Concordance Correlation Coefficient Decomposed into the Product of Precision and Accuracy

• Activity Number: 398
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Christopher Tong*+
• Companies: U.S. Department of Agriculture
• Keywords: Concordance correlation ; Pearson correlation ; Agreement ; Method comparison

Abstract

The concordance correlation coefficient (CCC) was introduced by Lin (1989) as an index of agreement for paired measurements. It may be written as the product of the Pearson (product-moment) correlation and a bias correction factor. Lin calls these factors measures of precision and accuracy, respectively. The Pearson correlation "measures how far each observation deviated from the best-fit line" while the bias correction factor "measures how far the best-fit line deviates from" the 45 degree line of agreement, in Lin's words. I demonstrate that these claims can be misleading. Loh (1987) showed that the Pearson correlation is not simply a measure of clustering of data around the best-fit line. The Pearson correlation is in fact sensitive to the departure of the best fit line from the line of agreement. Thus the Pearson correlation fails to be a pure measure of precision on the raw data. Other statistics are better suited for measuring the closeness of fit to a straight line, such as the root mean square error and measures based on the eigenvalues of the covariance matrix. The decomposition of the CCC should not be interpreted as the product of coefficients of precision and accuracy.