The sandwich estimator in generalized estimating equations (GEE) approach underestimates the true variance in small samples and, consequently, results in inflated type I error rates in hypothesis testing. This fact limits the application of the GEE in cluster-randomized trials (CRTs) with few clusters. Under various CRT scenarios with correlated binary outcomes, Dr. Peng Li, staff statistician in the office of energetics at the University of Alabama at Birmingham — collaborating with Dr. David T. Redden, professor and chair in UAB’s department of biostatistics — evaluated the small sample properties of the GEE Wald tests using bias-corrected sandwich estimators.
The study results suggest that the GEE Wald z-test should be avoided in the analyses of CRTs with few clusters even when bias-corrected sandwich estimators are used. With t-distribution approximation, the Kauermann and Carroll (KC)-correction can keep the test size to nominal levels even when the number of clusters is as low as 10 and is robust to the moderate variation of the cluster sizes. However, in cases with large variations in cluster sizes, the Fay and Graubard (FG)-correction should be used instead.
Furthermore, Drs. Li and Redden derived a formula to calculate the power and minimum total number of clusters needed using the t-test and KC-correction for the CRTs with binary outcomes. The power levels as predicted by the proposed formula agree well with the empirical powers from the simulations. The researchers illustrate the proposed methods using real CRT data.
With appropriate control of type I error rates under small sample sizes, they recommend the use of GEE approach in CRTs with binary outcomes because of fewer assumptions and robustness to the misspecification of the covariance structure.
“Small Sample Performance of Bias-corrected Sandwich Estimators for Cluster-randomized Trials with Binary Outcomes” was published in October in the journal Statistics in Medicine.