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**

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”.

**Attribution***Source : Link , Question Author : danielsbrewer , Answer Author : onestop*