McNemar's test is used to compare two marginal positive rates from an
independent-sample of paired binary data. When the pairs are not mutua
lly independent, the McNemar's test may not be valid. In this paper, w
e propose a random-effects regression model for comparing two marginal
probabilities from nonindependent matched pairs data with covariates.
An example of comparing positive rates of two blood culture systems i
llustrates this method. In this example, there is no external gold sta
ndard, the paired data are clustered, the data with negative results f
rom both systems are not available, and one culture-specific covariate
is involved. The computing method for the maximum likelihood estimati
on is efficient.