R2 {pec}

Explained variation for survival models

Description

This function computes a time-dependent $R^2$ like measure of the variation explained by a survival prediction model, by dividing the mean squared error (Brier score) of the model by the mean squared error (Brier score) of a reference model which ignores all the covariates.

Usage

R2(object, models, what, times, reference = 1)

Arguments

object

An object with estimated prediction error curves obtained with the function pec

models

For which of the models in object$models should we compute $R^2(t). By default all models are used except for the reference model.

what

The name of the entry in x to be used. Defauls to PredErr Other choices are AppErr, BootCvErr, Boot632, Boot632plus.

times

Time points at which the summaries are shown.

reference

Position of the model whose prediction error is used as the reference in the denominator when constructing $R^2$

Details

In survival analysis the prediction error of the Kaplan-Meier estimator plays a similar role as the total sum of squares in linear regression. Hence, it is a sensible reference model for $R^2$.

Value

A matrix where the first column holds the times and the following columns are the corresponding $R^2$ values for the requested prediction models.

Author(s)

Thomas A. Gerds [e-mail]

References

E. Graf et al. (1999), Assessment and comparison of prognostic classification schemes for survival data. Statistics in Medicine, vol 18, pp= 2529–2545.

Gerds TA, Cai T and Schumacher M (2008) The performance of risk prediction models Biometrical Journal, 50(4), 457–479

See Also

pec

Examples

set.seed(18713)
library(prodlim)
library(survival)
dat=SimSurv(100)
nullmodel=prodlim(Hist(time,status)~1,data=dat)
pmodel1=coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
pmodel2=coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
perror=pec(list(Cox1=pmodel1,Cox2=pmodel2),Hist(time,status)~1,data=dat,reference=TRUE)
R2(perror,times=seq(0,1,.1),reference=1)