[R] Difference between R and SAS in Corcordance index in ordinal logistic regression
f.harrell at vanderbilt.edu
Thu Jan 24 14:28:13 CET 2013
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=.968 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.
> 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 <http://r.789695.n4.nabble.com/file/n4656409/data.csv>
>>a<-read.csv2("/data.csv",row.names = 1,na.strings = c(""," "),dec=".")
> Logistic Regression Model
> lrm(formula = DA~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>=2 -0.6161 0.6715 -0.92 0.3589
> y>=3 -6.5949 2.3750 -2.78 0.0055
> y>=4 -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>=k|X) whereas SAS models the probabilities P(Y<=k|X)
> (see pdf attached, page 2 , table "Association des probabilités prédites
> et des réponses observées").
> I chose the order for levels.
> I controlled that the corresponding probabilities P(Y=k|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
Department of Biostatistics, Vanderbilt University
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