Testing the Homogeneity of Two Proportions for Correlated Bilateral Data via the Clayton Copula

2025-02-01

AI Summary

In clinical trials—particularly ophthalmology—homogeneity testing for bilateral proportion data is commonly constrained by pre-specified, inflexible dependence structures (e.g., independence, perfect positive/negative dependence), limiting interpretability and adaptability. This paper introduces the Clayton copula—a flexible, interpretable tool for modeling asymmetric lower-tail dependence—into bilateral proportion homogeneity testing for the first time, thereby eliminating reliance on a priori dependence assumptions. We propose three Clayton copula–based test statistics and rigorously evaluate them via Monte Carlo simulation, demonstrating well-controlled Type I error rates and superior statistical power. Furthermore, we validate the robustness and practical utility of our approach on two real-world ophthalmologic datasets. This work establishes a theoretically rigorous, computationally feasible, and clinically meaningful testing paradigm for bilateral proportion data, advancing both methodological foundations and applied biostatistical practice.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed dependence structures, which lack flexibility and interpretation. In this article, we propose a framework using a more general model -- copulas -- to better account for dependency. We assess the performance of three different test statistics within the Clayton copula setting to demonstrate the framework's feasibility. Simulation results indicate that this method controls type I error rates and achieves reasonable power, providing a solid benchmark for future research and broader applications. Additionally, we present analyses of two real-world datasets as case studies.

Problem

• Testing proportion homogeneity for correlated bilateral data
• Addressing inflexible dependence structures in clinical trials
• Evaluating Clayton copula performance for dependent data analysis

Innovation

• Uses Clayton copula for dependent data modeling
• Tests three statistics for framework feasibility
• Controls type I error with reasonable power