AUC estimator proposed by Song and Zhou

Song and Zhou's estimators of AUC for right-censored time-to-event data

sens.sh(Surv.rsp, lp, lpnew, times, type = "incident")

spec.sh(Surv.rsp, lp, lpnew, times)

AUC.sh(
  Surv.rsp,
  Surv.rsp.new = NULL,
  lp,
  lpnew,
  times,
  type = "incident",
  savesensspec = FALSE
)

Arguments

Surv.rsp

A Surv(.,.) object containing to the outcome of the training data.

lp

The vector of predictors estimated from the training data.

lpnew

The vector of predictors obtained from the test data.

times

A vector of time points at which to evaluate AUC.

type

A string defining the type of true positive rate (TPR): "incident" refers to incident TPR , "cumulative" refers to cumulative TPR.

Surv.rsp.new

A Surv(.,.) object containing the outcome of the test data.

savesensspec

A logical specifying whether sensitivities and specificities should be saved.

Value

AUC.sh returns an object of class survAUC. Specifically, AUC.sh returns a list with the following components:

auc

The cumulative/dynamic or incident/dynamic AUC estimates (evaluated at times).

times

The vector of time points at which AUC is evaluated.

iauc

The summary measure of AUC.

sens.sh and spec.sh return matrices of dimensions times x lpnew + 1. The elements of these matrices are the sensitivity and specificity estimates for each threshold of lpnew and for each time point specified in times.

Details

The sens.sh and spec.sh functions implement the estimators of time-dependent true and false positive rates proposed by Song and Zhou (2008).

The AUC.sh function implements the estimators of cumulative/dynamic and incident/dynamic AUC proposed by Song and Zhou (2008). These estimators are given by the areas under the time-dependent ROC curves estimated by sens.sh and spec.sh. In case of cumulative/dynamic AUC, the iauc summary measure is given by the integral of AUC on [0, max(times)] (weighted by the estimated probability density of the time-to-event outcome). In case of incident/dynamic AUC, iauc is given by the integral of AUC on [0, max(times)] (weighted by 2 times the product of the estimated probability density and the estimated survival function of the time-to-event outcome).

The results obtained from spec.sh, spec.sh and AUC.sh are valid as long as lp and lpnew are the predictors of a correctly specified Cox proportional hazards model. In this case, the estimators remain valid even if the censoring times depend on the values of the predictors.

References

Song, X. and X.-H. Zhou (2008).
A semiparametric approach for the covariate specific ROC curve with survival outcome.
Statistica Sinica 18, 947–965.

See also

AUC.uno, AUC.cd, AUC.hc, GHCI, IntAUC

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_sh <- AUC.sh(Surv.rsp, Surv.rsp.new, lp, lpnew, times)
names(AUC_sh)
#> [1] "auc"   "times" "iauc" 
AUC_sh$iauc
#> [1] 0.8430845