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One of the main goals of sequential, multiple assignment, randomized trials(SMART) is to find the most efficacious design embedded dynamic treatmentregimes. The analysis method known as multiple comparisons with the best (MCB)allows comparison between dynamic treatment regimes and identification of a setof optimal regimes in the frequentist setting for continuous outcomes, thereby,directly addressing the main goal of a SMART. In this paper, we develop aBayesian generalization to MCB for SMARTs with binary outcomes. Furthermore, weshow how to choose the sample size so that the inferior embedded DTRs arescreened out with a specified power. We compare log-odds between different DTRsusing their exact distribution without relying on asymptotic normality ineither the analysis or the power calculation. We conduct extensive simulationstudies under two SMART designs and illustrate our method's application to theAdaptive Treatment for Alcohol and Cocaine Dependence (ENGAGE) trial.

Bayesian Set of Best Dynamic Treatment Regimes and Sample Size Determination for SMARTs with Binary Outcomes