Bayesian design and analysis of two-arm cluster randomised trials using assurance

We consider the design of a two-arm superiority cluster randomised controlled trial (RCT) with a continuous outcome. We detail Bayesian inference for the analysis of the trial using a linear mixed-effects model. The treatment is compared to control using the posterior distribution for the treatment effect. We develop the form of the assurance to choose the sample size based on this analysis, and its evaluation using a two loop Monte Carlo sampling scheme. We assess the proposed approach, considering the effect of different forms of prior distribution, and the number of Monte Carlo samples needed in both loops for accurate determination of the assurance and sample size. Based on this assessment, we provide general advice on each of these choices. We apply the approach to the choice of sample size for a cluster RCT into post-stroke incontinence, and compare the resulting sample size to those from a power calculation and assurance based on a Wald test for the treatment effect. The Bayesian approach to design and analysis developed in this paper can offer advantages in terms of an increase in the robustness of the chosen sample size to parameter mis-specification and reduced sample sizes if prior information indicates the treatment effect is likely to be larger than the minimal clinically important difference.