Design and analysis considerations for utilizing a mapping function in a small sample, sequential, multiple...

Small sample, sequential, multiple assignment, randomized trials (snSMARTs) are multistage trials with the overall goal of determining the best treatment after a fixed amount of time. In snSMART trials, patients are first randomized to one of three treatments and a binary (e.g. response/nonresponse) outcome is measured at the end of the first stage. Responders to first stage treatment continue their treatment. Nonresponders to first stage treatment are rerandomized to one of the remaining treatments. The same binary outcome is measured at the end of the first and second stages, and data from both stages are pooled together to find the best first stage treatment. However, in many settings the primary endpoint may be continuous, and dichotomizing this continuous variable may reduce statistical efficiency. In this article, we extend the snSMART design and methods to allow for continuous outcomes. Instead of requiring a binary outcome at the first stage for rerandomization, the probability of staying on the same treatment or switching treatment is a function of the first stage outcome. Rerandomization based on a mapping function of a continuous outcome allows for snSMART designs without requiring a binary outcome. We perform simulation studies to compare the proposed design with continuous outcomes to standard snSMART designs with binary outcomes. The proposed design results in more efficient treatment effect estimates and similar outcomes for trial patients.