Regression analysis of correlated binary data: some small sample results for the estimating equation approach

Abstract

Liang and Zeger (1986Biometrika 73 13-22) and Zeger and Liang (1986Biometrics 42 121-30) proposed a generalized estimating equation approach to the estimation of covariate effects on correlated binary outcomes. They showed that estimates of the regression parameters are consistent and asymp¬totically normal even if the correlation structure is misspecified. We present the results of a simulation study designed to evaluate the small sample properties of the estimating equations and to make some comparisons with maximum likelihood. We consider the situation where the block sizes are small and the covariates (block and sub-unit level) are binary. The generalized estimating equations are shown to estimate the regression parameters well in small samples of this type, but estimation of the correlation parameters is more difficult. Misspecification of the correlation structure has some effect on bias and efficiency for small samples (100) but the effect is negligible for larger samples. In these cases, use of the independence working correlation matrix will often be adequate. The robust or “sandwich” estimate of the variance of the regression parameters was robust to misspecification of the covariance structure. Surprisingly, when the number of blocks was as small as 20 it performed just as well as the model-based variance estimate, even when the model was correctly specified.

Keywords:

• Estimating equations
• Quasi-likelihood
• Correlated binary data
• Logistic regression
• Simulation study