Alternative GEE estimation procedures for discrete longitudinal data

Liang and Zeger (1986) proposed a generalized estimating equations (GEE) approach to the analysis of longitudinal data. Liang and Zeger's method consists of two estimation steps. One is a quasi-likelihood method for estimating regression parameters. The other is a robust moment method for estimating correlation parameters which incorporates the dependence among outcomes. The estimation of correlation parameters is based upon the Pearson residuals, which are implicitly assumed to be normally distributed. However, the normality assumption of Pearson residuals does not hold for discrete responses such as Poisson and binary outcomes. Instead of Pearson residuals, we consider two alternative types of residuals to estimate correlation parameters: Anscombe and deviance residuals. For Poisson and binary outcomes, the three methods are compared through simulation studies. Our results show that the choice of residual has little or no effect on the properties of the resulting estimates. The simple Pearson residual is thus recommended. (C) 1998 Published by Elsevier Science B.V. All. rights reserved.