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

We develop two estimators of a common odds ratio psi 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 psi 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.