[R] Question on approximations of full logistic regression model

[Frank Harrell]

I think you are doing this correctly except for one thing.  The validation
and other inferential calculations should be done on the full model.  Use
the approximate model to get a simpler nomogram but not to get standard
errors.  With only dropping one variable you might consider just running the
nomogram on the entire model.
Frank


細田弘吉 wrote:
> 
> Hi,
> I am trying to construct a logistic regression model from my data (104
> patients and 25 events). I build a full model consisting of five
> predictors with the use of penalization by rms package (lrm, pentrace
> etc) because of events per variable issue. Then, I tried to approximate
> the full model by step-down technique predicting L from all of the
> componet variables using ordinary least squares (ols in rms package) as
> the followings. I would like to know whether I am doing right or not.
> 
>> library(rms)
>> plogit <- predict(full.model)
>> full.ols <- ols(plogit ~ stenosis+x1+x2+ClinicalScore+procedure, sigma=1)
>> fastbw(full.ols, aics=1e10)
> 
>  Deleted       Chi-Sq d.f. P      Residual d.f. P      AIC    R2
>  stenosis       1.41  1    0.2354   1.41   1    0.2354  -0.59 0.991
>  x2            16.78  1    0.0000  18.19   2    0.0001  14.19 0.882
>  procedure     26.12  1    0.0000  44.31   3    0.0000  38.31 0.711
>  ClinicalScore 25.75  1    0.0000  70.06   4    0.0000  62.06 0.544
>  x1            83.42  1    0.0000 153.49   5    0.0000 143.49 0.000
> 
> Then, fitted an approximation to the full model using most imprtant
> variable (R^2 for predictions from the reduced model against the
> original Y drops below 0.95), that is, dropping "stenosis".
> 
>> full.ols.approx <- ols(plogit ~ x1+x2+ClinicalScore+procedure)
>> full.ols.approx$stats
>           n  Model L.R.        d.f.          R2           g       Sigma
> 104.0000000 487.9006640   4.0000000   0.9908257   1.3341718   0.1192622
> 
> This approximate model had R^2 against the full model of 0.99.
> Therefore, I updated the original full logistic model dropping
> "stenosis" as predictor.
> 
>> full.approx.lrm <- update(full.model, ~ . -stenosis)
> 
>> validate(full.model, bw=F, B=1000)
>           index.orig training    test optimism index.corrected    n
> Dxy           0.6425   0.7017  0.6131   0.0887          0.5539 1000
> R2            0.3270   0.3716  0.3335   0.0382          0.2888 1000
> Intercept     0.0000   0.0000  0.0821  -0.0821          0.0821 1000
> Slope         1.0000   1.0000  1.0548  -0.0548          1.0548 1000
> Emax          0.0000   0.0000  0.0263   0.0263          0.0263 1000
> 
>> validate(full.approx.lrm, bw=F, B=1000)
>           index.orig training    test optimism index.corrected    n
> Dxy           0.6446   0.6891  0.6265   0.0626          0.5820 1000
> R2            0.3245   0.3592  0.3428   0.0164          0.3081 1000
> Intercept     0.0000   0.0000  0.1281  -0.1281          0.1281 1000
> Slope         1.0000   1.0000  1.1104  -0.1104          1.1104 1000
> Emax          0.0000   0.0000  0.0444   0.0444          0.0444 1000
> 
> Validatin revealed this approximation was not bad.
> Then, I made a nomogram.
> 
>> full.approx.lrm.nom <- nomogram(full.approx.lrm,
> fun.at=c(0.05,0.1,0.2,0.4,0.6,0.8,0.9,0.95), fun=plogis)
>> plot(full.approx.lrm.nom)
> 
> Another nomogram using ols model,
> 
>> full.ols.approx.nom <- nomogram(full.ols.approx,
> fun.at=c(0.05,0.1,0.2,0.4,0.6,0.8,0.9,0.95), fun=plogis)
>> plot(full.ols.approx.nom)
> 
> These two nomograms are very similar but a little bit different.
> 
> My questions are;
> 
> 1. Am I doing right?
> 
> 2. Which nomogram is correct
> 
> I would appreciate your help in advance.
> 
> -- 
> KH
> 
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> 


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