A method to estimate intra-cluster correlation for clustered categorical data

Abstract

Correlated categorical data often arise from studies involving cluster randomized trials, a cluster sampling scheme, or repeated measurements. The intra-cluster correlation coefficient (ICC) is used to estimate the average correlation within clusters. There have been numerous methods proposed to estimate ICC for correlated binary data, the ANOVA method for continuous data, and several methods for time-to-event outcomes. However, no method currently exists to estimate ICC for nominal or ordinal categorical responses with more than two categories. We developed a method based on resampling principles to estimate the ICC and its 95% confidence interval for categorical variables. We conducted a simulation study to show how our method estimates the population ICC under varying event rates, numbers of clusters, and cluster sizes. We also used real study datasets to estimate the ICC for ordinal and nominal categorical variables. We observed that the resampling method estimates the population ICC well for moderate to large numbers of clusters and moderate to large cluster sizes.