Confidence intervals for the difference of marginal probabilities in clustered matched-pair binary data

Although there are several available test statistics to assess the difference of marginal probabilities in clustered matched-pair binary data, associated confidence intervals (CIs) are not readily available. Herein, the construction of corresponding CIs is proposed, and the performance of each CI is investigated. The results from Monte Carlo simulation study indicate that the proposed CIs perform well in maintaining the nominal coverage probability: for small to medium numbers of clusters, the intracluster correlation coefficient-adjusted McNemar statistic and its associated Wald or Score CIs are preferred; however, this statistic becomes conservative when the number of clusters is larger so that alternative statistics and their associated CIs are preferred. In practice, a combination of the intracluster correlation coefficient-adjusted McNemar statistic with an alternative statistic is recommended. To illustrate the practical application, a real clustered matched-pair collection of data is used to illustrate testing the difference of marginal probabilities and constructing the associated CIs.