Modified robust variance estimator for generalized estimating equations with improved small-sample performance

Generalized estimating equations (GEE (Biometrika 1986; 73(1):13-22) is a general statistical method to fit marginal models for correlated or clustered responses, and it uses a robust sandwich estimator to estimate the variance-covariance matrix of the regression coefficient estimates. While this sandwich estimator is robust to the misspecification of the correlation structure of the responses, its finite sample performance deteriorates as the number of clusters or observations per cluster decreases. To address this limitation, Pan (Biometrika 2001; 88(3):901-906) and Mancl and DeRouen (Biometrics 2001; 57(1):126-134) investigated two modifications to the original sandwich variance estimator. Motivated by the ideas underlying these two modifications, we propose a novel robust variance estimator that combines the strengths of these estimators. Our theoretical and numerical results show that the proposed estimator attains better efficiency and achieves better finite sample performance compared with existing estimators. In particular, when the sample size or cluster size is small, our proposed estimator exhibits lower bias and the resulting confidence intervals for GEE estimates achieve better coverage rates performance. We illustrate the proposed method using data from a dental study.