Adaptive Sequential Multiple Assignment Randomized Trial Designs

Abstract

Sequential Multiple Assignment Randomized Trial (SMART) is an experimental trial framework for evaluating multiple adaptive interventions that tailor treatment sequences to individual responses over time. Traditional SMART designs rely on fixed (non-adaptive) randomization probabilities at each stage and fail to leverage information accumulated during the trial. This may raise ethical concerns by continuing to allocate participants to inferior treatment options. This thesis presents a comprehensive methodology for developing optimal adaptive randomization in SMART designs to enhance both ethical and statistical efficiency. The primary contribution of this work is the derivation of optimal adaptive allocation ratios and procedures for two-stage SMART designs, applicable to both binary and continuous primary outcomes. Building on optimal adaptive randomization theory for two-arm randomized controlled trials, we formulate constrained optimization problems that minimize the total expected number of treatment failures for a binary outcome, subject to fixed asymptotic-variance constraints for prespecified objective functions. For continuous outcomes, the objective function differs. Optimal second-stage allocation ratios are first obtained and are then recursively propagated backward to derive the optimal first-stage allocation.