| 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 [aut, cre], Gonzalo Peon Pena [aut] |
| Maintainer: | Josep Lluis Carrasco <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 3.0.2 |
| Built: | 2024-09-28 03:29:55 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.
bdawbdaw
A data frame with the following columns:
Subject identifier
Visit number
Area under the curve
Device identifier
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.
bfatbfat
A data frame with the following columns:
Subject identifier
Visit number
Percentage body fat
Device identifier
Systolic and diastolic blood pressure was measured in a sample of 384 subjects using a handle mercury sphygmomanometer 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.
bpresbpres
A data frame with the following columns:
Subject identifier
Systolic blood pressure in mmHg
Diastolic blood pressure in mmHg
Device identifier
Identifier of replicates
Height in cm
Age in years
Heart rate
Have the subject been informed about he is hypertense?
Weight in Kg
Gender. 1 for Male. 2 for Female
Was the subject's blood pressure measured the last year? 1=Yes, 2=No, 9=Unknown
Does the subject receive treatment for hypertension? 1=Yes, 2=No, 3=Doubtful, 8=not applicable, 9=Insufficient data.
The fixed effects and standard deviations of random effects can be set to specific values or, alternatively, obtained from an object of class lme.
ccc_sim_data( n = 30, nrep = 1, nsim = 1, model = NULL, b = NULL, g = NULL, mu = 0, sa = 1, sab = 0, sag = 0, bg = NULL, se = 1, future_seed = TRUE, workers = 15, extra.info = TRUE, ... )ccc_sim_data( n = 30, nrep = 1, nsim = 1, model = NULL, b = NULL, g = NULL, mu = 0, sa = 1, sab = 0, sag = 0, bg = NULL, se = 1, future_seed = TRUE, workers = 15, extra.info = TRUE, ... )
n |
Integer. Number of subjects |
nrep |
Integer. Number of replicates |
nsim |
Integer. Number of data sets simulated. |
model |
Object of class |
b |
Vector. Method fixed effects. |
g |
Vector. Time fixed effects. |
mu |
Integer. Overall mean. |
sa |
Integer. Standard deviation of subject's random effect. |
sab |
Integer. Standard deviation of subject-method interaction's random effect. |
sag |
Integer. Standard deviation of subject-time interaction's random effect. |
bg |
Vector. Method-time interaction's fixed effects. The vector of effects have to be ordered by method and time. |
se |
Integer. Standard deviation of random error effect. |
future_seed |
Logical/Integer. The seed to be used for parallellization. Further details in |
workers |
Integer. Number of cores to be used for parallellization. Default is 15. Capped to number of available cores minus 1. |
extra.info |
Logical. Should the information about CCC/ICC and variance components simulated be shown? Default is set to TRUE. |
... |
To pass further arguments. |
Random effects are simulated as normal distributions with mean 0 and the correspondign standard deviations. The simulated data is obtained
as the addition of the simulated values and the fixed efffects. Parallel computation is used except if data is simulated from an object of class 'lme'. In this case.
data is simulated using the simulateY function from nlmeU package.
A data frame with the simulated data.
# # Reliability data: # 50 subjects, one method, one time, 2 replicates # Overall mean: -0.25; Subjects standard deviation: 1.5, Random error standard deviation: 1 set.seed(101) df <- ccc_sim_data(n=50, b = NULL, g = NULL, mu = -0.25, sa = 1.5, se = 1, nrep=2) # Method comparison data (non-longitudinal) # 50 subjects, two methods, 2 replicates # Overall mean: -0.25; Subjects standard deviation: 1.5, Random error standard deviation: 1 # Difference of means between methods 2 and 1: 1 # Three data sets simulated set.seed(202) df <- ccc_sim_data(n=50, nsim=3,b = c(0,1), mu = -0.25, sa = 1.5, se = 1, nrep=2) # Method comparison data (longitudinal) # 50 subjects, two methods, 3 times, 1 replicate, # Overall mean: -0.25; Subjects standard deviation: 1.5, Random error standard deviation: 1 # Difference of means between methods 2 and 1: 1 # Difference of means between times 3,2 and 1 respectively: 0.5 and 0.25. # Subject-methods interaction standard deviation: 0.25 # Subject-times interaction standard deviation: 0.5 # Same difference of means at each time set.seed(202) df <- ccc_sim_data(n=50, b = c(0,1), g=c(0,0.25,0.5), mu = -0.25, sa = 1.5, sab=0.25,sag=0.5,se = 1, nrep=2) # Simulate data using the estimates of a linear mixed model set.seed(2024) df3 <- ccc_sim_data(n=50, b = c(0,1), g=c(0,0.25,0.5), mu = -0.25, sa = 1.5, sab=0.25,sag=0.5,bg=c(0,0.5,0.75,0,1,1),se = 1, nrep=2) mod3 <- lme_model(df3,"y","id","times","met",control.lme=nlme::lmeControl(opt = 'optim')) ccc_sim_data(nsim=10,model=mod3)# # Reliability data: # 50 subjects, one method, one time, 2 replicates # Overall mean: -0.25; Subjects standard deviation: 1.5, Random error standard deviation: 1 set.seed(101) df <- ccc_sim_data(n=50, b = NULL, g = NULL, mu = -0.25, sa = 1.5, se = 1, nrep=2) # Method comparison data (non-longitudinal) # 50 subjects, two methods, 2 replicates # Overall mean: -0.25; Subjects standard deviation: 1.5, Random error standard deviation: 1 # Difference of means between methods 2 and 1: 1 # Three data sets simulated set.seed(202) df <- ccc_sim_data(n=50, nsim=3,b = c(0,1), mu = -0.25, sa = 1.5, se = 1, nrep=2) # Method comparison data (longitudinal) # 50 subjects, two methods, 3 times, 1 replicate, # Overall mean: -0.25; Subjects standard deviation: 1.5, Random error standard deviation: 1 # Difference of means between methods 2 and 1: 1 # Difference of means between times 3,2 and 1 respectively: 0.5 and 0.25. # Subject-methods interaction standard deviation: 0.25 # Subject-times interaction standard deviation: 0.5 # Same difference of means at each time set.seed(202) df <- ccc_sim_data(n=50, b = c(0,1), g=c(0,0.25,0.5), mu = -0.25, sa = 1.5, sab=0.25,sag=0.5,se = 1, nrep=2) # Simulate data using the estimates of a linear mixed model set.seed(2024) df3 <- ccc_sim_data(n=50, b = c(0,1), g=c(0,0.25,0.5), mu = -0.25, sa = 1.5, sab=0.25,sag=0.5,bg=c(0,0.5,0.75,0,1,1),se = 1, nrep=2) mod3 <- lme_model(df3,"y","id","times","met",control.lme=nlme::lmeControl(opt = 'optim')) ccc_sim_data(nsim=10,model=mod3)
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.
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, ... )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, ... )
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. |
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 |
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 |
future_seed |
Logical/Integer. The seed to be used for parallellization. Further details in |
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 |
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. |
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.
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.
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.
# 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_int=ccc_vc(bpres,"DIA","ID","METODE",int=TRUE,control.lme=nlme::lmeControl(opt = 'optim')) ccc_mc_int summary(ccc_mc_int) # 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)# 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_int=ccc_vc(bpres,"DIA","ID","METODE",int=TRUE,control.lme=nlme::lmeControl(opt = 'optim')) ccc_mc_int summary(ccc_mc_int) # 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)
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)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.
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 newdat=bpres[bpres$NM==1,] estccc=cccUst(newdat,"DIA","METODE") estccc estccc=cccUst(bdaw,"AUC","MET","VNUM") estccc estccc=cccUst(bfat,"BF","MET","VISITNO",Dmat=diag(c(2,1,1))) estccc# Non-longitudinal scenario newdat=bpres[bpres$NM==1,] estccc=cccUst(newdat,"DIA","METODE") estccc estccc=cccUst(bdaw,"AUC","MET","VNUM") estccc estccc=cccUst(bfat,"BF","MET","VISITNO",Dmat=diag(c(2,1,1))) estccc
Fits a Linear Mixed Effects Model
lme_model( dataset, ry, rind, rtime = NULL, rmet = NULL, vecD = NULL, covar = NULL, rho = 0, int = FALSE, cl = 0.95, control.lme = list(), apVar = TRUE, ... )lme_model( dataset, ry, rind, rtime = NULL, rmet = NULL, vecD = NULL, covar = NULL, rho = 0, int = FALSE, cl = 0.95, control.lme = list(), apVar = TRUE, ... )
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 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. |
rho |
Within subject correlation structure. A value of 0 (default option) stands for compound symmetry and 1 is used for autoregressive of order 1 structure. |
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 |
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. |
an object of class lme.
# Reliability ICC set.seed(2024) df <- ccc_sim_data(b = NULL, g = NULL, mu = -0.25, sa = 1.5, se = 1) mod1 <- lme_model(df,"y","id") mod1 #Non-longitudinal Methods comparison data set.seed(2024) df2 <- ccc_sim_data(n=50,b = c(0,1), mu = -0.25, sa = 1.5, se = 1, nrep=2) mod2 <- lme_model(df2,"y","id",rmet="met") mod2 # Longitudinal Methods comparison data set.seed(2024) df3 <- ccc_sim_data(n=50, b = c(0,1), g=c(0,0.25,0.5), mu = -0.25, sa = 1.5, sab=0.25,sag=0.5,bg=c(0,0.5,0.75,0,1,1),se = 1, nrep=2) mod3 <- lme_model(df3,"y","id","times","met",control.lme=nlme::lmeControl(opt = 'optim')) mod3# Reliability ICC set.seed(2024) df <- ccc_sim_data(b = NULL, g = NULL, mu = -0.25, sa = 1.5, se = 1) mod1 <- lme_model(df,"y","id") mod1 #Non-longitudinal Methods comparison data set.seed(2024) df2 <- ccc_sim_data(n=50,b = c(0,1), mu = -0.25, sa = 1.5, se = 1, nrep=2) mod2 <- lme_model(df2,"y","id",rmet="met") mod2 # Longitudinal Methods comparison data set.seed(2024) df3 <- ccc_sim_data(n=50, b = c(0,1), g=c(0,0.25,0.5), mu = -0.25, sa = 1.5, sab=0.25,sag=0.5,bg=c(0,0.5,0.75,0,1,1),se = 1, nrep=2) mod3 <- lme_model(df3,"y","id","times","met",control.lme=nlme::lmeControl(opt = 'optim')) mod3
Power and confidence interval range obtained by simulation
sim_power_ccc( n = 30, nrep = 2, nsim = 300, r0 = 0, alpha = 0.05, model = NULL, b = NULL, g = NULL, mu = 0, sa = 1, sab = 0, sag = 0, bg = NULL, se = 1, extra.info = TRUE, vecD = NULL, covar = NULL, int = FALSE, rho = 0, cl = 0.95, control.lme = list(), transf = "F2", future_seed = TRUE, workers = 15 )sim_power_ccc( n = 30, nrep = 2, nsim = 300, r0 = 0, alpha = 0.05, model = NULL, b = NULL, g = NULL, mu = 0, sa = 1, sab = 0, sag = 0, bg = NULL, se = 1, extra.info = TRUE, vecD = NULL, covar = NULL, int = FALSE, rho = 0, cl = 0.95, control.lme = list(), transf = "F2", future_seed = TRUE, workers = 15 )
n |
Integer. Number of subjects |
nrep |
Integer. Number of replicates |
nsim |
Integer. Number of data sets simulated. |
r0 |
Integer. Null hypothesis value. |
alpha |
Type-I error rate. |
model |
object of class |
b |
Vector. Method fixed effects. |
g |
Vector. Time fixed effects. |
mu |
Integer. Overall mean. |
sa |
Integer. Standard deviation of subject's random effect. |
sab |
Integer. Standard deviation of subject-method interaction's random effect. |
sag |
Integer. Standard deviation of subject-time interaction's random effect. |
bg |
Vector. Method-time interaction's fixed effects |
se |
Integer. Standard deviation of random error effect. |
extra.info |
Logical. Should the information about CCC and variance components simulated be shown? Default is set to TRUE. |
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 |
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 transformasion; "None", no transformation is applied. See *Details* for further information. |
future_seed |
Logical/Integer. The seed to be used for parallellization. Further details in |
workers |
Integer. Number of cores to be used for parallellization. Default is 15. Capped to number of available cores minus 1. |
The power and the range of the confidence interval are computed using the approach suggested in Choudhary and Nagaraja (2018). Data sets are simulated by setting the fixed effects values and the standard deviation of the random effects. The CCC and its standard error are estimated in each data set, along with its 95% confidence interval and the Wald test Ztest.
A data frame with the following components:
n Number of subjects
reps Number of replicates
CCC. Median of the CCC estimates.
Power. Empirical power computed as proportion of times the null hypothesis is rejected using a type-I error rate of alpha.
SEICC. Average of CCC standard errors.
SEZ. Average of transformed CCC standard errors.
Range IC95. Average of CCC confidence interval widths.
Choudhary, P.K. and Nagaraja, H.N. (2018). Measuring Agreement-Models, Methods, and Applications. John Wiley & Sons
# Power to test the CCC is above 0.8 with 35 subjects and 4 replicates. # Two methods, three times. Simulated CCC=0.87. sim_pw<-sim_power_ccc(n = 35, nrep=4, nsim=500, r0=0.8, b = c(-0.5,0.5), g=c(-0.25,0,0.25), mu = -0.25, sa = 4,sab=0.5,sag=1, bg=c(-0.5,-0.25,0.25,-0.5,0.25,0.75),se = 1)# Power to test the CCC is above 0.8 with 35 subjects and 4 replicates. # Two methods, three times. Simulated CCC=0.87. sim_pw<-sim_power_ccc(n = 35, nrep=4, nsim=500, r0=0.8, b = c(-0.5,0.5), g=c(-0.25,0,0.25), mu = -0.25, sa = 4,sab=0.5,sag=1, bg=c(-0.5,-0.25,0.25,-0.5,0.25,0.75),se = 1)
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.
Ztest(cccfit, r0 = 0, tr = TRUE)Ztest(cccfit, r0 = 0, tr = TRUE)
cccfit |
An object of class |
r0 |
Integer. Null hypothesis value. |
tr |
Logical. Should the transformed CCC be used? Only applies if a transformation was applied in the |
A one sided test to the null hypothesis value
.
where
stands for the CCC estimate and
its standard error. The p-value is computed as
where X follows a standard Normal distribution.
A data frame with two columns: Z, the statistical test value; and the P-value associated.
# Testing the CCC is above 0.8 ccc_mc=ccc_vc(bpres,"DIA","ID","METODE") ccc_mc Ztest(ccc_mc,r0=0.8)# Testing the CCC is above 0.8 ccc_mc=ccc_vc(bpres,"DIA","ID","METODE") ccc_mc Ztest(ccc_mc,r0=0.8)