  Sequential Multiple Assignment Randomized Trials (SMARTs) are considered the
gold standard for estimation and evaluation of treatment regimes. SMARTs are
typically sized to ensure sufficient power for a simple comparison, e.g., the
comparison of two fixed treatment sequences. Estimation of an optimal treatment
regime is conducted as part of a secondary and hypothesis-generating analysis
with formal evaluation of the estimated optimal regime deferred to a follow-up
trial. However, running a follow-up trial to evaluate an estimated optimal
treatment regime is costly and time-consuming; furthermore, the estimated
optimal regime that is to be evaluated in such a follow-up trial may be far
from optimal if the original trial was underpowered for estimation of an
optimal regime. We derive sample size procedures for a SMART that ensure: (i)
sufficient power for comparing the optimal treatment regime with standard of
care; and (ii) the estimated optimal regime is within a given tolerance of the
true optimal regime with high-probability. We establish asymptotic validity of
the proposed procedures and demonstrate their finite sample performance in a
series of simulation experiments.
