Covariance estimators for generalized estimating equations in longitudinal analysis with small samples

Abstract

The Generalized Estimating Equations (GEE) statistical method is a simple andeffcient approach to estimate the regression coeffcient of a marginal model forcorrelated responses when the associational structure is regarded as a \nuisance". Itsmost common use is to fit marginal models for longitudinal data in several fields such asbiomedical studies and social sciences. The most attractive feature of the GEEmethodology is that consistent estimates for marginal regression coeffcients areobtained even if the correlation structure is misspecified. However, the techniquerequires that the sample size is large. The variance-covariance matrix of the regressionparameter coeffcients is often estimated by the so-called \sandwich" variance estimator,which is robust and performs well when the size of the sample is large. However, whenthe sample size is small, the \sandwich" estimator does not have a good performance.Specifically, in that case, bias and ineffciency appear. The main goal is to find ways inorder to decrease the bias and improve the effciency. For this reason, some recentlydevelopped modified variance estimators have been proposed. The current GEEmethodology focuses on the modeling of the working correlation matrix assuming aknown variance function. However, Wang, Y.-G., Lin, X. and Zhu, M. (2005) showedthat the correct choice of the correlation structure may not necessarily improve theestimation effciency for the regression parameters if the variance function ismisspecified.