Comparison of statistical methods for analysis of clustered binary observations

When correlated observations are obtained in a randomized controlled trial, the assumption of independence among observations within cluster likely will not hold because the observations share the same cluster (e.g. clinic, physician, or subject). Further, the outcome measurements of interest are often binary. The objective of this paper is to compare the performance of four statistical methods for analysis of clustered binary observations: namely (1) full likelihood method; (2) penalized quasi-likelihood method; (3) generalized estimating equation method; (4) fixed-effects logistic regression method. The first three methods take correlations into account in inferential processes whereas the last method does not. Type I error rate, power, bias, and standard error are compared across the four statistical methods through computer simulations under varying effect sizes, intraclass correlation coefficients, number of clusters, and number of observations per cluster, including large numbers 20 and 100 of observations per cluster. The results show that the performance of the full likelihood and the penalized quasi-likelihood methods is superior for analysis of clustered binary observations, and is not necessarily inferior to that of the fixed-effects logistic regression fit even when within-cluster correlations are zero.