Extended generalized estimating equations for longitudinal data

Longitudinal data consist of repeated observations on each of several individuals. Typically, the analysis of such data is complicated by correlation among repeated responses. Estimating equation approaches to the fitting of generalized linear models to longitudinal data have recently attracted a great deal of attention. This paper proposes an extension to the generalized estimating equations (GEE) approach proposed by Liang and Zeger (1986). In their original paper on the subject these authors treated correlations as nuisance parameters. This paper, using ideas from extended quasi-likelihood, provides estimating equations for regression and association parameters simultaneously. The estimators implied by these equations are proven to be asymptotically normal and consistent under certain conditions. The consistency of regression estimators does not require a correct model specification for the correlation among repeated responses. The approach proposed here is applied to three data sets and monte carlo simulations are performed comparing the small-sample performance of this method with GEE and an alternative procedure proposed by Prentice and Zhao (1991).