R: AUC estimator proposed by Song and Zhou

AUC.sh {survAUC} | R Documentation

## AUC estimator proposed by Song and Zhou

### Description

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

### Usage

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

### 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.
`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.
`savesensspec` | A logical specifying whether sensitivities and specificities should be saved.

### 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.

### 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`.

### 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

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

    lp <- predict(train.fit)
    lpnew <- predict(train.fit, newdata=TE)
    Surv.rsp <- Surv(TR$futime, TR$fustat)
    Surv.rsp.new <- 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)
    AUC_sh$iauc

[Package survAUC version 1.0-5 Index]