[R] C-index : typical values

[Frank E Harrell Jr]

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

correct

> 
> 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 ).

You're right about the optimism but that's not the cause in this case.

> 
> 
> 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.

Will do  -Frank

> 
> 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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>>>
>>
>>
> 
> 


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