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

Generalized estimating equations (GEE) is a general statistical method to fit marginal models for longitudinal data in biomedical studies. The variance-covariance matrix of the regression parameter coefficients is usually estimated by a robust "sandwich" variance estimator, which does not perform satisfactorily when the sample size is small. To reduce the downward bias and improve the efficiency, several modified variance estimators have been proposed for bias-correction or efficiency improvement. In this paper, we provide a comprehensive review on recent developments of modified variance estimators and compare their small-sample performance theoretically and numerically through simulation and real data examples. In particular, Wald tests and t-tests based on different variance estimators are used for hypothesis testing, and the guideline on appropriate sample sizes for each estimator is provided for preserving type I error in general cases based on numerical results. Moreover, we develop a user-friendly R package "geesmv" incorporating all of these variance estimators for public usage in practice.