ROCt (version 0.9.5)

crude.ROCt:

Description

This function performs the characteristics of a time-dependent ROC curve based on k-nearest neighbor's (knn) estimator or only based on the Kaplan and Meier estimator.

Usage

crude.ROCt(times, failures, variable, pro.time, cut.off, estimator, prop)

Arguments

times

A numeric vector with the follow up times.

failures

A numeric vector with the event indicator (0=right censored, 1=event).

variable

A numeric vector with the prognostic variable. This variable is collected at the baseline.

pro.time

The value of prognostic time represents the maximum delay for which the capacity of the variable is evaluated. The same unit than the one used in the argument time.

cut.off

The cut-off values of the variable used to define the possible binary tests.

estimator

Three possible estimators can be used: 'kaplan-meier', 'akritas' or 'naive'. The naive estimator is selected by default.

prop

This is the unilateral proportion of the nearest neighbors. The estimation will be based on 2*prop (both right and left proportions) of the total sample size. This parameter will only be used if estimator='akritas'.

Value

table

This data frame presents the sensitivities and specificities associated with the cut-off values. One can observe NA if the value cannot be computed.

auc

The area under the time-dependent ROC curve for a prognostic up to prognostic time.

missing

Number of deleted observations due to missing data.

Details

This function computes time-dependent ROC curve with right-censored data. It can use Akritas approach (nearest neighbor's estimation) for ensuring monotone increasing ROC curve, instead of the simple Kaplan-Meier estimator. This Akritas approach may be avoid if the sample size is large because of computing time. Both estimators were defined by Heagerty, Lumley and Pepe (2000). A third alternative is the use of the naive estimator as explained by Blanche, Dartigues and Jacqmin-Gadda (2013). This estimator is less time-consuming compared to the Akritas approach.

References

Heagerty PJ., Lumley T., Pepe MS. (2000) Time-dependent ROC Curves for Censored Survival Data and a Diagnostic Marker. Biometrics, 56, 337-344. <doi:10.1111/j.0006-341X.2000.00337.x> Blanche P, Dartigues J, Jacqmin-Gadda H. (2013) Review and comparison of roc curve estimators for a time-dependent outcome with marker-dependent censoring. Biometrical Journal, 55, 687-704. <doi:10.1002/bimj.201200045>

Examples

# import and attach the data example

data(dataDIVAT)

# A subgroup analysis to reduce the time needed for this exemple

dataDIVAT <- dataDIVAT[1:400,]

# cut-off values definition (choose more values in prectice)

age.cut <- quantile(dataDIVAT$ageR, probs=seq(0.1, 0.9, by=0.1))

# the ROC curve (with the naive estimator) to predict the all-cause
# mortality up to the 3000 days

roc1 <- crude.ROCt(times=dataDIVAT$death.time,
 failures=dataDIVAT$death, variable=dataDIVAT$ageR,
 pro.time=3000, cut.off=age.cut, estimator="naive")

# the sensibilities and specificities associated with the cut off values

roc1$table

# the ROC curve (Kaplan-Meier estimator without the knn correction)
# to predict the all-cause mortality up to the 3000 days

# the ROC graph

plot(1-roc1$table$sp, roc1$table$se, ylim=c(0,1), xlim=c(0,1), ylab="sensitivity",
 xlab="1-specificity", type="l", lty=1, col=2, lwd=2)
 
abline(c(0,0), c(1,1), lty=2)

legend("bottomright", paste("Naive, (AUC=", round(roc1$auc, 2), ")", sep=""),
lty=1, lwd=2, col=2)

# the AUC

roc1$auc

AUC(sens=roc1$table$se, spec=roc1$table$sp)