Confidence intervals for differences in correlated binary proportions.

Abstract

An experiment to assess the efficacy of a particular treatment or process often produces dichotomous responses, either favourable or unfavourable. When we administer the treatment on two occasions to the same subjects, we often use McNemar's test to investigate the hypothesis of no difference in the proportions on the two occasions, that is, the hypothesis of marginal homogeneity. A disadvantage in using McNemar's statistic is that we estimate the variance of the sample difference under the restriction that the marginal proportions are equal. A competitor to McNemar's statistic is a Wald statistic that uses an unrestricted estimator of the variance. Because the Wald statistic tends to reject too often in small samples, we investigate an adjusted form that is useful for constructing confidence intervals. Quesenberry and Hurst and Goodman discussed methods of construction that we adapt for constructing confidence intervals for the differences in correlated proportions. We empirically compare the coverage probabilities and average interval lengths for the competing methods through simulation and give recommendations based on the simulation results.