[R] Question on approximations of full logistic regression model

[khosoda at med.kobe-u.ac.jp]

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