R2 {PHeval}

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)

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.

Details

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

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.

Author(s)

Cecile Chauvel

References

OQuigley, J. (2008) Proportional hazards regression. Springer New-York. Chapter 12.
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)