On the comparison of correlated proportions for clustered data.

TLDR: The proposed method, which extends McNemar's test to the case where the observations are sampled in clusters, is a good alternative to Eliasziw and Donner's test when, in practice, little is known about the correlation pattern of the data.

Abstract: McNemar's test is often used to compare two proportions estimated from paired observations. We propose a method extending this to the case where the observations are sampled in clusters. The proposed method is simple to implement and makes no assumptions about the correlation structure. We conducted a Monte Carlo simulation study to compare the size and power of the proposed method with a test developed earlier by Eliasziw and Donner. In the presence of intracluster correlation, the size of McNemar's test can greatly exceed the nominal level. The size of Eliasziw and Donner's test is also inflated for some correlation patterns. The proposed method, on the other hand, is close to the nominal size for a variety of correlation patterns, although it is slightly less powerful than Eliasziw and Donner's procedure. The proposed method is a good alternative to Eliasziw and Donner's test when, in practice, little is known about the correlation pattern of the data.