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

From: <khosoda_at_med.kobe-u.ac.jp>
Date: Wed, 20 Apr 2011 23:44:04 +0900

Dear Prof. Harrel,

Thank you very much for your quick advice. I will try rms package.

Regarding model reduction, is my model 2 method (clustering and recoding that are blinded to the outcome) permissible?

Sincerely,

```--
KH

(11/04/20 22:01), Frank Harrell wrote:

> 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.
>>
>>
>> --
>> KH
>>
>> ______________________________________________
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>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
> -----
> Frank Harrell
> Department of Biostatistics, Vanderbilt University
> --
> View this message in context: http://r.789695.n4.nabble.com/BMA-logistic-regression-odds-ratio-model-reduction-etc-tp3462416p3462919.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help_at_r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.

--
*************************************************
神戸大学大学院医学研究科 脳神経外科学分野
細田 弘吉

〒650-0017　神戸市中央区楠町7丁目5-1
Phone: 078-382-5966
Fax  : 078-382-5979
Office: khosoda_at_med.kobe-u.ac.jp
Home  : khosoda_at_venus.dti.ne.jp

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