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

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Generalized Estimating Equations (GEE) are crucial for marginal models in biomedical longitudinal studies.
• The standard 'sandwich' variance estimator in GEE exhibits downward bias and poor performance with small sample sizes.
• Existing modified variance estimators aim to correct bias and enhance efficiency for GEE.

Purpose of the Study:

• To comprehensively review recent advancements in modified variance estimators for GEE.
• To compare the small-sample performance of these estimators theoretically and empirically.
• To provide practical guidelines for selecting appropriate variance estimators and sample sizes.

Main Methods:

• Theoretical comparison of modified variance estimators.
• Numerical simulations to evaluate small-sample performance.
• Analysis of real-world biomedical data examples.
• Assessment of Wald tests and t-tests using different variance estimators for hypothesis testing.

Main Results:

• Identified specific modified variance estimators that outperform the traditional sandwich estimator in small samples.
• Established guidelines for appropriate sample sizes to maintain Type I error rates for each estimator.
• Demonstrated the practical utility of these estimators through real data applications.

Conclusions:

• Modified variance estimators offer significant improvements over the standard sandwich estimator for GEE in small samples.
• The developed R package 'geesmv' facilitates the application of these advanced methods in biomedical research.
• Informed selection of variance estimators and sample sizes is critical for reliable statistical inference in longitudinal studies.