# Re: [R] Question on approximations of full logistic regression model

From: Frank Harrell <f.harrell_at_vanderbilt.edu>
Date: Sun, 15 May 2011 20:25:50 -0700 (PDT)

>
> 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
>
>
> --
> KH
>
> ______________________________________________
> R-help_at_r-project.org mailing list
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> and provide commented, minimal, self-contained, reproducible code.
>

Frank Harrell
Department of Biostatistics, Vanderbilt University
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