Bayesian optimal cluster designs

Designing cluster trials depends on the knowledge of the intracluster correlation coefficient. To overcome the issue of parameter dependence, Bayesian designs are proposed for two level models with and without covariates. These designs minimize the variance of the treatment contrast under certain cost constraints. A pseudo Bayesian design approach is advocated that integrates and averages the objective function over a prior distribution of the intracluster correlation coefficient. Theoretical results on the Bayesian criterion are noted when the intracluster correlation follows a uniform distribution. Two data sets based on educational surveys conducted in schools are used to illustrate the proposed methodology.