A Simulation Study of the Analysis of Sets of 2 × 2 Contingency Tables under Cluster Sampling: Estimation of a Common Odds Ratio

Abstract This article presents the results of a simulation study of the estimation of a common odds ratio in multiple-contingency tables when the data are correlated within clusters. The correlation is modeled by the beta-binomial distribution. The three objectives of the study were to determine (a) the variances, biases, and relative efficiencies of the beta-binomial maximum likelihood estimator (MLE), the binomial MLE, and the Mantel-Haenszel estimator of the common odds ratio; (b) the variances and biases of two estimators of the intracluster correlation coefficient, ρ; and (c) the effectiveness of adjusting variance estimates of the binomial and Mantel-Haenszel estimators using the two estimators of ρ. The simulation shows that increasing the size of the intracluster correlation coefficient increases the variance and the positive bias of all three estimators of the odds ratio. The Mantel-Haenszel estimator displays less variance and bias than the MLE except for large values of Ψ and ρ. An unexpected b...