predErr: Distance-based estimators of survival predictive accuracy

Description

Inverse-probability-of-censoring weighted estimators of absolute and squared deviations between survival functions

Usage

predErr(Surv.rsp, Surv.rsp.new, lp, lpnew, times, 
        type = "brier", int.type = "unweighted")

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.

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 the prediction error curve.

type

A string specifying the type of prediction error curve: 'brier' refers to the squared deviation between predicted and observed survival (Brier score), 'robust' refers to the absolute deviation between predicted and observed survival.

int.type

A string specifying the type of integration method for the prediction error curves. Either 'unweighted' or 'weighted'.

Value

predErr returns an object of class survErr. Specifically, predErr returns a list containing the following components:

error

The prediction error estimates (evaluated at times).

times

The vector of time points at which prediction errors are evaluated.

ierror

The integrated prediction error.

Details

This function implements two types of prediction error curves for right-censored time-to-event data: The Brier Score (type = "brier", Gerds and Schumacher 2006) estimates the squared deviation between predicted and observed survival whereas the method proposed by Schmid et al. (2011) estimates the absolute deviation between predicted and observed survival (type = "robust").

Both methods are based on inverse-probability-of-censoring weights and do not assume a specific working model for survival prediction. Note, however, that the estimators implemented in predErr, are restricted to situations where the random censoring assumption holds.

Time-independent summary measures of prediction error are given by the the areas under the prediction error curves. If int.type = "weighted", prediction errors are weighted by the estimated probability density of the time-to-event outcome.

References

Gerds, T. A. and M. Schumacher (2006). Consistent estimation of the expected Brier score in general survival models with right-censored event times. Biometrical Journal 48, 1029--1040.

Schmid, M., T. Hielscher, T. Augustin, and O. Gefeller (2011). A robust alter- native to the Schemper-Henderson estimator of prediction error. Biometrics 67, 524--535.

Examples

Run this code

# NOT RUN {
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 <- 1:500                  

predErr(Surv.rsp, Surv.rsp.new, lp, lpnew, times, 
        type = "brier", int.type = "unweighted")

predErr(Surv.rsp, Surv.rsp.new, lp, lpnew, times, 
        type = "robust", int.type = "unweighted")

predErr(Surv.rsp, Surv.rsp.new, lp, lpnew, times, 
        type = "brier", int.type = "weighted")

# }

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