A comparison of bias-corrected empirical covariance estimators with generalized estimating equations in small-sample longitudinal study settings

Data arising from longitudinal studies are commonly analyzed with generalized estimating equations. Previous literature has shown that liberal inference may result from the use of the empirical sandwich covariance matrix estimator when the number of subjects is small. Therefore, two different approaches have been used to improve the validity of inference. First, many different small-sample corrections to the empirical estimator have been offered in order to reduce bias in resulting standard error estimates. Second, critical values can be obtained from a t-distribution or an F-distribution with approximated degrees of freedom. Although limited studies on the comparison of these small-sample corrections and degrees of freedom have been published, there is a need for a comprehensive study of currently existing methods in a wider range of scenarios. Therefore, in this manuscript, we conduct such a simulation study, finding two methods to attain nominal type I error rates more consistently than other methods in a variety of settings: First, a recently proposed method by Westgate and Burchett (2016, Statistics in Medicine 35, 3733-3744) that specifies both a covariance estimator and degrees of freedom, and second, an average of two popular corrections developed by Mancl and DeRouen (2001, Biometrics 57, 126-134) and Kauermann and Carroll (2001, Journal of the American Statistical Association 96, 1387-1396) with degrees of freedom equaling the number of subjects minus the number of parameters in the marginal model.