Estimation of a common odds ratio in paired‐cluster randomization designs

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Abstract
We develop two estimators of a common odds ratio Ψ for designs in which the investigator randomly assigns each of two clusters to interventions within strata. The estimators rely on an empirical adjustment for clustering to provide improved estimators of Ψ relative to the standard Woolf and Mantel—Haenszel estimators, respectively. The results of a simulation study show that the suggested adjustment improves the accuracy of both of these well-known estimators under conditions likely to arise in practice. We find the clustered Woolf estimator as particularly effective in terms of mean squared error reduction. We also discuss interval estimation.