Calculate Concordance Correlation Coefficient (CCC)

CCC <- function(x, y)
{
    ## Purpose: 
    ##   Calculate Concordance Correlation Coefficient (CCC).
    ##   Evaluate agreement in a unitless way: CCC is between -1 and 1, with perfect (reverse) agreement at 1 (-1). 
    ##   Ref: (Page 258-289) Lawrence, I., and Kuei Lin. "A concordance correlation coefficient to evaluate reproducibility." Biometrics (1989): 255-268. 
    ## 
    ## Author: Feiming Chen (Copyright 2026; GPLv3; No Warranty; gnu.org/licenses)
    ## 
    ## Arguments: 
    ##   - x : a numeric vector
    ##   - y : a numeric vector (equal length as "x"; not checked)
    ## 
    ## Return: 
    ##   - CCC : Concordance Correlation Coefficient (for a paired sample)
    ## ________________________________________________

    CCC <- 2 * cov(x, y) / (var(x) + var(y) + (mean(x) - mean(y))^2)
    CCC
}
if (F) {                                # Unit Test
    CCC(1:10, 1:10)                     # 1
    CCC(1:10, 10:1)                     # -1
    CCC(1:10, rep(1, 10))               # 0
    CCC(1:10, 11:20)                    # 0.15493
}