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)

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
>
> ______________________________________________
> R-help_at_r-project.org mailing list
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> PLEASE do read the posting guide
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> and provide commented, minimal, self-contained, reproducible code.
>


Frank Harrell
Department of Biostatistics, Vanderbilt University
--
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Received on Mon 16 May 2011 - 03:30:44 GMT

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