C-index : typical values

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

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 ) ?

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

3) Should I be using some other measurement instead of C-index.

Thank you very much in advance.

Regards, Adai

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

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