Bayesian Sample Size Calculation in Small n, Sequential Multiple Assignment Randomized Trials (snSMART).

A recent study design for clinical trials with small sample sizes is the small n, sequential, multiple assignment, randomized trial (snSMART). An snSMART design has been previously proposed to compare the efficacy of two dose levels versus placebo. In such a trial, participants are initially randomized to receive either low dose, high dose or placebo in stage 1. In stage 2, participants are re-randomized to either dose level depending on their initial treatment and a dichotomous response. A Bayesian analytic approach borrowing information from both stages was proposed and shown to improve the efficiency of estimation. In this paper, we propose two sample size determination (SSD) methods for the proposed snSMART comparing two dose levels with placebo. Both methods adopt the average coverage criterion (ACC) approach. In the first approach, the sample size is calculated in one step, taking advantage of the explicit posterior variance of the treatment effect. In the other two step approach, we update the sample size needed for a single-stage parallel design with a proposed adjustment factor (AF). Through simulations, we demonstrate that the required sample sizes calculated using the two SSD approaches both provide the desired power. We also provide an applet to allow for convenient and fast sample size calculation in this snSMART setting.