Bayesian Response-Adaptive Randomization for Cluster Randomized Controlled Trials

Cluster randomized controlled trials where groups (or clusters) of individuals, rather than single individuals, are randomized are especially useful when individual-level randomization is not feasible or when interventions are naturally delivered at the group level. Balanced randomization in the cluster randomized trial setting can pose logistical challenges and strain resources if subjects are randomized to a non-optimal arm. We propose a Bayesian response-adaptive randomization design for cluster randomized controlled trials based on Thompson sampling, which dynamically allocates clusters to the most efficacious treatment arm based on the interim posterior distributions of treatment effects using Markov chain Monte Carlo sampling. Our design also incorporates early stopping rules for efficacy and futility determined by prespecified posterior probability thresholds. The performance of the proposed design is evaluated across various operating characteristics under multiple settings, including varying intra-cluster correlation coefficients, cluster sizes, and effect sizes. Our adaptive approach is also compared with a standard, parallel two-arm cluster randomized controlled clinical trial design, highlighting improvements in both ethical considerations and efficiency. From our simulation studies based on an HIV behavioral trial, we demonstrate these improvements by preferentially assigning more clusters to the more efficacious intervention while maintaining robust statistical power and controlling false positive rates.