Power and Sample Size Calculations for Generalized Estimating Equations via Local Asymptotics

Area of Science:

• Biostatistics
• Statistical Methods
• Correlated Data Analysis

Background:

• Generalized estimating equations (GEE) are crucial for analyzing clustered or correlated data.
• Existing power and sample size calculations for GEE often rely on asymptotic approximations under fixed alternatives.
• These approximations may lead to inaccuracies in sample size determination for studies with correlated data.

Purpose of the Study:

• To develop a more accurate method for calculating statistical power and sample size for tests using GEE.
• To derive explicit sample size formulas for Wald and quasi-score test statistics within various GEE frameworks.
• To compare the accuracy of the proposed method against existing approaches.

Main Methods:

• The study proposes a novel approach by examining the asymptotic behavior of test statistics under local alternatives converging to the null hypothesis at a root-m rate.
• Explicit sample size formulas were derived based on this refined theoretical framework.
• Simulations were conducted to evaluate the performance of the new method.

Main Results:

• The proposed method offers improved accuracy in power and sample size calculations for GEE.
• In logistic regression with exchangeable correlation, previous methods overestimated sample sizes by over 10% for 90% power.
• The new approach demonstrated an accuracy of approximately 2% in the same scenario.

Conclusions:

• The developed method provides a more precise approach to sample size calculation for GEE, particularly beneficial for longitudinal and clustered data studies.
• This enhanced accuracy helps in optimizing study design and resource allocation.
• The findings suggest a significant improvement over traditional methods, leading to more reliable study planning.