Estimation of response probability in correlated binary data: A new approach

We consider analysis of binary observations from multiple sites of each subject. In this case, observations from the same subject tend to be correlated. In estimating the common response probability in correlated binary data, two weighting systems have been most popular: equal weights to sites, and equal weights to subjects. When the number of sites varies subject by subject, performance of these two weighting systems depends on the extent of correlation among sites within each subject. In this paper, we describe a new weighting method that minimizes the variance of the estimator. We apply these methods to data from a study involving an enzymatic diagnostic test to illustrate the estimation of the sensitivity and the specificity of periodontal diagnostic tests. Simulation studies were conducted to compare the performance of the new estimator with that of other estimators.