timeROC (version 0.4)

confint: Confidence intervals for areas under time-dependent ROC curves

Description

This function computes pointwise confidence interval and simultaneous confidence bands for areas under time-dependent ROC curves (time-dependent AUC). Pointwise confidence intervals and simultaneous confidence bands are computed from the asymptotic normality of time-dependent AUC estimators. Standard errors are estimated from the iid-representation of the estimator. The method is at present only implemented for inverse probability of censoring weights computed from a Kaplan-Meier estimator.

Usage

# S3 method for ipcwsurvivalROC
confint(object, parm=NULL, level = 0.95,n.sim=2000, ...)
# S3 method for ipcwcompetingrisksROC
confint(object, parm=NULL, level = 0.95,n.sim=2000, ...)

Arguments

object

An object of class "ipcwsurvivalROC" or "ipcwcompetingrisksROC". The object object must have been estimated by the timeROC function with arguments weighting="marginal" and iid = TRUE.

parm

Dummy argument. (Not used).

level

The confidence level required. Default is 0.95.

n.sim

The number of simulations for computing simultaneous confidence bands.

...

Dummy argument. (Not used).

Value

Without competing risks, a list containing :

• CI_AUC : a matrix. Columns correspond to the lower and the upper bounds of the pointwise confidence intervals of AUC. Rows correspond to the time points for which time-dependent AUC estimator was computed.

• CB_AUC : a matrix. Columns correspond to the lower and the upper bounds of the simultaneous confidence band of the AUC curve. Rows correspond to the time points for which time-dependent AUC estimator was computed.

• C.alpha : a numeric value corresponding to the quantile required for simultaneous confidence band computation (estimated by simulations).

With competing risks, a list containing :

• CI_AUC_1 : a matrix. Columns correspond to the lower and the upper bounds of the pointwise confidence intervals of AUC with definition (i) of controls. Rows correspond to the time points for which time-dependent AUC estimator was computed.

• CB_AUC_1 : a matrix. Columns correspond to the lower and the upper bounds of the simultaneous confidence band of the AUC curve with definition (i) of controls. Rows correspond to the time points for which time-dependent AUC estimator was computed.

• C.alpha.1 : a numeric value corresponding to the quantile required for simultaneous confidence bands computation CB_AUC_1 (estimated by simulations).

• CI_AUC_2 : a matrix. Columns correspond to the lower and the upper bounds of the pointwise confidence intervals of AUC with definition (ii) of controls. Rows correspond to the time points for which time-dependent AUC estimator was computed.

• CB_AUC_2 : a matrix. Columns correspond to the lower and the upper bounds of the simultaneous confidence band of the AUC curve with definition (ii) of controls. Rows correspond to the time points for which time-dependent AUC estimator was computed.

• C.alpha.2 : a numeric value corresponding to the quantile required for simultaneous confidence band computation CB_AUC_2 (estimated by simulations).

For AUC definitions (i) and (ii), see details about timeROC function.

Details

Time-dependent AUC estimators are asymptotically normally distributed. Then, confidence intervals are computed using an estimate of the variance and the quantiles of the standard normal distribution. To compute the variance estimates, the function computes the empirical variance estimates of the estimated iid-representations of the time-dependent AUC estimators. A simulation technique is used for computing appropriate quantiles of simultaneous confidence bands.

References

Hung, H. and Chiang, C. (2010). Estimation methods for time-dependent AUC with survival data. Canadian Journal of Statistics, 38(1):8-26

Blanche, P., Dartigues, J. F., & Jacqmin-Gadda, H. (2013). Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks. Statistics in medicine, 32(30), 5381-5397.

See Also

timeROC, compare, plotAUCcurve, plotAUCcurveDiff

Examples

# NOT RUN {
##-------------Without competing risks-------------------
library(survival)
data(pbc)
head(pbc)
pbc<-pbc[!is.na(pbc$trt),] # select only randomised subjects
pbc$status<-as.numeric(pbc$status==2) # create event indicator: 1 for death, 0 for censored

# we evaluate bilirubin as a prognostic biomarker for death.
ROC.bili<-timeROC(T=pbc$time,
                  delta=pbc$status,marker=pbc$bili,
                  cause=1,weighting="marginal",
                  times=quantile(pbc$time,probs=seq(0.2,0.8,0.1)),
                  iid=TRUE)
ROC.bili
confint(ROC.bili)


##-------------With competing risks-------------------

data(Melano)
head(Melano)

# Evaluate tumor thickness as a prognostic biomarker for
# death from malignant melanoma.
ROC.thick<-timeROC(T=Melano$time,delta=Melano$status,
                   marker=Melano$thick,cause=1,
                   times=quantile(Melano$time,probs=seq(0.2,0.8,0.2)),
                   iid=TRUE)
ROC.thick
confint(ROC.thick)

# }
# NOT RUN {
	data(Paquid)
	head(Paquid)
	
	# Computation requires approximately 30 seconds 
	# (because iid=TRUE and n=2561 subjects)	
	# evaluate DDST cognitive score as a prognostic tool for
	# dementia onset, accounting for death without dementia competing risk.	
	ROC.DSST<-timeROC(T=Paquid$time,
                      delta=Paquid$status,marker=-Paquid$DSST,
                      cause=1,weighting="marginal",times=c(3,5),
                      ROC=TRUE,iid=TRUE)
	ROC.DSST
	confint(ROC.DSST)
# }