PHeval (version 1.1)

R2: R2 coefficient

Description

This function calcultates the \(R^2\) coefficient of OQuigley and Flandre (1994) to evaluate the predictive capacity of the proportional hazards model (or Cox model).

Usage

R2(formula, data)

Value

• If one covariate Z is present in the model, the \(R^2\) coefficient is $$ R^2=1-\frac{\sum(Zi-E_b(Zi))^2}{\sum(Zi-E_0(Zi))^2}, $$ where the sums are over the failures. \(E_b(Zi)\) is the expectation of \(Z\) at the ith failure time under the model of parameter \(b\) = the maximum partial likelihood estimator of the regression coefficient. \(E_0(Zi)\) is the expectation of \(Z\) under the model of parameter 0 at the ith failure time.

• If several covariates are present in the model, the \(R^2\) coefficient is evaluated as in the previous case except that the covariate Z is replaced by the prognostic index \(b'Z\).

Arguments

formula

A formula object or character string with the time and censoring status separated by "+" on the left hand side and the covariates separated by "+" on the right. For instance, if the time name is "Time", the censoring status is "Status" and the covariates are called "Cov1" and "Cov2", the formula is "Time+Status~Cov1+Cov2".

data

A data.frame with the data. The censoring status should be 1 for failure and 0 for censoring. No missing data accepted.

Author

Cecile Chauvel

Details

The program does not handle ties in the data. We suggest to randomly split the ties before using the program.

References

OQuigley J, Flandre P. (1994) Predictive capability of proportional hazards regression. PNAS 91, 2310-2314.

Examples

library(survival)
data(ovarian)
R2(futime+fustat~age,data=ovarian)
R2(futime+fustat~age+rx,data=ovarian)