Modeling Intraclass Correlation in Cluster-Randomized Trials with Binary Outcomes
Keywords: Cluster-randomized trials, intraclass correlation, correlated binary data
Cluster-randomized trials are an increasingly common study design in health research. The design of a cluster-randomized trial requires prediction of the intraclass correlation that will be realized in the observed data. However, current methods of predicting the intraclass correlation, such as using estimates from previous studies, are unreliable. We propose a new framework for explaining and modeling the correlation among the members of a cluster when the outcome is binary, based on the theory of exchangeable binary distributions. In contrast to the commonly used random effects approach, which regards intracluster correlation as arising from between-cluster differences, our approach regards correlation as arising from within-cluster interactions and relationships among cluster members. To illustrate the methods, we present applications to cancer prevention trials.