Design of Bayesian Clinical Trials With Clustered Data

In the design of clinical trials, it is essential to assess the design operating characteristics (e.g., power and the type I error rate). Common practice for the evaluation of operating characteristics in clinical trials that employ Bayesian analysis and decision procedures relies on estimating the sampling distribution of posterior summaries via Monte Carlo simulation. It is computationally intensive to repeat this estimation process for each design configuration considered, particularly for clustered data that are analyzed using complex, high-dimensional models. In this paper, we propose an efficient method to assess operating characteristics and determine sample sizes for Bayesian trials with clustered data. We prove theoretical results that enable posterior probabilities to be modeled as a function of the number of clusters. Using these functions, we assess operating characteristics at a range of sample sizes given simulations conducted at only two values for the number of clusters. These theoretical results are also leveraged to quantify the impact of simulation variability on our sample size recommendations. The applicability of our methodology is illustrated using an example Bayesian cluster-randomized clinical trial.