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@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > 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 -- 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@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
