Title: | Concordance Correlation Coefficient for Repeated (and Non-Repeated) Measures |
---|---|
Description: | Estimates the Concordance Correlation Coefficient to assess agreement. The scenarios considered are non-repeated measures, non-longitudinal repeated measures (replicates) and longitudinal repeated measures. It also includes the estimation of the one-way intraclass correlation coefficient also known as reliability index. The estimation approaches implemented are variance components and U-statistics approaches. Description of methods can be found in Fleiss (1986) <doi:10.1002/9781118032923> and Carrasco et al. (2013) <doi:10.1016/j.cmpb.2012.09.002>. |
Authors: | Josep Lluis Carrasco <jlcarrasco@ub.edu>, Josep Puig Martinez <j.puig04@gmail.com> |
Maintainer: | Josep Lluis Carrasco <jlcarrasco@ub.edu> |
License: | GPL (>= 2) |
Version: | 2.2.1 |
Built: | 2024-02-12 08:10:50 UTC |
Source: | CRAN |
Plasma cortisol area under curve (AUC) was calculated from the trapezoidal rule over the 12-h period of the hourly blood draws. The subjects were required to repeat the process in five visits. The aim of the agreement study was to assess how well the plasma cortisol AUC from hourly measurements agreed with plasma cortisol AUC that was measured every two hours.
data("bdaw")
King, TS; Chinchilli, VM: Carrasco, JL. (2007). A repeated measures concordance correlation coefficient, Statistics in Medicine 26, 3095-3113.
Percentage body fat was estimated from skinfold calipers and DEXA on a cohort of 90 adolescent girls. Skinfold caliper and DEXA measurements were taken at ages 12.5, 13 and 13.5. The objective was to determine the amount of agreement between the skinfold caliper and DEXA measurements of percentage body fat.
data("bfat")
King, TS; Chinchilli, VM: Carrasco, JL. (2007). A repeated measures concordance correlation coefficient, Statistics in Medicine 26, 3095-3113.
Systolic and diastolic blood pressure was measured in a sample of 384 subjects using a handle mercury sphyg momanometer device and an automatic device. The blood pressure was simultaneously measured twice by each instrument, thus every subject had four measurements, two by each method.
data("bpres")
Carrasco, JL; Jover, L. (2003). Estimating the generalized concordance correlation coefficient through variance components. Biometrics, 59, 849:858.
Estimation of the concordance correlation coefficient for repeated measurements using the variance components from a linear mixed model. The appropriate intraclass correlation coefficient is used as estimator of the concordance correlation coefficient.
ccclon(dataset, ry, rind, rtime, rmet, covar = NULL, rho = 0, cl = 0.95,
control.lme=list())
dataset |
An object of class |
ry |
Character string. Name of the outcome in the data set. |
rind |
Character string. Name of the subject variable in the data set. |
rtime |
Character string. Name of the time variable in the data set. |
rmet |
Character string. Name of the method variable in the data set. |
covar |
Character vector. Name of covariables to include in the linear mixed model as fixed effects. |
rho |
Within subject correlation structure. A value of 0 (default option) stands for compound simmetry and 1 is used for autoregressive of order 1 structure. |
cl |
Confidence level. |
control.lme |
A list of control values for the estimation algorithm used in |
The concordance correlation coefficient is estimated using the appropriate intraclass correlation coefficient (see Carrasco et al, 2009; Carrasco et al, 2013). The variance components estimates are obtained from a linear mixed model (LMM) estimated by restricted maximum likelihood. The function lme from package nlme (Pinheiro et al., 2021) is used to estimate the LMM. The standard error of CCC is computed using an Taylor's series expansion of 1st order (Ver Hoef, 2012). Confidence interval is built by applying the Fisher's Z-transformation.
An object of class ccc
. Generic function summary
show a summary of the results. The output is a list with the following components:
ccc |
Concordance Correlation Coefficient estimate |
model |
nlme object with the fitted linear mixed model |
vc |
Variance components estimates |
sigma |
Variance components asymptotic covariance matrix |
Josep Puig-Martinez and Josep L. Carrasco
Carrasco, JL; King, TS; Chinchilli, VM. (2009). The concordance correlation coefficient for repeated measures estimated by variance components. Journal of Biopharmaceutical Statistics, 19, 90:105.
Carrasco, JL; Phillips, BR; Puig-Martinez, J; King, TS; Chinchilli, VM. (2013). Estimation of the concordance correlation coefficient for repeated measures using SAS and R. Computer Methods and Programs in Biomedicine, 109, 293-304.
Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2021). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-152, https://CRAN.R-project.org/package=nlme.
Ver Hoef, J.M. (2012) Who Invented the Delta Method?, The American Statistician, 66:2, 124-127.
data(bdaw)
estccc<-ccclon(bdaw,"AUC","SUBJ","VNUM","MET")
estccc
summary(estccc)
Estimation of the concordance correlation coefficient (CCC) for repeated measurements using the variance components from a linear mixed model. The appropriate intraclass correlation coefficient is used as estimator of the concordance correlation coefficient. Weights are assigned to repeated measurements in the CCC computation process.
ccclonw(dataset, ry, rind, rtime, rmet, vecD, covar = NULL, rho = 0, cl = 0.95,
control.lme=list())
dataset |
an object of class |
ry |
Character string. Name of the outcome in the data set. |
rind |
Character string. Name of the subject variable in the data set. |
rtime |
Character string. Name of the time variable in the data set. |
rmet |
Character string. Name of the method variable in the data set. |
vecD |
Vector of weigths. The length of the vector must be the same as the number of repeated measures. |
covar |
Character vector. Name of covariables to include in the linear mixed model as fixed effects. |
rho |
Within subject correlation structure. A value of 0 (default option) stands for compound simmetry and 1 is used for autoregressive of order 1 structure. |
cl |
Confidence level. |
control.lme |
A list of control values for the estimation algorithm used in |
The concordance correlation coefficient is estimated using the appropriate intraclass correlation coefficient which expression is modified accordingly to assign different weights to each repeated measurement (see Carrasco et al, 2009; Carrasco et al, 2013). The variance components estimates are obtained from a linear mixed model (LMM) estimated by restricted maximum likelihood. The function lme from package nlme (Pinheiro et al., 2021) is used to estimate the LMM. The standard error of CCC is computed using an Taylor's series expansion of 1st order (Ver Hoef, 2012). Confidence interval is built by applying the Fisher's Z-transformation.
An object of class ccc
. Generic function summary
show a summary of the results. The output is a list with the following components:
ccc |
Concordance Correlation Coefficient estimate |
model |
nlme object with the fitted linear mixed model |
vc |
Variance components estimates |
sigma |
Variance components asymptotic covariance matrix |
Josep Puig-Martinez and Josep L. Carrasco
Carrasco, JL; King, TS; Chinchilli, VM. (2009). The concordance correlation coefficient for repeated measures estimated by variance components. Journal of Biopharmaceutical Statistics, 19, 90:105.
Carrasco, JL; Phillips, BR; Puig-Martinez, J; King, TS; Chinchilli, VM. (2013). Estimation of the concordance correlation coefficient for repeated measures using SAS and R. Computer Methods and Programs in Biomedicine, 109, 293-304.
Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2021). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-152, https://CRAN.R-project.org/package=nlme.
Ver Hoef, J.M. (2012) Who Invented the Delta Method?, The American Statistician, 66:2, 124-127.
data(bfat)
estccc<-ccclonw(bfat,"BF","SUBJECT","VISITNO","MET",vecD=c(2,1,1))
estccc
summary(estccc)
Estimation of the concordance correlation coefficient for repeated measurements using the U-statistics approach. The function is also applicable for the non-repeated measurements scenario.
cccUst(dataset, ry, rmet, rtime = NULL, Dmat = NULL, delta = 1, cl = 0.95)
dataset |
An object of class |
ry |
Character string. Name of the outcome in the data set. |
rmet |
Character string. Name of the method variable in the data set. |
rtime |
Character string. Name of the time variable in the data set. |
Dmat |
Matrix of weights. |
delta |
Power of the differences. A value of 0 provides an estimate that is comparable to a repeated measures version of kappa index. |
cl |
Confidence level. |
A vector that includes the point estimate, confidence interval and standard error of the CCC. Additionally the Fisher's Z-transformation value and its standard error are also provided.
Josep Puig-Martinez and Josep L. Carrasco
King, TS and Chinchilli, VM. (2001). A generalized concordance correlation coefficient for continuous and categorical data. Statistics in Medicine, 20, 2131:2147.
King, TS; Chinchilli, VM; Carrasco, JL. (2007). A repeated measures concordance correlation coefficient. Statistics in Medicine, 26, 3095:3113.
Carrasco, JL; Phillips, BR; Puig-Martinez, J; King, TS; Chinchilli, VM. (2013). Estimation of the concordance correlation coefficient for repeated measures using SAS and R. Computer Methods and Programs in Biomedicine, 109, 293-304.
# Non-longitudinal scenario
data(bpres)
newdat=bpres[bpres$NM==1,]
estccc=cccUst(newdat,"DIA","METODE")
estccc
# Longitudinal scenario
data(bdaw)
estccc=cccUst(bdaw,"AUC","MET","VNUM")
estccc
# Weighted CCC
data(bfat)
estccc=cccUst(bfat,"BF","MET","VISITNO",Dmat=diag(c(2,1,1)))
estccc
Estimation of the concordance correlation coefficient for non-repeated measurements and non-longitudinal repeated measurements (replicates) using the variance components from a linear mixed model. The appropriate intraclass correlation coefficient is used as estimator of the concordance correlation coefficient.
cccvc(dataset, ry, rind, rmet, covar = NULL, int = FALSE, cl=0.95, control.lme=list())
dataset |
an object of class |
ry |
Character string. Name of the outcome in the data set. |
rind |
Character string. Name of the subject variable in the data set. |
rmet |
Character string. Name of the method variable in the data set. |
covar |
Character vector. Name of covariables to include in the linear mixed model as fixed effects. |
int |
Boolean indicating if the subject-method interaction has to be included in the model |
cl |
Confidence level. |
control.lme |
A list of control values for the estimation algorithm used in |
The concordance correlation coefficient is estimated using the appropriate intraclass correlation coefficient (see Carrasco and Jover, 2003; Carrasco et al., 2009; Carrasco et al, 2013). The scenarios considered are non-repeated measurements (only one measurement by subject and method) and non-longitudinal repeated measurements, i.e. replicates (multiple measurements by subject and method). The variance components estimates are obtained from a linear mixed model (LMM) estimated by restricted maximum likelihood. The function lme from package nlme (Pinheiro et al., 2021) is used to estimate the LMM. The standard error of CCC is computed using an Taylor's series expansion of 1st order (Ver Hoef, 2012). Confidence interval is built by applying the Fisher's Z-transformation.
An object of class ccc
. Generic function summary
show a summary of the results. The output is a list with the following components:
ccc |
Concordance Correlation Coefficient estimate |
model |
nlme object with the fitted linear mixed model |
vc |
Variance components estimates |
sigma |
Variance components asymptotic covariance matrix |
Josep Puig-Martinez and Josep L. Carrasco
Carrasco, JL; Jover, L. (2003). Estimating the generalized concordance correlation coefficient through variance components. Biometrics, 59, 849:858.
Carrasco, JL; King, TS; Chinchilli, VM. (2009). The concordance correlation coefficient for repeated measures estimated by variance components. Journal of Biopharmaceutical Statistics, 19, 90:105.
Carrasco, JL; Phillips, BR; Puig-Martinez, J; King, TS; Chinchilli, VM. (2013). Estimation of the concordance correlation coefficient for repeated measures using SAS and R. Computer Methods and Programs in Biomedicine, 109, 293-304.
Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2021). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-152, https://CRAN.R-project.org/package=nlme.
Ver Hoef, J.M. (2012) Who Invented the Delta Method?, The American Statistician, 66:2, 124-127.
data(bpres)
# Scenario 1.
#Only 1 measure by subject and method.
#No subject-method interaction included in the model.
newdat=bpres[bpres$NM==1,]
estccc=cccvc(newdat,"DIA","ID","METODE")
estccc
summary(estccc)
# Scenario 2.
#Two measures by subject and method.
#No subject-method interaction included in the model.
estccc=cccvc(bpres,"DIA","ID","METODE")
estccc
summary(estccc)
Estimates the one-way intraclass correlation coefficient using the variance components from a linear mixed model.
icc(dataset, ry, rind, covar = NULL, cl=0.95, control.lme=list())
dataset |
an object of class |
ry |
Character string. Name of the outcome in the data set. |
rind |
Character string. Name of the subject variable in the data set. |
covar |
Character vector. Name of covariables to include in the linear mixed model as fixed effects. |
cl |
Confidence level. |
control.lme |
A list of control values for the estimation algorithm used in |
The intraclass correlation coefficient (ICC) (Fleiss, 1986) is estimated using a linear mixed model with subjects (cluster) random effect and random error as components. The effects are assumed to follow Normal distributions with variances Sa and Se respectively. The expression of the ICC is $Sa/(Sa + Se)$
. This intraclass correlation coefficient is also known as reliability index. The variance components estimates are obtained from a linear mixed model (LMM) estimated by restricted maximum likelihood. The function lme from package nlme (Pinheiro et al., 2021) is used to estimate the LMM. The standard error of CCC is computed using an Taylor's series expansion of 1st order (Ver Hoef, 2012). Confidence interval is built by applying the Fisher's Z-transformation.
An object of class icc
. Generic function summary
show a summary of the results. The output is a list with the following components:
icc |
Intraclass Correlation Coefficient estimate |
model |
nlme object with the fitted linear mixed model |
vc |
Variance components estimates |
sigma |
Variance components asymptotic covariance matrix |
Josep L. Carrasco
Fleiss, JL. (1986). Reliability of Measurement in *Design and analysis of clinical experiments*. New York:Wiley.
Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2021). nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-152, https://CRAN.R-project.org/package=nlme.
Ver Hoef, J.M. (2012) Who Invented the Delta Method?, The American Statistician, 66:2, 124-127.
data(bpres)
# Reliability of method 1
newdat=bpres[(bpres$METODE==1),]
est=icc(newdat,"DIA","ID")
est
summary(est)
# Reliability of method 2
newdat=bpres[(bpres$METODE==2),]
est=icc(newdat,"DIA","ID")
est
summary(est)