R help - Mar 2011 - which does the "S.D." returned by {Hmisc} rcorr.cens measure?

Dear R-help,

This is an example in the {Hmisc} manual under rcorr.cens function:
> set.seed(1)
> x <- round(rnorm(200))
> y <- rnorm(200)
> round(rcorr.cens(x, y, outx=F),4)
       C Index            Dxy           S.D.              n        missing    
uncensored Relevant Pairs     Concordant      Uncertain 
        0.4831        -0.0338         0.0462       200.0000         0.0000      
200.0000     39800.0000     19228.0000         0.0000

That S.D. confuses me!!
It is obviously not the standard deviation of x or y.. but there is only one
realization of the c-index or Dxy for this sample dataset, where does the
variation come from..??  if I use the conventional formula for calculating
the standard deviation of proportions: sqrt((C Index)*(1-C Index)/n), I get
0.0353 instead of 0.0462..

Any advice is appreciated.


Vikki

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Vikki,

The formula you used for std. error of C is not correct.  C is not a simple
per-observation proportion.

SD in the output is the standard error of Dxy.  Dxy = 2(C - .5).  Backsolve
for std err of C.  

Variation in Dxy or C comes from the usual source: sampling variability. 
You can also see this by sampling from the original dataset (a la
bootstrap).

Frank


vikkiyft wrote:
> 
> Dear R-help,
> 
> This is an example in the {Hmisc} help manual in the section of
> rcorr.cens:
> 
>> set.seed(1)
>> x <- round(rnorm(200))
>> y <- rnorm(200)
>> round(rcorr.cens(x, y, outx=F),4)
>        C Index            Dxy           S.D.              n        missing
> uncensored Relevant Pairs     Concordant      Uncertain 
>         0.4831        -0.0338         0.0462       200.0000         0.0000
> 200.0000     39800.0000     19228.0000         0.0000
> 
> That S.D. confuses me!!
> It is obviously not the standard deviation of x or y.. but there is only
> one realization of the c-index or Dxy for this sample dataset, where does
> the variation come from..??  if I use the conventional formula for
> calculating the standard deviation of proportions: sqrt((C Index)*(1-C
> Index)/n), I get 0.0353 instead of 0.0462..
> 
> Any advice is appreciated.
> 
> 
> Vikki
> 

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