Rodriguez Duque Daniel, Stephens David A, Moodie Erica E M, Klein Marina B
Department of Epidemiology, Biostatistics, and Occupational Health, 2001 McGill College Avenue, Suite 1200 Montreal, QC, H3A 1G1, Canada.
Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West Montreal, QC, H3A 0B9, Canada.
Biostatistics. 2023 Jul 14;24(3):708-727. doi: 10.1093/biostatistics/kxac007.
Considerable statistical work done on dynamic treatment regimes (DTRs) is in the frequentist paradigm, but Bayesian methods may have much to offer in this setting as they allow for the appropriate representation and propagation of uncertainty, including at the individual level. In this work, we extend the use of recently developed Bayesian methods for Marginal Structural Models to arrive at inference of DTRs. We do this (i) by linking the observational world with a world in which all patients are randomized to a DTR, thereby allowing for causal inference and then (ii) by maximizing a posterior predictive utility, where the posterior distribution has been obtained from nonparametric prior assumptions on the observational world data-generating process. Our approach relies on Bayesian semiparametric inference, where inference about a finite-dimensional parameter is made all while working within an infinite-dimensional space of distributions. We further study Bayesian inference of DTRs in the double robust setting by using posterior predictive inference and the nonparametric Bayesian bootstrap. The proposed methods allow for uncertainty quantification at the individual level, thereby enabling personalized decision-making. We examine the performance of these methods via simulation and demonstrate their utility by exploring whether to adapt HIV therapy to a measure of patients' liver health, in order to minimize liver scarring.
在频率主义范式下已经对动态治疗方案（DTRs）开展了大量统计工作，但贝叶斯方法在这种情况下可能有很大的用武之地，因为它们能够对不确定性进行适当的表示和传播，包括在个体层面。在这项工作中，我们扩展了最近开发的用于边际结构模型的贝叶斯方法的应用，以得出动态治疗方案的推断。我们通过以下方式做到这一点：（i）将观察世界与所有患者都被随机分配到一个动态治疗方案的世界联系起来，从而实现因果推断，然后（ii）通过最大化后验预测效用，其中后验分布是从关于观察世界数据生成过程的非参数先验假设中获得的。我们的方法依赖于贝叶斯半参数推断，即在无限维分布空间内对有限维参数进行推断。我们还通过使用后验预测推断和非参数贝叶斯自助法，在双重稳健设置下进一步研究动态治疗方案的贝叶斯推断。所提出的方法允许在个体层面进行不确定性量化，从而实现个性化决策。我们通过模拟检验了这些方法的性能，并通过探讨是否根据患者肝脏健康指标调整HIV治疗方案以尽量减少肝纤维化，展示了它们的实用性。
