Bias-reduced and separation-proof GEE with small or sparse longitudinal binary data.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Generalized estimating equation (GEE) is widely used for correlated binary data.
• Separation issues, where covariates lead to infinite estimates, are problematic in GEE, especially with small or sparse data.
• Existing GEE methods lack robust solutions for separation problems.

Purpose of the Study:

• To investigate the consequences of separation in GEE.
• To introduce a penalized GEE (PGEE) to address separation issues.
• To propose a bias-corrected covariance estimator for PGEE.

Main Methods:

• Introduced a Firth-type penalty to the GEE score equation, creating the penalized GEE (PGEE).
• Developed a small-sample bias correction for the sandwich covariance estimator of PGEE.
• Conducted simulations to compare PGEE with GEE under various separation scenarios.

Main Results:

• GEE failed to converge or produced infinite estimates in the presence of complete/quasi-complete separation.
• PGEE consistently achieved convergence and finite estimates, even in near-separation cases.
• The bias-corrected sandwich estimator for PGEE reduced bias in type I error rates compared to the standard estimator.

Conclusions:

• PGEE effectively resolves separation issues in correlated binary data analysis.
• The bias-corrected PGEE offers improved accuracy, particularly for type I error rates.
• PGEE with bias correction is recommended for small-to-moderate sample sizes and large samples with separation evidence.