Bayesian and frequentist two-stage treatment strategies based on sequential failure times subject to interval censoring

For many diseases, therapy involves multiple stages, with the treatment in each stage chosen adaptively based on the patient's current disease status and history of previous treatments and clinical outcomes. Physicians routinely use such multi-stage treatment strategies, also called dynamic treatment regimes or treatment policies. We present a Bayesian framework for a clinical trial comparing two-stage strategies based on the time to overall failure, defined as either second disease worsening or discontinuation of therapy. Each patient is randomized among a set of treatments at enrollment, and if disease worsening occurs the patient is then re-randomized among a set of treatments excluding the treatment received initially. The goal is to select the two-stage strategy having the largest average overall failure time. A parametric model is formulated to account for non-constant failure time hazards, regression of the second failure time on the patient's first worsening time, and the complications that the failure time in either stage may be interval censored and there may be a delay between first worsening and the start of the second stage of therapy. Four different criteria, two Bayesian and two frequentist, for selecting a best strategy are considered. The methods are applied to a trial comparing two-stage strategies for treating metastatic renal cancer, and a simulation study in the context of this trial is presented. Advantages and disadvantages of this design compared to standard methods are discussed.