Optimal adaptive SMART designs with binary outcomes.

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 critical concerns about SMART designs from an ethical point of view. In this work, we develop an optimal adaptive allocation procedure using a constrained optimization that minimizes the total expected number of treatment failures for a SMART with a binary primary outcome, subject to a fixed asymptotic variance of a predefined objective function. 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 for incoming first-year college students as a bridge to desirable treatments to address alcohol-related risks.