Re: [R] BMA, logistic regression, odds ratio, model reduction etc

From: Frank Harrell <f.harrell_at_vanderbilt.edu>
Date: Wed, 20 Apr 2011 06:01:11 -0700 (PDT)

Deleting variables is a bad idea unless you make that a formal part of the BMA so that the attempt to delete variables is penalized for. Instead of BMA I recommend simple penalized maximum likelihood estimation (see the lrm function in the rms package) or pre-modeling data reduction that is blinded to the outcome variable.
Frank

細田弘吉 wrote:
>
> Hi everybody,
> I apologize for long mail in advance.
>
> I have data of 104 patients, which consists of 15 explanatory variables
> and one binary outcome (poor/good). The outcome consists of 25 poor
> results and 79 good results. I tried to analyze the data with logistic
> regression. However, the 15 variables and 25 events means events per
> variable (EPV) is much less than 10 (rule of thumb). Therefore, I used R
> package, "BMA" to perform logistic regression with BMA to avoid this
> problem.
>
> model 1 (full model):
> x1, x2, x3, x4 are continuous variables and others are binary data.
>

>> x16.bic.glm <- bic.glm(outcome ~ ., data=x16.df,

> glm.family="binomial", OR20, strict=FALSE)
>> summary(x16.bic.glm)

> (The output below has been cut off at the right edge to save space)
>
> 62 models were selected
> Best 5 models (cumulative posterior probability = 0.3606 ):
>
> p!=0 EV SD model 1 model2
> Intercept 100 -5.1348545 1.652424 -4.4688 -5.15
> -5.1536
> age 3.3 0.0001634 0.007258 .
> sex 4.0
> .M -0.0243145 0.220314 .
> side 10.8
> .R 0.0811227 0.301233 .
> procedure 46.9 -0.5356894 0.685148 . -1.163
> symptom 3.8 -0.0099438 0.129690 . .
> stenosis 3.4 -0.0003343 0.005254 .
> x1 3.7 -0.0061451 0.144084 .
> x2 100.0 3.1707661 0.892034 3.2221 3.11
> x3 51.3 -0.4577885 0.551466 -0.9154 .
> HT 4.6
> .positive 0.0199299 0.161769 . .
> DM 3.3
> .positive -0.0019986 0.105910 . .
> IHD 3.5
> .positive 0.0077626 0.122593 . .
> smoking 9.1
> .positive 0.0611779 0.258402 . .
> hyperlipidemia 16.0
> .positive 0.1784293 0.512058 . .
> x4 8.2 0.0607398 0.267501 . .
>
>
> nVar 2 2
> 1 3 3
> BIC -376.9082
> -376.5588 -376.3094 -375.8468 -374.5582
> post prob 0.104
> 0.087 0.077 0.061 0.032
>
> [Question 1]
> Is it O.K to calculate odds ratio and its 95% confidence interval from
> "EV" (posterior distribution mean) and“SD”(posterior distribution
> standard deviation)?
> For example, 95%CI of EV of x2 can be calculated as;
>> exp(3.1707661)

> [1] 23.82573 -----> odds ratio
>> exp(3.1707661+1.96*0.892034)

> [1] 136.8866
>> exp(3.1707661-1.96*0.892034)

> [1] 4.146976
> ------------------> 95%CI (4.1 to 136.9)
> Is this O.K.?
>
> [Question 2]
> Is it permissible to delete variables with small value of "p!=0" and
> "EV", such as age (3.3% and 0.0001634) to reduce the number of
> explanatory variables and reconstruct new model without those variables
> for new session of BMA?
>
> model 2 (reduced model):
> I used R package, "pvclust", to reduce the model. The result suggested
> x1, x2 and x4 belonged to the same cluster, so I picked up only x2.
> Based on the subject knowledge, I made a simple unweighted sum, by
> counting the number of clinical features. For 9 features (sex, side,
> HT2, hyperlipidemia, DM, IHD, smoking, symptom, age), the sum ranges
> from 0 to 9. This score was defined as ClinicalScore. Consequently, I
> made up new data set (x6.df), which consists of 5 variables (stenosis,
> x2, x3, procedure, and ClinicalScore) and one binary outcome
> (poor/good). Then, for alternative BMA session...
>
>> BMAx6.glm <- bic.glm(postopDWI_HI ~ ., data=x6.df,

> glm.family="binomial", OR=20, strict=FALSE)
>> summary(BMAx6.glm)

> (The output below has been cut off at the right edge to save space)
> Call:
> bic.glm.formula(f = postopDWI_HI ~ ., data = x6.df, glm.family =
> "binomial", strict = FALSE, OR = 20)
>
>
> 13 models were selected
> Best 5 models (cumulative posterior probability = 0.7626 ):
>
> p!=0 EV SD model 1 model 2
> Intercept 100 -5.6918362 1.81220 -4.4688 -6.3166
> stenosis 8.1 -0.0008417 0.00815 . .
> x2 100.0 3.0606165 0.87765 3.2221 3.1154
> x3 46.5 -0.3998864 0.52688 -0.9154 .
> procedure 49.3 0.5747013 0.70164 . 1.1631
> ClinicalScore 27.1 0.0966633 0.19645 . .
>
>
> nVar 2 2 1
> 3 3
> BIC -376.9082 -376.5588
> -376.3094 -375.8468 -375.5025
> post prob 0.208 0.175
> 0.154 0.122 0.103
>
> [Question 3]
> Am I doing it correctly or not?
> I mean this kind of model reduction is permissible for BMA?
>
> [Question 4]
> I still have 5 variables, which violates the rule of thumb, "EPV > 10".
> Is it permissible to delete "stenosis" variable because of small value
> of "EV"? Or is it O.K. because this is BMA?
>
> Sorry for long post.
>
> I appreciate your help very much in advance.
>
> --
> KH
>
> ______________________________________________
> R-help_at_r-project.org mailing list
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


Frank Harrell
Department of Biostatistics, Vanderbilt University
--
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