A Hybrid Approach to Sample Size Re-Estimation in Cluster Randomized Trials with Continuous Outcomes.

This study presents a hybrid (Bayesian-frequentist) approach to sample size re-estimation (SSRE) for cluster randomised trials with continuous outcome data, allowing for uncertainty in the intra-cluster correlation (ICC). In the hybrid framework, pre-trial knowledge about the ICC is captured by placing a Truncated Normal prior on it, which is then updated at an interim analysis using the study data, and used in expected power control. On average, both the hybrid and frequentist approaches mitigate against the implications of misspecifying the ICC at the trial's design stage. In addition, both frameworks lead to SSRE designs with approximate control of the type I error-rate at the desired level. It is clearly demonstrated how the hybrid approach is able to reduce the high variability in the re-estimated sample size observed within the frequentist framework, based on the informativeness of the prior. However, misspecification of a highly informative prior can cause significant power loss. In conclusion, a hybrid approach could offer advantages to cluster randomised trials using SSRE. Specifically, when there is available data or expert opinion to help guide the choice of prior for the ICC, the hybrid approach can reduce the variance of the re-estimated required sample size compared to a frequentist approach. As SSRE is unlikely to be employed when there is substantial amounts of such data available (ie, when a constructed prior is highly informative), the greatest utility of a hybrid approach to SSRE likely lies when there is low-quality evidence available to guide the choice of prior.