Estimation of a common odds ratio under binary cluster sampling

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Abstract
We present results from a simulation study for the estimation of a common odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. We model the correlation of the data by the beta‐binomial distribution. Through a simulation study, we compare the Mantel—Haenszel estimator with Rao and Scott'S estimator in terms of their biases, observed variances, relative efficiencies of their variances and 95 per cent coverage proportions. We limit the simulation study to the case where there are the same number of subjects in each cluster and the same number of observations in each row of each stratum. When ρ = 0, we recommend use of the Mantel—Haenszel estimator γMH with an unadjusted variance and Rao and Scott'S estimator γ with a pooled design effect. In general, when ρ >0, we recommend the Mantel—Haenszel estimator γMH with an adjusted variance and Rao and Scott'S estimator γ with a pooled design effect.