  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.
