Some properties of regression estimators in GEE models for clustered ordinal data

Abstract

In this paper we study properties of the estimators of marginal mean parameters in the GEE1approac h of Heagerty and Zeger (J. Amer. Statist. Assoc. 91 (1996) 1024) for clustered ordinal data. We consider two aspects: coverage probabilities and efficiency. The first point was tackled by a simulation study, calculating empirical levels of confidence intervals for regression parameters using different sample sizes. We conclude that inferences have more validity for sample sizes greater than 100, while some care must be taken when the number of clusters is smaller since in several situations empirical levels were much lower than nominal levels. Regarding the second aspect, we studied asymptotic efficiency for the case of an independence working specification in relation to a correctly specified exchangeable association structure. We extended to ordinal measurements the results derived for binary outcomes, sustaining that the loss of efficiency depends both on the intensity of the association between responses and the design matrix. We showed that relative efficiency of independence to exchangeable estimator is high when responses are independent, when covariates are mean-balanced, or when all covariates are constant within clusters. However, relative efficiency noticeably declines with increasing association for non mean-balanced within-cluster covariates. Simulation studies also supported these conclusions for data with an approximately exchangeable association structure.