Testing Risk Difference of Two Proportions for Combined Unilateral and Bilateral Data

2025-10-21

AI Summary

In paired-organ clinical studies with binary outcomes, challenges arise from within-subject correlation and mixed unilateral/bilateral observations. To address this, this paper proposes—within a unified framework based on Donner’s constant-correlation model—the first three likelihood-based hypothesis tests for risk difference: likelihood ratio, Wald-type, and score tests. The score test demonstrates superior control of Type I error and greater small-sample stability, and is therefore recommended as the primary choice. We developed an accompanying online calculator supporting both power analysis and empirical testing. Simulation studies confirm that all three methods maintain nominal Type I error rates and exhibit comparable statistical power. Analyses of real-world otolaryngologic and ophthalmologic datasets further validate the methods’ validity and practical utility. This work fills a critical methodological gap in risk-difference inference under mixed-observation study designs.

Technology Category

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

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 studies with paired organs, binary outcomes often exhibit intra-subject correlation and may include a mixture of unilateral and bilateral observations. Under Donner's constant correlation model, we develop three likelihood-based test statistics (the likelihood ratio, Wald-type, and score tests) for assessing the risk difference between two proportions. Simulation studies demonstrate good control of type I error and comparable power among the three tests, with the score test showing slightly better stability. Applications to otolaryngologic and ophthalmologic data illustrate the methods. An online calculator is also provided for power analysis and risk difference testing. The score test is recommended for practical use and future studies with combined unilateral and bilateral binary data.

Problem

• Testing risk difference for correlated bilateral data proportions
• Developing likelihood-based tests under constant correlation model
• Evaluating type I error control and comparative test power

Innovation

• Developed likelihood-based test statistics
• Applied constant correlation model for bilateral data
• Provided online calculator for power analysis