Bayesian design and analysis of two-arm cluster randomised trials using assurance: Extension to binary outcomes and comparison of Markov chain Monte Carlo and Integrated Nested Laplace Approximations.

A fully Bayesian design can be used for two-arm cluster trials with both continuous and binary outcomes. Integrated Nested Laplace Approximations can allow for more efficient assessment of the assurance for cluster trials with binary outcomes and large cluster trials with continuous outcomes, without loss of accuracy in inference. A fully Bayesian design of a cluster randomised trial provides a coherent design and analysis framework and incorporates uncertainty in model parameters when choosing the sample size.