Concordance correlation coefficient


In statistics, the concordance correlation coefficient measures the agreement between two variables, e.g., to evaluate reproducibility or for inter-rater reliability.

Definition

Lawrence Lin has the form of the concordance correlation coefficient as
where and are the means for the two variables and and are the corresponding variances. is the correlation coefficient between the two variables.
This follows from its definition as
When the concordance correlation coefficient is computed on a -length data set, the form is
where the mean is computed as
and the variance
and the covariance
Whereas the ordinary correlation coefficient is immune to whether the biased or unbiased versions for estimation of the variance is used, the concordance correlation coefficient is not. In the original article Lin suggested the 1/N normalization,
while in another article Nickerson appears to have used the 1/,
i.e., the concordance correlation coefficient may be computed slightly differently between implementations.

Relation to other measures of correlation

The concordance correlation coefficient is nearly identical to some of the measures called intra-class correlations. Comparisons of the concordance correlation coefficient with an "ordinary" intraclass correlation on different data sets found only small differences between the two correlations, in one case on the third decimal. It has also been stated that the ideas for concordance correlation coefficient "are quite similar to results already published by Krippendorff
in 1970".
In the original article Lin suggested a form for multiple classes. Over ten years later a correction to this form was issued.
One example of the use of the concordance correlation coefficient is in a comparison of analysis method for functional magnetic resonance imaging brain scans.