The sequential multiple assignment randomized trial (SMART) is the ideal study design for the evaluation of multistage treatment regimes, which comprise sequential decision rules that recommend treatments for a patient at each of a series of decision points based on their evolving characteristics. A common goal is to compare the set of so-called embedded regimes represented in the design on the basis of a primary outcome of interest. In the study of chronic diseases and disorders, this outcome is often a time to an event, and a goal is to compare the distributions of the time-to-event outcome associated with each regime in the set. We present a general statistical framework in which we develop a logrank-type test for comparison of the survival distributions associated with regimes within a specified set based on the data from a SMART with an arbitrary number of stages that allows incorporation of covariate information to enhance efficiency and can also be used with data from an observational study. The framework provides clarification of the assumptions required to yield a principled test procedure, and the proposed test subsumes or offers an improved alternative to existing methods. We demonstrate performance of the methods in a suite of simulation studies. The methods are applied to a SMART in patients with acute promyelocytic leukemia.

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