ccc_vc: Concordance Correlation Coefficient estimation by variance...

In cccrm: Concordance Correlation Coefficient for Repeated (and Non-Repeated) Measures

Concordance Correlation Coefficient estimation by variance components.

Description

Estimation of the concordance correlation coefficient for either non-repeated, non-longitudinal, or longitudinal 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.

Usage

ccc_vc(
  dataset,
  ry,
  rind,
  rmet = NULL,
  rtime = NULL,
  vecD = NULL,
  covar = NULL,
  int = F,
  rho = 0,
  cl = 0.95,
  control.lme = list(),
  transf = "F2",
  boot = FALSE,
  boot_param = FALSE,
  boot_ci = "BCa",
  nboot = 300,
  parallel = FALSE,
  future_seed = TRUE,
  workers = 15,
  sd_est = TRUE,
  apVar = TRUE,
  ...
)

Arguments

dataset	an object of class data.frame.
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.
rtime	Character string. Name of the time variable in the data set.
vecD	Vector of weights. The length of the vector must be the same as the number of repeated measures.
covar	Character vector. Name of covariates to include in the linear mixed model as fixed effects.
int	Binary indicating if the subject-method interaction has to be included in the model when analyzing the non-longitudinal setting (defaults to FALSE).
rho	Within subject correlation structure. A value of 0 (default option) stands for compound symmetry and 1 is used for autorregressive of order 1 structure.
cl	Confidence level.
control.lme	A list of control values for the estimation algorithm used in lme function. For further details see lme help.
transf	Character string. Whether to apply a transformation of the coefficient for inference. Valid options are: "F" for Fisher's Z-transformation; "F2" For Fisher's Z-transformation setting m=2 (default); "KG" Konishi-Gupta transformation; "None", no transformation is applied. See *Details* for further information.
boot	Logical. Whether to compute the CCC confidence interval by bootstrapping or asymptotic methods (defaults to FALSE).
boot_param	Logical. Whether to compute a parametric bootstrap or a non-parametric bootstrap (defaults to FALSE).
boot_ci	Character. Type of bootstrap confidence interval. Either "BCa" (which is the default) or "empirical".
nboot	Integer. Number of bootstrap resamples. Default is 300.
parallel	Logical. Whether the code is parallellized. The parallellization method is multisession.
future_seed	Logical/Integer. The seed to be used for parallellization. Further details in furrr_options.
workers	Integer. Number of cores to be used for parallellization. Default is 15. Capped to number of available cores minus 1.
sd_est	Logical. Whether to estimate the asymptotic standard deviation (defaults to TRUE) or to only report the ccc/icc value.
apVar	Logical. Should the asymptotic variance-covariance matrix of the variance components be estimated in the linear mixed model? (Defaults to TRUE).
...	To pass further arguments.

Details

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: a) reliability assessment (several measurements taken with one method); b) methods comparison data with non-repeated measurements (only one measurement by subject and method); c) Methods comparison data with non-longitudinal repeated measurements, i.e. replicates (multiple measurements by subject and method); and d) Methods comparison data with longitudinal repeated measurements (multiple longitudinal 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 and its confidence interval can be obtained: a) asymptotically, using Taylor's series expansion of 1st order (Ver Hoef, 2012); b) using balanced randomized cluster bootstrap approach (Davison and Hinkley, 1997; Field and Welsh, 2007); c) using parametric bootstrap (Davison and Hinkley, 1997).

When estimating asymptotically the standard error, the confidence intervals are built using the point estimate of the CCC/ICC, its standard error, and the appropriate quantile of the standard Normal distribution. However, the approximation to the asymptotic Normal distribution is improved if the CCC/ICC is transformed using the Fisher's Z-transformation (Fisher, 1925), or the Konishi-Gupta transformation (Konishi and Gupta, 1989). In case the number of replicates is equal to 2, both transformations give the same result.

Value

A ccc class object. Generic function summary show a summary of the results. The output is a list with the following components:

• ccc. CCC/ICC estimate

• model. nlme object with the fitted linear mixed model.

• vc. Variance components estimates.

• sigma. Variance components asymptotic covariance matrix.

References

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.

Davison A.C., Hinkley D.V. (1997). Bootstrap Methods and Their Application. Cambridge: Cambridge University Press.

Field, C.A., Welsh, A.H. (2007). Bootstrapping Clustered Data. Journal of the Royal Statistical Society. Series B (Statistical Methodology). 69(3), 369-390.

Fisher, R. A. (1925) Statistical Methods for Research Workers. Edinburgh: Oliver

Konishi, S. and Gupta, A. K. (1989) Testing the equality of several intraclass correlation coefficients. J Statist. Planng Inf., 21, 93-105.

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.

Examples

## Not run: 
# Scenario 1. Reliability 
newdat <- bpres |> dplyr::filter(METODE==1)
icc_rel<-ccc_vc(newdat,"DIA","ID")
icc_rel
summary(icc_rel)


# Confidence interval using non-parametric bootstrap

icc_rel_bt<-ccc_vc(newdat,"DIA","ID",boot=TRUE,sd_est=FALSE,
nboot=500,parallel=TRUE)
icc_rel_bt
summary(icc_rel_bt)


#' # Scenario 2. Non-longitudinal methods comparison.
# Only 1 measure by subject and method. 
# No subjects-method interaction included in the model.

newdat <- bpres |> dplyr::filter(NM==1)
ccc_mc<-ccc_vc(newdat,"DIA","ID","METODE")
ccc_mc
summary(ccc_mc)


# Confidence interval using parametric bootstrap

ccc_mc_bt<-ccc_vc(newdat,"DIA","ID",boot=TRUE,boot_param=TRUE,
sd_est=FALSE,nboot=500,parallel=TRUE)
ccc_mc_bt
summary(ccc_mc_bt)


# Scenario 3. Non-longitudinal methods comparison. 
# Two measures by subject and method. 
# No subject-method interaction included in the model.

ccc_mc=ccc_vc(bpres,"DIA","ID","METODE")
ccc_mc
summary(ccc_mc)



# Scenario 4. Methods comparison in longitudinal repeated measures setting.
ccc_mc_lon<-ccc_vc(bdaw,"AUC","SUBJ","MET","VNUM")
ccc_mc_lon
summary(ccc_mc_lon)

# Scenario 5. Methods comparison in longitudinal repeated measures setting.
# More weight given to readings from first time.

ccc_mc_lonw<-ccc_vc(bfat,"BF","SUBJECT","MET","VISITNO",vecD=c(2,1,1))
ccc_mc_lonw
summary(ccc_mc_lonw)

## End(Not run)

cccrm documentation built on Oct. 19, 2024, 9:06 a.m.