A new coefficient to measure agreement between continuous variables

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.