[R] C-index : typical values

[Adaikalavan Ramasamy]

Thank you ! So to be absolutely sure, the C-index in my case is
  0.5 * ( 0.3634 + 1 ) = 0.6817  right ?

If the above calculation is correct then why do I get the following :

  rcorr.cens( predict(fit), Surv( GBSG$rfst, GBSG$cens ) )[ "C Index" ]
    C Index
  0.3115156

( I am aware that is a re-substitution error rate and optimistic, but
this is what led me to believe that my C-index was < 0.5 ).


Can I suggest that it is probably worth adding a sentence about the
relationship between C-index and Dxy in validate.cph or elsewhere if
this is not a widely known issue.

Thank you again.

Regards, Adai



On Fri, 2005-09-02 at 19:55 -0400, Frank E Harrell Jr wrote:
> 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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