Improved standard error estimator for maintaining the validity of inference in cluster randomized trials with a small number of clusters

Cluster randomized trials (CRTs) are studies in which clusters of subjects are randomized to different trial arms. Due to the nature of outcomes within the same cluster to be correlated, generalized estimating equations (GEE) are growing as a popular choice for the analysis of data arising from CRTs. In the past, research has shown that analyses using GEE could result in liberal inference due to the use of the empirical sandwich covariance matrix estimator, which can yield negatively biased standard error estimates when the number of clusters is not large. Many techniques have been presented to correct this negative bias; however, use of these corrections can still result in biased standard error estimates and thus test sizes that are not consistently at their nominal level. Therefore, there is a need for an improved correction such that nominal type I error rates will consistently result. In this manuscript, we study the use of recently developed corrections for empirical standard error estimation and the use of a combination of two popular corrections. In an extensive simulation study, we found that nominal type I error rates can be consistently attained when using an average of two popular corrections developed by Mancl and DeRouen (, Biometrics57, 126-134) and Kauermann and Carroll (, Journal of the American Statistical Association96, 1387-1396). Therefore, use of this new correction was found to notably outperform the use of previously recommended corrections.