Notwithstanding the insensitive nature of the c-index, we have been challenged by a reviewer to generate bootstrap confidence intervals for a change in c-index between a “simple” and a “full” cph model where we are interested in added value. With rms::validate, one can get the optimism-adjusted (resampling-validated) c-index (i.e. (Dxy/2)+0.5) for both the simple and full models. For either model, one can bootstrap confidence intervals for Dxy (as shown in the following post: Confidence intervals for bootstrap-validated bias-corrected performance estimates - #10 by f2harrell). It is unclear to me (1) whether delta c would correspond to the difference between the two optimism-adjusted c-indexes (i.e. full - simple), and (2) how to bootstrap confidence intervals for this change.
There may be no reliable method to do this and interpretation thereof. Would greatly appreciate any help on these two points.
(For what it’s worth, we also reported output using the lrtest() function.)