Sample size determination for Bayesian analysis of small n sequential, multiple assignment, randomized trials...

The small n, Sequential, Multiple Assignment, Randomized Trial (snSMART) is a two-stage clinical trial design for rare diseases motivated by the comparison of three active treatments for isolated skin vasculitis in the ongoing clinical trial ARAMIS (a randomized multicenter study for isolated skin vasculitis, NCT09239573). In Stage 1, all patients are randomized to one of three treatments. In Stage 2, patients who respond to their initial treatment receive the same treatment again, while those who fail to respond are re-randomized to one of the two remaining treatments. A Bayesian method for estimating the response rate of each individual treatment in a three-arm snSMART demonstrated efficiency gains for a given sample size relative to other existing frequentist approaches. However, these efficiency gains are dependent upon knowing how many subjects are required to determine a specific difference in the treatment response rates. Because few sample size calculation methods for snSMARTs exist, we propose a Bayesian sample size calculation for an snSMART designed to distinguish the best treatment from the second-best treatment. Although our methods are based on asymptotic approximations, we demonstrate via simulations that our proposed sample size calculation approach produces the desired statistical power, even in small samples. Moreover, our methods and applet produce sample sizes quickly, thereby saving time relative to using simulations to determine the appropriate sample size. We compare our proposed sample size to an existing frequentist method based upon a weighted $$-statistic and demonstrate that the Bayesian method requires far fewer patients than the frequentist method for a study with the same design parameters.