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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