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

TL;DR

This paper introduces a flexible copula-based framework using Clayton copulas to test the homogeneity of proportions in highly dependent bilateral data, improving inference accuracy in clinical studies.

Contribution

It proposes a novel, general copula-based approach for dependency modeling in correlated data, extending beyond traditional fixed dependence structures.

Findings

The method controls type I error rates effectively.

It achieves reasonable statistical power in simulations.

Case studies demonstrate practical applicability.

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.