ESTIMATING EQUATIONS FOR MEASURES OF ASSOCIATION BETWEEN REPEATED BINARY RESPONSES

Moment-based methods for analyzing repeated binary responses using the marginal odds ratio as a measure of association have been proposed by a number of authors. Carey, Zeger, and Diggle (1993, Biometrika 80, 5 17-526) have recently described how the marginal odds ratio can be est imated using generalized estimating equations (GEE) based on condition al residuals (deviations about conditional expectations). In this pape r, we show that other measures of association between pairs of binary responses, e.g., the correlation, can also be estimated using conditio nal residuals. We demonstrate that the estimator of the correlation ba sed on conditional residuals is nearly efficient when compared with ma ximum likelihood or second order estimating equations (GEE2) except wh en the correlation is large. This estimator also yields more efficient estimates of the correlation than the usual GEE estimator that is bas ed on unconditional residuals. Furthermore, the gains in efficiency ca n be quite considerable when some of the responses are missing or inco mplete, or, alternatively, when cluster sizes are unequal (in the clus tered data setting).