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Bayesian Semiparametric Models for Informatively Timed Sequential Treatments

Bayesian Semiparametric Models for Informatively Timed Sequential Treatments

We develop a Bayesian semi-parametric model for the impact of dynamic treatment rules on survival in settings where the treatment process is informatively timed. The work is motivated by a secondary analysis of a Phase III clinical trial in which patients diagnosed with pediatric acute myeloid leukemia (AML) move through a sequence of four treatment courses. At each course, they undergo treatment that may or may not include anthracycline chemotherapy (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 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 chemotherapy course depending on when they recover from the previous course, making timing potentially informative of subsequent ACT treatment and survival. Third, patients may die or drop out before ever completing the full treatment sequence. We develop a generative Bayesian semi-parametric 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.

## Department of Mathematics and Statistics