Semiparametric Bayesian inference for optimal dynamic treatment regimes via dynamic marginal structural models

Abstract

Summary 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.

On “Reflections on the concept of optimality of single decision point treatment regimes”

“…It may be useful for physicians and patients alike to receive guidance both on the recommended treatment and the certainty of that recommendation for a given covariate profile—and for any evaluations of the treatment regime to be made in light of those measures of confidence. There has been some work on Bayesian methods of estimation of optimal tailored treatment regimes, which can be leveraged to provide probability statements about the optimality of a treatment for a given patient profile (Rodriguez Duque et al., 2022). Many of these approaches are highly parametric (Arjas & Saarela, 2010), but more recent work has moved towards semi‐parametric approaches that are less dependent on strong modeling and assumptions (Saarela et al., 2016).…”

Dynamic Treatment Regimes Using Bayesian Additive Regression Trees for Censored Outcomes

“…Two textbooks and an edited volume have been published on the topic of DTRs (Chakraborty and Moodie (2013); Kosorok and Moodie (2015); Tsiatis et al (2020)), and a recent paper surveying value-search approaches by Jiang et al (2019) was the subject of a lively discussion. Bayesian approaches have received relatively little attention in the DTR literature, though exceptions exist (Arjas and Saarela 2010;Saarela et al 2015Saarela et al , 2016Rodriguez Duque et al 2022). However much of the Bayesian DTR methodology is relatively parametric.…”