Comparison of Intracluster Correlation Coefficient Estimates For Binary Variables

The present study evaluates bias and standard deviation of fourteen estimators of the intracluster correlation for binary data. The comparisons were performed in an extensive simulation study. The correlated binary data, assuming an exchangeable correlation structure were simulated incorporating variations of overall event rate, event rate variation, the number of clusters, cluster size, cluster size variation and the population intracluster correlation coefficients. The estimators including ANOVA estimators, moment estimators, estimators based on a direct probabilistic interpretation, estimators based on a direct calculation of correlation within each group, and the estimator based on resampling method were computed and compared in terms of bias and standard deviation. The results showed that the distribution of bias and standard deviation for most estimators is positively skewed in most instances. The bias and standard deviation of estimators tended to be closer to zero as the event rate and the event rate variation decreased, and the number of cluster as well as the cluster size increased in our study. Of the 14 estimators, 11 of them including , , , , , , , , , , were found to have less amounts of bias and standard deviation for each combination of variables. Therefore, using our simulation technique, these estimators can be applied to approximate the population ICC for binary data