Concordance correlation coefficients for multivariate measurements

When evaluating new measurement tools, it is crucial to ensure their effectiveness through comparison with existing methods. The concordance correlation coefficient (CCC) is widely used for this purpose in univariate settings. However, assessing agreement in multivariate measurements presents unique challenges that existing methods fail to address adequately. In this study, we introduce a novel concordance correlation coefficient for multivariate measurements (CCCM) that effectively handles multiple variables and observers simultaneously. CCCM expands the traditional CCC framework while maintaining its interpretability and incorporating three key innovations: independence from variable correlations, the ability to handle multiple observers, and computational efficiency through random matrix modeling. Through extensive simulations under various correlation structures and distributional assumptions, we demonstrate that CCCM exhibits superior stability and coverage properties compared to an existing method, the matrix-based concordance correlation coefficient (MCCC), particularly in scenarios with a small number of subjects. Application to a dental restorative study validates its practical utility, showing improved performance over MCCC. The derived theoretical properties demonstrate the large-sample behavior of CCCM, including asymptotic normality under Fisher’s Z-transformation. Our findings suggest that CCCM provides a robust and theoretically sound framework for assessing agreement in multivariate settings, offering practitioners a reliable tool for method comparison studies.