[R] rcorrp.cens

Frank E Harrell Jr f.harrell at vanderbilt.edu
Fri Apr 21 14:05:26 CEST 2006

Stefano Mazzuco wrote:
> Hi R-users,
> I'm having some problems in using the Hmisc package.
> I'm estimating a cox ph model and want to test whether the drop in
> concordance index due to omitting one covariate is significant. I think (but
> I'm not sure) here are two ways to do that:
> 1) predict two cox model (the full model and model without the covariate of
> interest) and estimate the concordance index (i.e. area under the ROC curve)
> with rcorr.cens for both models, then compute the difference
> 2) predict the two cox models and estimate directly the difference between
> the two c-indices using rcorrp.cens. But it seems that the rcorrp.cens gives
> me the drop of Dxy index.
> Do you have any hint?
> Thanks
> Stefano

First of all, any method based on comparing rank concordances loses 
powers and is discouraged.  Likelihood ratio tests (e.g., by embedding a 
smaller model in a bigger one) are much more powerful.  If you must base 
comparisons on rank concordance (e.g., ROC area=C, Dxy) then rcorrp.cens 
can work if the sample size is large enough so that uncertainty about 
regression coefficient estimates may be ignored.  rcorrp.cens doesn't 
give the drop in C; it gives the probability that one model is "more 
concordant" with the outcome than another, among pairs of paired 

The bootcov function in the Design package has a new version that will 
output bootstrap replicates of C for a model, and its help file tells 
you how to use that to compare C for two models.  This should only be 
done to show how low a power such a procedure has.  rcporrp is likely to 
be more powerful than that, but likelihood ratio is what you want.  You 
will find many cases where one model increases C by only 0.02 but it has 
many more useful (more extreme) predictions.

Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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