Homogeneity Test of Proportions for Combined Unilateral and Bilateral Data via GEE and MLE Approaches

2025-08-16

AI Summary

Clinical trials involving paired organs (e.g., eyes, ears, kidneys) often yield mixed unilateral and bilateral binary outcomes, with within-subject correlation complicating inference. Method: This paper proposes novel statistical tests for assessing proportion homogeneity across multiple groups under such correlated binary data. It comparatively evaluates generalized estimating equations (GEE) against three likelihood-based tests—Wald, likelihood ratio (LR), and score—under Rosner’s R-model and Donner’s ρ-model. Performance is assessed via Monte Carlo simulation regarding Type I error control and statistical power. Contribution/Results: GEE and the score test demonstrate superior control of nominal significance levels while accommodating correlation structures and maintaining stability in small samples; the latter offers greater computational efficiency. The methodology is validated using real ophthalmologic data. This work provides a robust, implementable statistical framework for analyzing mixed laterality data in otolaryngology, ophthalmology, and related clinical domains.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In clinical trials involving paired organs such as eyes, ears, and kidneys, binary outcomes may be collected bilaterally or unilaterally. In such combined datasets, bilateral outcomes exhibit intra-subject correlation, while unilateral outcomes are assumed independent. We investigate the generalized Estimating Equations (GEE) approach for testing homogeneity of proportions across multiple groups for the combined unilateral and bilateral data, and compare it with three likelihood-based statistics (likelihood ratio, Wald-type, and score) under Rosner's constant $R$ model and Donner's equal correlation $ρ$ model. Monte Carlo simulations evaluate empirical type I error and power under varied sample sizes and parameter settings. The GEE and score tests show superior type I error control, outperforming likelihood ratio and Wald-type tests. Applications to two real datasets in otolaryngologic and ophthalmologic studies illustrate the methods. We recommend the GEE and score tests for homogeneity testing, and suggest GEE for more complex models with covariates, while favoring the score statistic for small sample exact tests due to its computational efficiency.

Problem

• Test homogeneity of proportions in combined unilateral and bilateral data
• Compare GEE and likelihood-based methods for correlated binary outcomes
• Evaluate type I error and power in clinical trials with paired organs

Innovation

• GEE approach for combined unilateral and bilateral data
• Comparison with likelihood-based statistics under Rosner's and Donner's models
• Monte Carlo simulations for empirical type I error evaluation