Uno's estimator of cumulative/dynamic AUC for right-censored time-to-event data
Usage
sens.uno(Surv.rsp, Surv.rsp.new, lpnew, times)
spec.uno(Surv.rsp.new, lpnew, times)
AUC.uno(Surv.rsp, Surv.rsp.new, lpnew, times, savesensspec = FALSE)Arguments
- Surv.rsp
A
Surv(.,.)object containing to the outcome of the training data.- Surv.rsp.new
A
Surv(.,.)object containing the outcome of the test data.- lpnew
The vector of predictors obtained from the test data.
- times
A vector of time points at which to evaluate AUC.
- savesensspec
A logical specifying whether sensitivities and specificities should be saved.
Value
AUC.uno returns an object of class survAUC.
Specifically, AUC.uno returns a list with the following components:
- auc
The cumulative/dynamic AUC estimates (evaluated at
times).- times
The vector of time points at which AUC is evaluated.
- iauc
The summary measure of AUC.
sens.uno and
spec.uno 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.uno and spec.uno functions implement the estimators
of time-dependent true and false positive rates proposed in Section 5.1 of
Uno et al. (2007).
The AUC.uno function implements the estimator of cumulative/dynamic
AUC that is based on the TPR and FPR estimators proposed by Uno et al.
(2007). It is given by the area(s) under the time-dependent ROC curve(s)
estimated by sens.uno and spec.uno. 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).
Uno's estimators are based on inverse-probability-of-censoring weights and
do not assume a specific working model for deriving the predictor
lpnew. It is assumed, however, that there is a one-to-one
relationship between the predictor and the expected survival times
conditional on the predictor. Note that the estimators implemented in
sens.uno, spec.uno and AUC.uno are restricted to
situations where the random censoring assumption holds.
References
Uno, H., T. Cai, L. Tian, and L. J. Wei (2007).
Evaluating prediction
rules for t-year survivors with censored regression models.
Journal
of the American Statistical Association 102, 527–537.
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)
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_Uno <- AUC.uno(Surv.rsp, Surv.rsp.new, lpnew, times)
names(AUC_Uno)
#> [1] "auc" "times" "iauc"
AUC_Uno$iauc
#> [1] 0.7552083