Analyzing correlated binary data using SAS

We discuss methods for analyzing repeated binary measurements on the same individual. In spite of the fact that the repeated measurements on the same individual are correlated, the ordinary logistic regression maximum likelihood estimates (which assume that the repeated measures are independent) are consistent and asymptotically normal (K. Y. Liang and S. L. Zeger, Biometrika 73, 13 (1986]. However, the inverse of the estimated information matrix (assuming independence) can give inconsistent estimates of the asymptotic variance of estimated parameters. We describe how to obtain the logistic regression estimates, as well as a consistent estimate of their covariance matrix, in SAS, with minimal matrix manipulations.