To present a model you need to show both calibration and discrimination.  Goodness of fit is normally a calibration issue - graphical means are sometimes sufficient.  R2 is one of the discrimination metrics.  Frank Harrell sees it as one of the better ones (see his book "Regression Modeling Strategies."  He also has some excellent material online in (Click on the links under "Course Material" on http://biostat.mc.vanderbilt.edu/wiki/Main/FrankHarrell)  

the significance of the model depends on the probability values given in the last column of the simulation results table and the likelihood ratio test.

Hello John, Hello Wajih,

Thank you for your input. I am well aware of the purpose of a goodness-of-fit test and the calibration/discrimination issue in the modeling procedure. As for the likelihood ratio test, it is used to test whether adding/removing a certain variable to/from the existing model improves the model fit or not.

This is not the purpose of my question, so let me explain my point a little more.

I am looking for the best goodness-of-fit test and how to calculate the R-squared statistics in the particular case of the Cox model.

To assess the fit of a model, we usually make use of residuals. In a survival data setting, residuals are different than for other types of models, mainly due to the censoring. In a different but related vein, the definition of the R-squared statistic in a censored data setting, is not easy. I am being told that different measures of explained variation can be used, one of which is the generalized R-squared whose calculation is based on the chi-square statistic for the likelihood ratio test for the model. However, its value seems to be heavily influenced by the number of censored cases.

I am looking forward to a detailed explanation on how I can assess my Cox model in the light of these considerations. Thank you.

Thank you Marco Barbàra for the articles provided.

Hello, I met the same question recently. Did you work it out?