R help - May 2011 - How to calculate confidence interval of C statistic by rcorr.cens

Hi,

I'm trying to calculate 95% confidence interval of C statistic of
logistic regression model using rcorr.cens in rms package. I wrote a
brief function for this purpose as the followings;

CstatisticCI <- function(x)   # x is object of rcorr.cens.
  {
    se <- x["S.D."]/sqrt(x["n"])
    Low95 <- x["C Index"] - 1.96*se
    Upper95 <- x["C Index"] + 1.96*se
    cbind(x["C Index"], Low95, Upper95)
  }

Then,
> MyModel.lrm.rcorr <- rcorr.cens(x=predict(MyModel.lrm), S=df$outcome)
> MyModel.lrm.rcorr
       C Index            Dxy           S.D.              n
missing     uncensored
     0.8222785      0.6445570      0.1047916    104.0000000
0.0000000    104.0000000
Relevant Pairs     Concordant      Uncertain
  3950.0000000   3248.0000000      0.0000000
> CstatisticCI(x5factor_final.lrm.pen.rcorr)
                      Low95   Upper95
C Index 0.8222785 0.8021382 0.8424188

I'm not sure what "S.D." in object of rcorr.cens means. Is this
standard
deviation of "C Index" or standard deviation of "Dxy"?
I thought it is standard deviation of "C Index". Therefore, I wrote
the
code above. Am I right?

I would appreciate any help in advance.

--
Kohkichi Hosoda M.D.

    Department of Neurosurgery,
    Kobe University Graduate School of Medicine,

S.D. is the standard deviation (standard error) of Dxy.  It already includes
the effective sample size in its computation so the sqrt(n) terms is not
needed.  The help file for rcorr.cens has an example where the confidence
interval for C is computed.  Note that you are making the strong assumption
that there is no overfitting in the model or that you are evaluating C on a
sample not used in model development.
Frank


???? wrote:
> 
> Hi,
> 
> I'm trying to calculate 95% confidence interval of C statistic of
> logistic regression model using rcorr.cens in rms package. I wrote a
> brief function for this purpose as the followings;
> 
> CstatisticCI <- function(x)   # x is object of rcorr.cens.
>   {
>     se <- x["S.D."]/sqrt(x["n"])
>     Low95 <- x["C Index"] - 1.96*se
>     Upper95 <- x["C Index"] + 1.96*se
>     cbind(x["C Index"], Low95, Upper95)
>   }
> 
> Then,
> 
>> MyModel.lrm.rcorr <- rcorr.cens(x=predict(MyModel.lrm),
S=df$outcome)
>> MyModel.lrm.rcorr
>        C Index            Dxy           S.D.              n
> missing     uncensored
>      0.8222785      0.6445570      0.1047916    104.0000000
> 0.0000000    104.0000000
> Relevant Pairs     Concordant      Uncertain
>   3950.0000000   3248.0000000      0.0000000
> 
>> CstatisticCI(x5factor_final.lrm.pen.rcorr)
>                       Low95   Upper95
> C Index 0.8222785 0.8021382 0.8424188
> 
> I'm not sure what "S.D." in object of rcorr.cens means. Is
this standard
> deviation of "C Index" or standard deviation of "Dxy"?
> I thought it is standard deviation of "C Index". Therefore, I
wrote the
> code above. Am I right?
> 
> I would appreciate any help in advance.
> 
> --
> Kohkichi Hosoda M.D.
> 
>     Department of Neurosurgery,
>     Kobe University Graduate School of Medicine,
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
--
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