  We develop a Bayesian semi-parametric model for the estimating 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 the phase III AAML1031 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 was not randomized in the trial, 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 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 under a given rule. A g-computation procedure is used to compute a
posterior over potential survival probability that is adjusted for time-varying
confounding. Using this approach, we conduct posterior inference for the
efficacy of hypothetical treatment rules that dynamically modify ACT based on
evolving cardiac function.
