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

In this paper we study properties of the estimators of marginal mean parameters in the GEE1 approach of Heagerty and Zeger [Heagerty, P.J., Zeger, S.L., 1996. Marginal regression models for clustered ordinal measurements. J. Amer. Statist. Assoc. 91, 1024-1036] 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 showed that the difference between empirical and nominal levels widens when sample size decreases, especially when the probability for a given response category is low in a group of clusters with the same covariate vector. 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. For equal cluster sizes, we showed that relative efficiency 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.