Interval estimation of the difference in proportions under m-to-one matching

When the number of potential controls is large relative to the number of available cases, or when little effort needs to be expended in collecting the relevant information on the controls, we often apply multiple matching to attain the validity or increase the efficiency of our inference in epidemiological studies. In this paper, we focus interval estimation on the difference in proportions for m-to-one matching. We consider four asymptotic interval estimators, including the estimator directly using the Mantel-Haenszel (MH) point estimator, the estimator using the tanh(-1)(x) transformation, the estimator derived from the Cochran-Mantel-Haenszel (CMH) test statistic, and the estimator derived from the quadratic inequality developed in this paper. To evaluate and compare the performance of these estimators, we employ Monte Carlo simulation. We find that the estimator directly using the MH estimator can have the coverage probability less than the desired confidence level when the number of matched sets is small. We note that the estimator derived from the quadratic inequality can perform well when the underlying difference is close to 0 even for a small number of matched sets. However, this estimator tends to have the coverage probability less than the desired confidence level as well when the underlying difference in proportions is large. By contrast, the estimator using the CMH statistic tends to have the coverage probability larger than the desired confidence level when the underlying difference is small. We also find that the estimator using the tanh(-1)(x) transformation consistently outperforms the interval estimator directly using the MH estimator. We use the data regarding the association between induced abortions and ectopic pregnancy to illustrate the use of these estimators.