What is the “$R^2$” value given in the summary of a coxph model in R

Question

What is the $R^2$ value given in the summary of a coxph model in R? For example,

Rsquare= 0.186   (max possible= 0.991 )

I foolishly included it a manuscript as an $R^2$ value and the reviewer jumped on it saying he wasn't aware of an analogue of the $R^2$ statistic from the classic linear regression being developed for the Cox model and if there was one please provide a reference. Any help would be great!

Answer 1

Using getS3method("summary","coxph") you can look at how it is calculated.

The relevant code lines are the following:

logtest <- -2 * (cox$loglik[1] - cox$loglik[2])
rval$rsq <- c(rsq = 1 - exp(-logtest/cox$n), maxrsq = 1 - 
        exp(2 * cox$loglik[1]/cox$n))

Here cox$loglik is "a vector of length 2 containing the log-likelihood with the initial values and with the final values of the coefficients" (see ?coxph.object) and cox$n is "number of observations used in the fit".