  In a sequential multiple-assignment randomized trial (SMART), a sequence of
treatments is given to a patient over multiple stages. In each stage,
randomization may be done to allocate patients to different treatment groups.
Even though SMART designs are getting popular among clinical researchers, the
methodologies for adaptive randomization at different stages of a SMART are few
and not sophisticated enough to handle the complexity of optimal allocation of
treatments at every stage of a trial. Lack of optimal allocation methodologies
can raise serious concerns about SMART designs from an ethical point of view.
In this work, we develop an optimal adaptive allocation procedure to minimize
the expected number of treatment failures for a SMART with a binary primary
outcome. Issues related to optimal adaptive allocations are explored
theoretically with supporting simulations. The applicability of the proposed
methodology is demonstrated using a recently conducted SMART study named
M-Bridge for developing universal and resource-efficient dynamic treatment
regimes (DTRs) for incoming first-year college students as a bridge to
desirable treatments to address alcohol-related risks.
