Bayesian methods to compare dose levels with placebo in a small n, sequential, multiple assignment, randomized trial

Clinical trials studying treatments for rare diseases are challenging to design and conduct due to the limited number of patients eligible for the trial. One design used to address this challenge is the small n, sequential, multiple assignment, randomized trial (snSMART). We propose a new snSMART design that investigates the response rates of a drug tested at a low and high dose compared with placebo. Patients are randomized to an initial treatment (stage 1). In stage 2, patients are rerandomized, depending on their initial treatment and their response to that treatment in stage 1, to either the same or a different dose of treatment. Data from both stages are used to determine the efficacy of the active treatment. We present a Bayesian approach where information is borrowed between stage 1 and stage 2. We compare our approach to standard methods using only stage 1 data and a log-linear Poisson model that uses data from both stages where parameters are estimated using generalized estimating equations. We observe that the Bayesian method has smaller root-mean-square-error and 95% credible interval widths than standard methods in the tested scenarios. We conclude that it is advantageous to utilize data from both stages for a primary efficacy analysis and that the specific snSMART design shown here can be used in the registration of a drug for the treatment of rare diseases.