ccc: Lin's concordance correlation coefficient

In fastmatrix: Fast Computation of some Matrices Useful in Statistics

Lin's concordance correlation coefficient

Description

Calculates Lin's concordance correlation coefficient for evaluating the degree of agreement between measurements generated by two different methods.

Usage

ccc(x, data, method = "z-transform", level = 0.95, equal.means = FALSE, 
    ustat = TRUE, subset, na.action)

Arguments

x	a formula or a numeric matrix or an object that can be coerced to a numeric matrix.
data	an optional data frame (or similar: see model.frame), used only if x is a formula. By default the variables are taken from environment(formula).
method	a character string, indicating the method for the computation of the required confidence interval. Options available are "z-transform" or "asymp" (see details in Lin, 1989, 2000).
level	the confidence level required, must be a single number between 0 and 1 (by default 95%).
equal.means	logical, should the means of the measuring devices be considered equal? In which case the restricted estimation is carried out under this assumption.
ustat	logical, should the concordance correlation coefficient be estimated using U-statistics?
subset	an optional expression indicating the subset of the rows of data that should be used in the fitting process.
na.action	a function that indicates what should happen when the data contain NAs.

Value

A list with class 'ccc' containing the following named components:

call	a list containing an image of the ccc call that produced the object.
x	data.frame used in the estimation process.
ccc	estimate of the concordance correlation coefficient.
var.ccc	asymptotic variance of the concordance correlation coefficient estimate.
accuracy	estimate of the accuracy (or bias) coefficient that measures how far the best-fit line deviates from a line at 45 degrees. No deviation from the 45 degree line occurs when accuracy = 1.
precision	estimate of the precision (or Pearson correlation) coefficient.
shifts	list with the location and scale shifts.
z	Z-transformation parameter estimate.
var.z	asymptotic variance of the Z-transformation parameter estimate.
confint	confidence interval for the Lin's concordance correlation coefficient.
bland	a data frame with two columns containing the average of each pair of measurements, and difference between the measurements.
center	the estimated mean vector.
cov	the estimated covariance matrix.
ustat	available only if ustat = TRUE, in which case this element corresponds to a list containing the following elements rhoc, var.rhoc, ustat, and cov.
Restricted	available only if equal.means = TRUE, in which case this element corresponds to a list containing the following elements ccc, accuracy, precision, shifts, center, and cov.

References

Bland, J., Altman, D. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. The Lancet 327, 307-310.

King, T.S., Chinchilli, V.M. (2001). A generalized concordance correlation coefficient for continuous and categorical data. Statistics in Medicine 20, 2131-2147.

King, T.S., Chinchilli, V.M. (2001). Robust estimators of the concordance correlation coefficient. Journal of Biopharmaceutical Statistics 11, 83-105.

Lin, L. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45, 255-268.

Lin, L. (2000). A note on the concordance correlation coefficient. Biometrics 56, 324-325.

Vallejos, R., Osorio, F., Ferrer, C. (2025+). A new coefficient to measure agreement between two continuous variables. Working paper.

Examples

## data in Fig.1 from Bland and Altman (1986).
x <- list(Large = c(494,395,516,434,476,557,413,442,650,433,
          417,656,267,478,178,423,427),
          Mini  = c(512,430,520,428,500,600,364,380,658,445,
          432,626,260,477,259,350,451))
x <- as.data.frame(x)

plot(Mini ~ Large, data = x, xlim = c(100,800), ylim = c(100,800),
     xlab = "PERF by Large meter", ylab = "PERF by Mini meter")
abline(c(0,1), col = "gray", lwd = 2)

## estimating CCC
z <- ccc(~ Mini + Large, data = x, method = "asymp")
z
## output:
# Call:
# ccc(x = ~ Mini + Large, data = x, method = "asymp")
#
# Coefficients:
#  estimate  variance  accuracy precision 
#   0.9427    0.0008    0.9994    0.9433 
#
# Asymptotic 95% confidence interval:
#     CCC     SE  lower  upper 
#  0.9427 0.0286 0.8867 0.9988 

fastmatrix documentation built on Aug. 8, 2025, 6:19 p.m.