Normalization of mean squared differences to measure agreement for continuous data

Abstract

Agreement among observations on two variables for reliability or validation purposes is usually assessed by the evaluation of the mean squared differences (MSD). Many transformations of MSD have been proposed to interpret and make statistical inferences about the agreement between the two variables, including the concordance correlation coefficient (CCC) and the random marginal agreement coefficient (RMAC). This paper presents a normalization of MSD based on a reference range and uses it to derive CCC and RMAC (or ACC alternatively). The normalization of MSD enables the comparison between these two coefficients. The paper compares thoroughly the differences between these two coefficients and their properties at different agreement levels. Results show that ACC has promising properties over CCC. A Monte Carlo simulations as well as real data applications are performed. ACC for more than two variables are also derived.