Small sample performance of bias-corrected sandwich estimators for cluster-randomized trials with binary outcomes

Area of Science:

• Statistics
• Biostatistics
• Clinical Trials

Background:

• Generalized estimating equations (GEE) with sandwich estimators often underestimate variance in small samples.
• This leads to inflated Type I error rates, limiting GEE application in cluster-randomized trials (CRTs) with few clusters.

Purpose of the Study:

• To evaluate the small sample properties of GEE Wald tests in CRTs with correlated binary outcomes.
• To assess the performance of bias-corrected sandwich estimators for hypothesis testing.

Main Methods:

• Simulations under various CRT scenarios with correlated binary outcomes.
• Evaluation of GEE Wald tests using bias-corrected sandwich estimators (Kauermann and Carroll, Fay and Graubard).
• Derivation of a formula for power and minimum cluster number using t-test and KC-correction.

Main Results:

• GEE Wald z-tests are not recommended for CRTs with few clusters, even with bias correction.
• The Kauermann and Carroll (KC)-correction maintains nominal test size with t-distribution approximation, even for 10 clusters, and is robust to moderate cluster size variations.
• The Fay and Graubard (FG)-correction is recommended for large variations in cluster sizes.

Conclusions:

• Bias-corrected GEE methods, particularly KC-correction, offer reliable hypothesis testing in small CRTs with binary outcomes.
• The derived power formula accurately predicts empirical power, aiding in study design.
• GEE is recommended for CRTs with binary outcomes due to fewer assumptions and robustness.