Bayesian semiparametric model for sequential treatment decisions with informative timing

We develop a Bayesian semiparametric model for the impact of dynamic treatment rules on survival among patients diagnosed with pediatric acute myeloid leukemia (AML). The data consist of a subset of patients enrolled in a phase III clinical trial in which patients move through a sequence of four treatment courses. At each course, they undergo treatment that may or may not include anthracyclines (ACT). While ACT is known to be effective at treating AML, it is also cardiotoxic and can lead to early death for some patients. Our task is to estimate the potential survival probability under hypothetical dynamic ACT treatment strategies, but there are several impediments. First, since ACT is not randomized, its effect on survival is confounded over time. Second, subjects initiate the next course depending on when they recover from the previous course, making timing potentially informative of subsequent treatment and survival. Third, patients may die or drop out before ever completing the full treatment sequence. We develop a generative Bayesian semiparametric model based on Gamma Process priors to address these complexities. At each treatment course, the model captures subjects' transition to subsequent treatment or death in continuous time. G-computation is used to compute a posterior over potential survival probability that is adjusted for time-varying confounding. Using our approach, we estimate the efficacy of hypothetical treatment rules that dynamically modify ACT based on evolving cardiac function.