Constructing intervals for the intracluster correlation coefficient using Bayesian modelling, and application in cluster randomized trials.

Studies in health research are commonly carried out in clustered settings, where the individual response data are correlated within clusters. Estimation and modelling of the extent of between-cluster variation contributes to understanding of the current study and to design of future studies. It is common to express between-cluster variation as an intracluster correlation coefficient (ICC), since this measure is directly comparable across outcomes. ICCs are generally reported unaccompanied by confidence intervals. In this paper, we describe a Bayesian modelling approach to interval estimation of the ICC. The flexibility of this framework allows useful extensions which are not easily available in existing methods, for example assumptions other than Normality for continuous outcome data, adjustment for individual-level covariates and simultaneous interval estimation of several ICCs. There is also the opportunity to incorporate prior beliefs on likely values of the ICC. The methods are exemplified using data from a cluster randomized trial.