Integration of time-dependent AUC curves

Compute summary measures of a time-dependent AUC curve

Usage

IntAUC(AUC, times, S, tmax, auc.type = "cumulative")

Arguments

AUC: A vector of AUCs.
times: The vector of time points corresponding to AUC.
S: A vector of survival probabilities corresponding to times.
tmax: A number specifying the upper limit of the time range for which to compute the summary measure.
auc.type: A string defining the type of AUC. 'cumulative' refers to cumulative/dynamic AUC, 'incident' refers to incident/dynamic AUC.

Value

A scalar number corresponding to the summary measure of interest.

Details

This function calculates the integral under a time-dependent AUC curve (“IAUC” measure) using the integration limits [0, tmax]. The values of the AUC curve are specified via the AUC argument.

In case auc.type = "cumulative" (cumulative/dynamic IAUC), the values of AUC are weighted by the estimated probability density of the time-to-event outcome. In case auc.type = "incident" (incident/dynamic IAUC), the values of AUC are weighted by 2 times the product of the estimated probability density and the (estimated) survival function of the time-to-event outcome. The survival function has to be specified via the S argument.

As shown by Heagerty and Zheng (2005), the incident/dynamic version of IAUC can be interpreted as a global concordance index measuring the probability that observations with a large predictor value have a shorter survival time than observations with a small predictor value. The incident/dynamic version of IAUC has the same interpretation as Harrell's C for survival data.

References

Harrell, F. E., R. M. Califf, D. B. Pryor, K. L. Lee and R. A. Rosati (1982).
Evaluating the yield of medical tests.
Journal of the American Medical Association 247, 2543–2546.

Harrell, F. E., K. L. Lee, R. M. Califf, D. B. Pryor and R. A. Rosati (1984).
Regression modeling strategies for improved prognostic prediction.
Statistics in Medicine 3, 143–152.

Heagerty, P. J. and Y. Zheng (2005).
Survival model predictive accuracy and ROC curves.
Biometrics 61, 92–105.

Examples


data(cancer,package="survival")
TR <- ovarian[1:16,]
TE <- ovarian[17:26,]
train.fit  <- survival::coxph(survival::Surv(futime, fustat) ~ age,
                              x=TRUE, y=TRUE, method="breslow", data=TR)

lp <- predict(train.fit)
lpnew <- predict(train.fit, newdata=TE)
Surv.rsp <- survival::Surv(TR$futime, TR$fustat)
Surv.rsp.new <- survival::Surv(TE$futime, TE$fustat)
times <- seq(10, 1000, 10)                  


AUC_CD <- AUC.cd(Surv.rsp, Surv.rsp.new, lp, lpnew, times)
IntAUC(AUC_CD$auc, AUC_CD$times, runif(length(times),0,1), median(times), auc.type="cumulative")
#> [1] 0.7857908