A new coefficient to measure agreement between continuous variables

2025-07-10

AI Summary

In clinical studies, assessing agreement between two continuous measurement methods applied to the same subjects is a common yet challenging task. This paper proposes ρ₁, a novel agreement coefficient based on the L₁ distance, which requires no tuning parameters and exhibits strong robustness against outliers. Under bivariate normal and elliptically symmetric distributions, we rigorously derive its theoretical properties—including consistency, asymptotic normality, and invariance—and establish a complete statistical inference framework, supporting both confidence interval estimation and hypothesis testing. Extensive numerical experiments demonstrate that ρ₁ maintains stable performance across diverse distributions and contamination scenarios, consistently outperforming the classical Lin’s concordance correlation coefficient. By combining simplicity, robustness, and interpretability, ρ₁ provides a principled tool for agreement assessment in clinical comparisons, spatial analysis, and other applied settings requiring reliable quantification of method concordance.

Technology Category

• Multiagent Systems: Agreement, Argumentation & Negotiation
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

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

Abstract

Assessing agreement between two instruments is crucial in clinical studies to evaluate the similarity between two methods measuring the same subjects. This paper introduces a novel coefficient, termed rho1, to measure agreement between continuous variables, focusing on scenarios where two instruments measure experimental units in a study. Unlike existing coefficients, rho1 is based on L1 distances, making it robust to outliers and not relying on nuisance parameters. The coefficient is derived for bivariate normal and elliptically contoured distributions, showcasing its versatility. In the case of normal distributions, rho1 is linked to Lin's coefficient, providing a useful alternative. The paper includes theoretical properties, an inference framework, and numerical experiments to validate the performance of rho1. This novel coefficient presents a valuable tool for researchers assessing agreement between continuous variables in various fields, including clinical studies and spatial analysis.

Problem

• Measure agreement between continuous variables in clinical studies
• Introduce robust L1-based coefficient rho1 for outlier resistance
• Validate rho1 for bivariate normal and elliptical distributions

Innovation

• Novel coefficient rho1 for continuous variables
• Robust L1 distances, outlier-resistant, no nuisance parameters
• Linked to Lin's coefficient for normal distributions