Bias-Reduced GEE via Adjusted Estimating Equations, with Odds-Ratio Extensions

2026-06-14

AI Summary

This study addresses the substantial bias in generalized estimating equations (GEE) when the number of independent clusters is small. Viewing GEE as an M-estimator for clustered data, the authors derive a corrected estimating equation that achieves first-order bias reduction while accounting for the dependence of the working covariance on mean parameters. Innovatively, they formulate the bias-corrected GEE estimator under a pairwise odds-ratio parameterization, circumventing the stringent compatibility constraints imposed by traditional correlation-based parameterizations on marginal means and thereby enhancing suitability for small-sample settings. Six new estimators implemented in the R package geer demonstrate markedly reduced bias across various scenarios, while preserving efficiency and confidence interval coverage comparable to standard GEE. The practical utility of the proposed approach is further validated through application to clinical trial data analysis.

Abstract

Generalized estimating equations (GEE) are widely used for correlated data, but with small to moderate numbers of independent clusters the ordinary GEE regression estimators can be substantially biased. We develop a first-order bias-reduction principle for GEE by viewing the estimator as a clustered-data $M$-estimator and deriving an adjustment to the estimating equations that targets the leading bias term while accounting for the dependence of the working covariance on the mean parameters. The resulting class includes three bias-reduced estimators and three one-step bias-corrected analogs, nesting the bias-corrected estimator of Lunardon and Scharfstein (2017) and the bias-reduced and bias-corrected estimators of Paul and Zhang (2014) as special cases. The framework applies to general response types through correlation-coefficient parameterizations for the association structure and extends to correlated binary data through pairwise odds-ratio parameterizations, yielding the first bias-reduced and bias-corrected GEE estimators under this parameterization, for which the marginal-mean compatibility constraints are far less restrictive than those of correlation-coefficient parameterizations, making them better suited for small-sample settings. Under standard regularity conditions, all six estimators share the same asymptotic distribution as the ordinary GEE. Simulation studies show that the proposed estimators reduce bias while maintaining efficiency and coverage close to those of ordinary GEE across a range of settings, and a clinical trial analysis illustrates the proposed estimators in practice. Software is available in the R package geer.

Problem

• bias reduction
• generalized estimating equations
• correlated data
• odds ratio
• small-sample bias

Innovation

• bias-reduced GEE
• adjusted estimating equations
• odds-ratio parameterization
• correlated binary data
• small-sample inference