The Intra-Cluster Correlation Coefficient in Cluster Randomized Trials: A Review of Definitions

The intra-cluster correlation coefficient (ICC) of the primary outcome plays a key role in the design and analysis of cluster randomized trials (CRTs), but the precise definition of this parameter is somewhat elusive, especially in the context of non-normally distributed outcomes. In this paper, we provide a unified treatment of ICC as used in CRTs. We present a general definition of the ICC that may be expressed in different ways depending on the modelling approach used to describe the data, illustrating how this general definition is applied to continuous and dichotomous outcomes. Greater complexity arises for dichotomous outcomes; in particular, the usual definition of the ICC cannot be related directly to the parameters of the logistic-normal model that is commonly used for dichotomous outcomes. We show how the definition of the ICC is different when covariates are introduced. Finally, we use our framework and definition of the ICC to draw out implications for those interpreting and choosing values of the ICC when planning CRTs.