I need to calculate the AUC for a Cox regression model. SAS is giving me a time dependent AUC as below. How do I report this for the paper?

Thanks!!

Best Answer

What's routinely done with Cox survival models is to report the concordance or C-index. That's the fraction of comparable cases for which the predicted and observed order of event times agrees. In a binary regression model that type of index would be the AUC. See this page for example. It's possible that, in an abuse of terminology, someone asked you for AUC when the request was intended to be for a C-index.

For the time-dependent AUC you could simply show the plot itself if there's space, or report selected time points in the text and put the plot into supplemental material. It would be important also to show confidence intervals around the AUC estimates. Do make sure that you understand which method has been used to calculate the time-dependent AUC, as there are several.

1) SAS has the statement "assess ph / resample" that you can write out in the PROC PHREG statement which provide you with a visual plot of PH assumption but also a P-value for each covariate in the model. You could use this to assess PH for each covariate. You could also, and I see this often in medical research, introduce an interaction term between each covariate and (log) time; if the interaction is significant then that covariate assaults the PH assumption, and you should keep the interaction in the model to solve the problem!

2) I have no experience in graphical judgment of PH assumption.

3) I do not recall (but someone might correct me) that SAS provides a global test for Schoenfelds residuals, but the R package "survival" does. Perhaps RMS package does, since it's based on the survival package.

You should keep in mind that the AUC is itself an estimator, so it has a variance. Notwithstanding a programming error, it's possible that 0.85 and 0.98 are statistically indistinguishable from each other.

If you're interested, here's a paper on computing confidence intervals for the AUC
http://www.cs.nyu.edu/~mohri/pub/area.pdf
so you conceivably could compute the confidence interval for the training AUC and the testing AUC and see if they overlap.

Unless you made a programming error, though, you're most likely fine since the AUC of the training and testing datasets are pretty close.

## Best Answer

What's routinely done with Cox survival models is to report the concordance or C-index. That's the fraction of comparable cases for which the predicted and observed order of event times agrees. In a binary regression model that type of index would be the AUC. See this page for example. It's possible that, in an abuse of terminology, someone asked you for AUC when the request was intended to be for a C-index.

For the time-dependent AUC you could simply show the plot itself if there's space, or report selected time points in the text and put the plot into supplemental material. It would be important also to show confidence intervals around the AUC estimates. Do make sure that you understand which method has been used to calculate the time-dependent AUC, as there are several.