多数贝叶斯估计方法不同，我们提出的方法通过使用经验似然避免了对中间和最终结果的强分布假设。我们提出的方法允许对阶段结果使用线性或更灵活的均值函数形式。变分贝叶斯逼近用于计算，以避免与马尔可夫链蒙特卡罗方法结合经验似然相关的常见陷阱。通过对 STAR*D 序贯随机试验数据的模拟和分析，我们提出的方法在准确性方面优于 Q 学习和参数贝叶斯似然回归估计，尤其是在回归误差分布的参数假设可能被违反的情况下。
