ABSTRACT
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.
ABSTRACT
BACKGROUND/AIMS: To evaluate how uncertainty in the intra-cluster correlation impacts whether a parallel-group or stepped-wedge cluster-randomized trial design is more efficient in terms of the required sample size, in the case of cross-sectional stepped-wedge cluster-randomized trials and continuous outcome data. METHODS: We motivate our work by reviewing how the intra-cluster correlation and standard deviation were justified in 54 health technology assessment reports on cluster-randomized trials. To enable uncertainty at the design stage to be incorporated into the design specification, we then describe how sample size calculation can be performed for cluster- randomized trials in the 'hybrid' framework, which places priors on design parameters and controls the expected power in place of the conventional frequentist power. Comparison of the parallel-group and stepped-wedge cluster-randomized trial designs is conducted by placing Beta and truncated Normal priors on the intra-cluster correlation, and a Gamma prior on the standard deviation. RESULTS: Many Health Technology Assessment reports did not adhere to the Consolidated Standards of Reporting Trials guideline of indicating the uncertainty around the assumed intra-cluster correlation, while others did not justify the assumed intra-cluster correlation or standard deviation. Even for a prior intra-cluster correlation distribution with a small mode, moderate prior densities on high intra-cluster correlation values can lead to a stepped-wedge cluster-randomized trial being more efficient because of the degree to which a stepped-wedge cluster-randomized trial is more efficient for high intra-cluster correlations. With careful specification of the priors, the designs in the hybrid framework can become more robust to, for example, an unexpectedly large value of the outcome variance. CONCLUSION: When there is difficulty obtaining a reliable value for the intra-cluster correlation to assume at the design stage, the proposed methodology offers an appealing approach to sample size calculation. Often, uncertainty in the intra-cluster correlation will mean a stepped-wedge cluster-randomized trial is more efficient than a parallel-group cluster-randomized trial design.