Abstract
Response-adaptive randomization (RAR) has been studied extensively in conventional, single-stage clinical trials, where it has been shown to yield ethical and statistical benefits, especially in trials with many treatment arms. However, RAR and its potential benefits are understudied in sequential multiple assignment randomized trials (SMARTs), which are the gold-standard trial design for evaluation of multi-stage treatment regimes. We propose a suite of RAR algorithms for SMARTs based on Thompson Sampling (TS), a widely used RAR method in single-stage trials in which treatment randomization probabilities are aligned with the estimated probability that the treatment is optimal. We focus on two common objectives in SMARTs: (1) comparison of the regimes embedded in the trial and (2) estimation of an optimal embedded regime. We develop valid post-study inferential procedures for treatment regimes under the proposed algorithms. This is nontrivial, as even in single-stage settings standard estimators of an average treatment effect can have nonnormal asymptotic behavior under RAR. Our algorithms are the first for RAR in multi-stage trials that account for non-standard limiting behavior due to RAR. Empirical studies based on real-world SMARTs show that TS can improve in-trial subject outcomes without sacrificing efficiency for post-trial comparisons.