
Dear Dr Harrell,

About the mean probabilities, I was refering to the ones computed with the command predict(...,type="mean").
I tried to set the binwidth in SAS to 0.0001 as you suggested. 
After having negated the predictors, I found a C index of 0.968, which is exactly the same that rcorr.cens in R and almost the same that lrm, as you explained.
This solves the problem.
For information I tried to change the binwidth value several time before posting the message. The problem was that I found everytime the same results whatever the binwidth,
which I couldn't understand.
I just discover that Enterprise Guide did not take into account these changes, whereas SAS did it. This enabled me to found the correct results thanks to your advice.

Thank you again for you help,
With best wishes,
Olivier

> Date: Thu, 24 Jan 2013 13:09:46 -0600
> From: f.harrell@vanderbilt.edu
> To: R-help@stat.math.ethz.ch
> Subject: Re: [R] Difference between R and SAS in Corcordance index in ordinal logistic regression
> 
> Please define 'mean probabilities'.
> 
> To compute the C-index or Dxy you need anything that is monotonically 
> related to the prediction of interest, including the linear combination 
> of covariates ignoring all intercepts.   In other words you don't need 
> to go to the trouble of computing probabilities unless you are binning, 
> as the binning is usually done on a controllable 0-1 scale.   When I bin 
> I just choose the middle intercept, I seem to recall.  Also try running 
> SAS with a very tiny BINWIDTH and see if you get 1 - .968 as the answer 
> for C.  [I wrote the original algorithm SAS uses for this in the old SAS 
> PROC LOGIST.  Binning was just for speed.]
> 
> You might also re-run SAS after negating the response variable.
> Frank
> 
> blackscorpio wrote
> > Dear Dr Harrell,
> > Thank you very much for your answer. Actually I also tried to found the C
> > index by hand on these data using the mean probabilities and I found
> > 0.968, as you just showed.
> > I understand now why I had a slight difference with the outpout of lrm. I
> > am thus convinced that this result is correct.
> >
> > I read on the SAS help that the procedure logistic also proceed to some
> > binning (BINWIDTH option) :
> >
> > http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_logistic_sect010.htm
> >
> > But I cannot explain why the difference between the two softwares is that
> > huge, especially since the class probabilities are the same.
> >
> > Do you think it could be due to the fact that mean probabilities are
> > computed differently ?
> >
> > Thank for your help and best regards,
> > OC
> >
> >
> >> Date: Thu, 24 Jan 2013 05:28:13 -0800
> >> From:
> 
> > f.harrell@
> 
> >> To:
> 
> > r-help@
> 
> >> Subject: Re: [R] Difference between R and SAS in Corcordance index in
> >> ordinal logistic regression
> >>
> >> lrm does some binning to make the calculations faster.  The exact
> >> calculation
> >> is obtained by running
> >>
> >> f <- lrm(...)
> >> rcorr.cens(predict(f), DA), which results in:
> >>
> >>        C Index            Dxy           S.D.              n
> >> missing
> >>     0.96814404     0.93628809     0.03808336    32.00000000
> >> 0.00000000
> >>     uncensored Relevant Pairs     Concordant      Uncertain
> >>    32.00000000   722.00000000   699.00000000     0.00000000
> >>
> >> I.e., C=68 instead of .963.  But this is even farther away than the
> >> value
> >> from SAS you reported.
> >>
> >> If you don't believe the rcorr.cens result, create a tiny example and do
> >> the
> >> calculations by hand.
> >> Frank
> >>
> >>
> >> blackscorpio81 wrote
> >> > Dear R users,
> >> >
> >> > Please allow to me ask for your help.
> >> >  I am currently using Frank Harrell Jr package "rms" to model ordinal
> >> > logistic regression with proportional odds. In order to assess model
> >> > predictive ability, C concordance index is displayed and equals to
> >> 0.963.
> >> >
> >> > This is the code I used with the data attached
> >> > data.csv &lt;http://r.789695.n4.nabble.com/file/n4656409/data.csv&gt;
> >> >  :
> >> >
> >> >>require(rms)
> >> >>a<-read.csv2("/data.csv",row.names =,na.strings = c(""," "),dec=".")
> >> >>lrm(DA~SJ+TJ,data=
> >> >
> >> > Logistic Regression Model
> >> >
> >> > lrm(formula =A~SJ+TJ, data = a)
> >> >
> >> > Frequencies of Responses
> >> >
> >> >  1  2  3  4
> >> >  6 13  9  4
> >> >
> >> >                                               Model Likelihood
> >> > Discrimination                  Rank Discrim.
> >> >                                              Ratio Test
> >> > Indexes                               Indexes
> >> > Obs            32                      LR chi2      53.14
> >> R2
> >> > 0.875                      C       0.963
> >> > max |deriv| 6e-06             d.f.             2                    g
> >> > 8.690                Dxy     0.925
> >> >                                              Pr(> chi2) <0.0001
> >> gr
> >> > 5942.469                    gamma   0.960
> >> >
> >> > gp       0.486                      tau-a   0.673
> >> >
> >> > Brier    0.022
> >> >
> >> >                         Coef              S.E.        Wald  Z
> >> Pr(>|Z|)
> >> > y>=            -0.6161     0.6715        -0.92           0.3589
> >> > y>=            -6.5949     2.3750        -2.78          0.0055
> >> > y>=       -16.2358        5.3737         -3.02         0.0025
> >> > SJ                 1.4341      0.5180          2.77         0.0056
> >> > TJ                  0.5312      0.2483         2.14          0.0324
> >> >
> >> > I wanted to compare the results with SAS. I found the same slopes and
> >> > intercept with opposite signs, which is normal since R models the
> >> > probabilities P(Y>=X) whereas SAS models the probabilities P(Y<=k|X)
> >> > (see pdf attached, page 2 , table "Association des probabilités
> >> prédites
> >> > et des réponses observées").
> >> > SAS_Report_-_Logistic_Regression.pdf
> >> >
> >> &lt;http://r.789695.n4.nabble.com/file/n4656409/SAS_Report_-_Logistic_Regression.pdf&gt;
> >> >
> >> > I chose the order for levels.
> >> >
> >> > I controlled that the corresponding probabilities P(Y=X)  are the
> >> same
> >> > with both softwares. But I can't understand why in SAS the C index
> >> drops
> >> > from 0.963 down to 0.332.
> >> >
> >> > I read a lot of things about this and it seems to me that both
> >> softwares
> >> > use slightly different technique to compute the C index ; it is
> >> > nevertheless surprising to me to observe such a shift in the results.
> >> >
> >> > Does anyone have a clue on this ?
> >> > Thank you very much for you help
> >> > Blackscorpio
> >>
> >>
> >>
> >>
> 
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