Bayesian methods for cluster randomized trials with continuous responses

Bayesian methods for cluster randomized trials extend the random-effects formulation by allowing both the use of external evidence on parameters and straightforward relaxation of the standard normality and constant variance assumptions. Care is required in specifying prior distributions on variance components, and a number of different options are explored with implied prior distributions for other parameters given in closed form. Markov chain Monte Carlo (MCMC) methods permit the fitting of very general models and the introduction of parameter uncertainty into power calculations. We illustrate these ideas using a published example in which general practices were randomized to intervention or control, and show that different choices of supposedly 'non-informative' prior distributions can have substantial influence on conclusions. We also illustrate the use of forward simulation methods in power calculations with uncertainty on multiple inputs. Bayesian methods have the potential to be very useful but guidance is required as to appropriate strategies for robust analysis. Our current experience leads us to recommend a standard 'non-informative' prior distribution for the within-cluster sampling variance, and an independent prior on the intraclass correlation coefficient (ICC). The latter may exploit background evidence or, as a reference analysis, be a uniform ICC or a 'uniform shrinkage' prior.