A Bayesian-bandit adaptive design for N-of-1 clinical trials

N-of-1 trials, which are randomized, double-blinded, controlled, multiperiod, crossover trials on a single subject, have been applied to determine the heterogeneity of the individual's treatment effect in precision medicine settings. An aggregated N-of-1 design, which can estimate the population effect from these individual trials, is a pragmatic alternative when a randomized controlled trial (RCT) is infeasible. We propose a Bayesian adaptive design for both the individual and aggregated N-of-1 trials using a multiarmed bandit framework that is estimated via efficient Markov chain Monte Carlo. A Bayesian hierarchical structure is used to jointly model the individual and population treatment effects. Our proposed adaptive trial design is based on Thompson sampling, which randomly allocates individuals to treatments based on the Bayesian posterior probability of each treatment being optimal. While we use a subject-specific treatment effect and Bayesian posterior probability estimates to determine an individual's treatment allocation, our hierarchical model facilitates these individual estimates to borrow strength from the population estimates via shrinkage to the population mean. We present the design's operating characteristics and performance via a simulation study motivated by a recently completed N-of-1 clinical trial. We demonstrate that from a patient-centered perspective, subjects are likely to benefit from our adaptive design, in particular, for those individuals that deviate from the overall population effect.