A framework for testing non-inferiority in a three-arm,sequential,multiple assignment randomized trial

Sequential multiple assignment randomized trial design is becoming increasingly used in the field of precision medicine. This design allows comparisons of sequences of adaptive interventions tailored to the individual patient. Superiority testing is usually the initial goal in order to determine which embedded adaptive intervention yields the best primary outcome on average. When direct superiority is not evident, yet an adaptive intervention poses other benefits, then non-inferiority testing is warranted. Non-inferiority testing in the sequential multiple assignment randomized trial setup is rather new and involves the specification of non-inferiority margin and other important assumptions that are often unverifiable internally. These challenges are not specific to sequential multiple assignment randomized trial and apply to two-arm non-inferiority trials that do not include a standard-of-care (or placebo) arm. To address some of these challenges, three-arm non-inferiority trials that include the standard-of-care arm are proposed. However, methods developed so far for three-arm non-inferiority trials are not sequential multiple assignment randomized trial-specific. This is because apart from embedded adaptive interventions, sequential multiple assignment randomized trial typically does not include a third standard-of-care arm. In this article, we consider a three-arm sequential multiple assignment randomized trial from an National Institutes of Health-funded study of symptom management strategies among people undergoing cancer treatment. Motivated by that example, we propose a novel data analytic method for non-inferiority testing in the framework of three-arm sequential multiple assignment randomized trial for the first time. Sample size and power considerations are discussed through extensive simulation studies to elucidate our method.