Re: [R] C-index : typical values

From: Frank E Harrell Jr <f.harrell_at_vanderbilt.edu>
Date: Sat 03 Sep 2005 - 09:55:46 EST

Adaikalavan Ramasamy wrote:
> I am doing some coxPH model fitting and would like to have some idea
> about how good the fits are. Someone suggested to use Frank Harrell's
> C-index measure.
>
> As I understand it, a C-index > 0.5 indicates a useful model. I am

No, that just means predictions are better than random.

> probably making an error here because I am getting values less than 0.5
> on real datasets. Can someone tell me where I am going wrong please ?
>
> Here is an example using the German Breast Study Group data available in
> the mfp package. The predictors in the model were selected by stepAIC().
>
>
> library(Design); library(Hmisc); library(mfp); data(GBSG)
> fit <- cph( Surv( rfst, cens ) ~ htreat + tumsize + tumgrad +
> posnodal + prm, data=GBSG, x=T, y=T )
>
> val <- validate.cph( fit, dxy=T, B=200 )
> round(val, 3)
> index.orig training test optimism index.corrected n
> Dxy -0.377 -0.383 -0.370 -0.013 -0.364 200
> R2 0.140 0.148 0.132 0.016 0.124 200
> Slope 1.000 1.000 0.925 0.075 0.925 200
> D 0.028 0.030 0.027 0.004 0.025 200
> U -0.001 -0.001 0.002 -0.002 0.002 200
> Q 0.029 0.031 0.025 0.006 0.023 200
>
> 1) Am I correct in assuming C-index = 0.5 * ( Dxy + 1 ) ?

Yes

>
> 2) If so, I am getting 0.5*(-0.3634+1) = 0.318 for the C-index. Does
> this make sense ?

For the Cox model, the default calculation correlates the linear predictor with survival time. A large linear predictor (large log hazard) means shorter survival time. To phrase it in the more usually way, negate Dxy before computing C.

Frank

>
> 3) Should I be using some other measurement instead of C-index.
>
> Thank you very much in advance.
>
> Regards, Adai
>
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-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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Received on Sat Sep 03 10:15:36 2005

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