[R] C-index : typical values

[Frank E Harrell Jr]

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