From: <khosoda_at_med.kobe-u.ac.jp>

Date: Sat, 30 Apr 2011 00:08:12 +0900

Date: Sat, 30 Apr 2011 00:08:12 +0900

(11/04/29 22:09), Frank Harrell wrote:

> Yes I would select that as the final model.

Thank you for your comment. I am able to be confident about my model now.

The difference you saw is caused

> by different treatment of penalization of factor variables, related to the

*> use of the sum squared differences between the estimate at one category from
**> the average over all categories. I think that as long as you code it one
**> way consistently and pick the penalty using that coding you are OK. But if
**> the coefficients of the non-factor variables depend on how the binary
**> predictor is coded, there is a bit more concern.
*

A lot of previous studies have demonstrated that poor outcome is more frequent in treat2 than in treat 1. So, I coded treat1 as 0, and treat2 as 1 in the first mail. Then, I came back to the original coding of treat1 and treat2 in the newer mail. According to your answer, I guess I am OK. :-)

Prof Harrell, Your book (Rregression Modeling Strategies) and many kind comments helped me a lot. Thank you very much again.

-- KHReceived on Fri 29 Apr 2011 - 19:18:36 GMT

>

> Frank

>>> 細田弘吉 wrote:>>>> Thank you for you quick reply, Prof. Harrell.>> According to your advice, I ran pentrace using a very wide range.>>>> > pentrace.x6factor<- pentrace(x6factor.lrm, seq(0, 100, by=0.5))>> > plot(pentrace.x6factor)>>>> I attached this figure. Then,>>>> > pentrace.x6factor<- pentrace(x6factor.lrm, seq(0, 10, by=0.05))>>>> It seems reasonable that the best penalty is 2.55.>>>> > x6factor.lrm.pen<- update(x6factor.lrm, penalty=2.55)>> > cbind(coef(x6factor.lrm), coef(x6factor.lrm.pen),>> abs(coef(x6factor.lrm)-coef(x6factor.lrm.pen)))>> [,1] [,2] [,3]>> Intercept -4.32434556 -3.86816460 0.456180958>> stenosis -0.01496757 -0.01091755 0.004050025>> T1 3.04248257 2.42443034 0.618052225>> T2 -0.75335619 -0.57194342 0.181412767>> procedure -1.20847252 -0.82589263 0.382579892>> ClinicalScore 0.37623189 0.30524628 0.070985611>>>> > validate(x6factor.lrm, bw=F, B=200)>> index.orig training test optimism index.corrected n>> Dxy 0.6324 0.6849 0.5955 0.0894 0.5430 200>> R2 0.3668 0.4220 0.3231 0.0989 0.2679 200>> Intercept 0.0000 0.0000 -0.1924 0.1924 -0.1924 200>> Slope 1.0000 1.0000 0.7796 0.2204 0.7796 200>> Emax 0.0000 0.0000 0.0915 0.0915 0.0915 200>> D 0.2716 0.3229 0.2339 0.0890 0.1826 200>> U -0.0192 -0.0192 0.0243 -0.0436 0.0243 200>> Q 0.2908 0.3422 0.2096 0.1325 0.1582 200>> B 0.1272 0.1171 0.1357 -0.0186 0.1457 200>> g 1.6328 1.9879 1.4940 0.4939 1.1389 200>> gp 0.2367 0.2502 0.2216 0.0286 0.2080 200>>>>>> > validate(x6factor.lrm.pen, bw=F, B=200)>> index.orig training test optimism index.corrected n>> Dxy 0.6375 0.6857 0.6024 0.0833 0.5542 200>> R2 0.3145 0.3488 0.3267 0.0221 0.2924 200>> Intercept 0.0000 0.0000 0.0882 -0.0882 0.0882 200>> Slope 1.0000 1.0000 1.0923 -0.0923 1.0923 200>> Emax 0.0000 0.0000 0.0340 0.0340 0.0340 200>> D 0.2612 0.2571 0.2370 0.0201 0.2411 200>> U -0.0192 -0.0192 -0.0047 -0.0145 -0.0047 200>> Q 0.2805 0.2763 0.2417 0.0346 0.2458 200>> B 0.1292 0.1224 0.1355 -0.0132 0.1423 200>> g 1.2704 1.3917 1.5019 -0.1102 1.3805 200>> gp 0.2020 0.2091 0.2229 -0.0138 0.2158 200>>>> In the penalized model (x6factor.lrm.pen), the apparent Dxy is 0.64, and>> bias-corrected Dxy is 0.55. The maximum absolute error is estimated to>> be 0.034, smaller than non-penalized model (0.0915 in x6factor.lrm) The>> changes in slope and intercept are substantially reduced in penalized>> model. I think overfitting is improved at least to some extent. Should I>> select this as a final model?>>>> I have one more question. The "procedure" variable was defined as 0/1>> value in the previous mail. For some graphical reason, I redefined it as>> treat1/treat2 value. Then, the best penalty value was changed from 3.05>> to 2.55. I guess change from numeric to factorial caused this reduction>> in penalty. Which set up should I select?>>>> I appreciate your help in advance.>>>> -->> KH>>>> (11/04/26 0:21), Frank Harrell wrote:>>> You've done a lot of good work on this. Yes I would say you have>>> moderate>>> overfitting with the first model. The only thing that saved you from>>> having>>> severe overfitting is that there seems to be a signal present [I am>>> assume>>> this model is truly pre-specified and was not developed at all by looking>>> at>>> patterns of responses Y.]>>>>>> The use of backwards stepdown demonstrated much worse overfitting. This>>> is>>> in line with what we know about the damage of stepwise selection methods>>> that do not incorporate shrinkage. I would throw away the stepwise>>> regression model. You'll find that the model selected is entirely>>> arbitrary. And you can't use the "selected" variables in any re-fit of>>> the>>> model, i.e., you can't use lrm pretending that the two remaining>>> variables>>> were pre-specified. Stepwise regression methods only seem to help. When>>> assessed properly we see that is an illusion.>>>>>> You are using penalizing properly but you did not print the full table of>>> penalties vs. effective AIC. We don't have faith that you penalized>>> enough.>>> I tend to run pentrace using a very wide range of possible penalties to>>> make>>> sure I've found the global optimum.>>>>>> Penalization somewhat solves the EPV problem but there is no substitute>>> for>>> getting more data.>>>>>> You can run validate specifying your final penalty as an argument.>>>>>> Frank>>>>>>>>>>>> 細田弘吉 wrote:>>>>>>>> According to the advice, I tried rms package.>>>> Just to make sure, I have data of 104 patients (x6.df), which consists>>>> of 5 explanatory variables and one binary outcome (poor/good) (previous>>>> model 2 strategy). The outcome consists of 25 poor results and 79 good>>>> results. Therefore, My events per variable (EPV) is only 5 (much less>>>> than the rule of thumb of 10).>>>>>>>> My questions are about validate and pentrace in rms package.>>>> I present some codes and results.>>>> I appreciate anybody's help in advance.>>>>>>>> > x6.lrm<- lrm(outcome ~ stenosis+x1+x2+procedure+ClinicalScore,>>>> data=x6.df, x=T, y=T)>>>>>>>> > x6.lrm>>>> ...>>>> Obs 104 LR chi2 29.24 R2 0.367 C 0.816>>>> negative 79 d.f. 5 g 1.633 Dxy 0.632>>>> positive 25 Pr(> chi2)<0.0001 gr 5.118 gamma 0.632>>>> max |deriv| 1e-08 gp 0.237 tau-a 0.233>>>> Brier 0.127>>>>>>>> Coef S.E. Wald Z Pr(>|Z|)>>>> Intercept -5.5328 2.6287 -2.10 0.0353>>>> stenosis -0.0150 0.0284 -0.53 0.5979>>>> x1 3.0425 0.9100 3.34 0.0008>>>> x2 -0.7534 0.4519 -1.67 0.0955>>>> procedure 1.2085 0.5717 2.11 0.0345>>>> ClinicalScore 0.3762 0.2287 1.65 0.0999>>>>>>>> It seems not too bad. Next, validation by bootstrap ...>>>>>>>> > validate(x6.lrm, B=200, bw=F)>>>> index.orig training test optimism index.corrected n>>>> Dxy 0.6324 0.6960 0.5870 0.1091 0.5233 200>>>> R2 0.3668 0.4370 0.3154 0.1216 0.2453 200>>>> Intercept 0.0000 0.0000 -0.2007 0.2007 -0.2007 200>>>> Slope 1.0000 1.0000 0.7565 0.2435 0.7565 200>>>> Emax 0.0000 0.0000 0.0999 0.0999 0.0999 200>>>> D 0.2716 0.3368 0.2275 0.1093 0.1623 200>>>> U -0.0192 -0.0192 0.0369 -0.0561 0.0369 200>>>> Q 0.2908 0.3560 0.1906 0.1654 0.1254 200>>>> B 0.1272 0.1155 0.1384 -0.0229 0.1501 200>>>> g 1.6328 2.0740 1.4647 0.6093 1.0235 200>>>> gp 0.2367 0.2529 0.2189 0.0341 0.2026 200>>>>>>>> The apparent Dxy is 0.63, and bias-corrected Dxy is 0.52. The maximum>>>> absolute error is estimated to be 0.099. The changes in slope and>>>> intercept are also more substantial. In all, there is evidence that I am>>>> somewhat overfitting the data, right?.>>>>>>>> Furthermore, using step-down variable selection ...>>>>>>>> > validate(x6.lrm, B=200, bw=T)>>>>>>>> Backwards Step-down - Original Model>>>>>>>> Deleted Chi-Sq d.f. P Residual d.f. P AIC>>>> stenosis 0.28 1 0.5979 0.28 1 0.5979 -1.72>>>> ClinicalScore 2.60 1 0.1068 2.88 2 0.2370 -1.12>>>> x2 2.86 1 0.0910 5.74 3 0.1252 -0.26>>>>>>>> Approximate Estimates after Deleting Factors>>>>>>>> Coef S.E. Wald Z P>>>> Intercept -5.865 1.4136 -4.149 3.336e-05>>>> x1 2.915 0.8685 3.357 7.889e-04>>>> procedure 1.072 0.5590 1.918 5.508e-02>>>>>>>> Factors in Final Model>>>>>>>> [1] x1 procedure>>>> index.orig training test optimism index.corrected n>>>> Dxy 0.5661 0.6755 0.5559 0.1196 0.4464 200>>>> R2 0.2876 0.4085 0.2784 0.1301 0.1575 200>>>> Intercept 0.0000 0.0000 -0.2459 0.2459 -0.2459 200>>>> Slope 1.0000 1.0000 0.7300 0.2700 0.7300 200>>>> Emax 0.0000 0.0000 0.1173 0.1173 0.1173 200>>>> D 0.2038 0.3130 0.1970 0.1160 0.0877 200>>>> U -0.0192 -0.0192 0.0382 -0.0574 0.0382 200>>>> Q 0.2230 0.3323 0.1589 0.1734 0.0496 200>>>> B 0.1441 0.1192 0.1452 -0.0261 0.1702 200>>>> g 1.2628 1.9524 1.3222 0.6302 0.6326 199>>>> gp 0.2041 0.2430 0.2043 0.0387 0.1654 199>>>>>>>> If I select only two variables (x1 and procedure), bias-corrected Dxy>>>> goes down to 0.45.>>>>>>>> [Question 1]>>>> I have EPV problem. Even so, should I keep the full model (5-variable>>>> model)? or can I use the 2-variable (x1 and procedure) model which the>>>> validate() with step-down provides?>>>>>>>> [Question 2]>>>> If I use 2-variable model, should I do>>>> x2.lrm<- lrm(postopDWI_HI ~ T1+procedure2, data=x6.df, x=T, y=T)?>>>> or keep the value showed above by validate function?>>>>>>>> Next, shrinkage ...>>>>>>>> > pentrace(x6.lrm, seq(0, 5.0, by=0.05))>>>> Best penalty:>>>> penalty df>>>> 3.05 4.015378>>>>>>>> The best penalty is 3.05. So, I update it with this penalty to obtain>>>> the corresponding penalized model:>>>>>>>> > x6.lrm.pen<- update(x6.lrm, penalty=3.05, x=T, y=T)>>>> > x6.lrm.pen>>>> .....>>>> Penalty factors>>>>>>>> simple nonlinear interaction nonlinear.interaction>>>> 3.05 3.05 3.05 3.05>>>> Final penalty on -2 log L>>>> [,1]>>>> [1,] 3.8>>>>>>>> Obs 104 LR chi2 28.18 R2 0.313 C 0.818>>>> negative 79 d.f. 4.015 g 1.264 Dxy 0.635>>>> positive 25 Pr(> chi2)<0.0001 gr 3.538 gamma 0.637>>>> max |deriv| 3e-05 gp 0.201 tau-a 0.234>>>> Brier 0.129>>>>>>>> Coef S.E. Wald Z Pr(>|Z|) Penalty Scale>>>> Intercept -4.7246 2.2429 -2.11 0.0352 0.0000>>>> stenosis -0.0105 0.0240 -0.44 0.6621 17.8021>>>> x1 2.3605 0.7254 3.25 0.0011 0.6054>>>> x2 -0.5385 0.3653 -1.47 0.1404 1.2851>>>> procedure 0.9247 0.4844 1.91 0.0563 0.8576>>>> ClinicalScore 0.3046 0.1874 1.63 0.1041 2.4779>>>>>>>> Arrange the coefficients of the two models side by side, and also list>>>> the difference between the two:>>>>>>>> > cbind(coef(x6.lrm), coef(x6.lrm.pen),>>>> abs(coef(x6.lrm)-coef(x6.lrm.pen)))>>>> [,1] [,2] [,3]>>>> Intercept -5.53281808 -4.72464766 0.808170417>>>> stenosis -0.01496757 -0.01050797 0.004459599>>>> x1 3.04248257 2.36051833 0.681964238>>>> x2 -0.75335619 -0.53854750 0.214808685>>>> procedure 1.20847252 0.92474708 0.283725441>>>> ClinicalScore 0.37623189 0.30457557 0.071656322>>>>>>>> [Question 3]>>>> Is this penalized model the one I should present for my colleagues?>>>> I still have EPV problem. Or is EPV problem O.K. if I use penalization?>>>>>>>> I am still wondering about what I can do to avoid EPV problem.>>>> Collecting new data would be a long-time and huge work...>>>>>>>>>>>> (11/04/22 1:46), khosoda_at_med.kobe-u.ac.jp wrote:>>>>> Thank you for your comment.>>>>> I forgot to mention that varclus and pvclust showed similar results for>>>>> my data.>>>>>>>>>> BTW, I did not realize rms is a replacement for the Design package.>>>>> I appreciate your suggestion.>>>>> -->>>>> KH>>>>>>>>>> (11/04/21 8:00), Frank Harrell wrote:>>>>>> I think it's OK. You can also use the Hmisc package's varclus>>>>>> function.>>>>>> Frank>>>>>>>>>>>>>>>>>> 細田弘吉 wrote:>>>>>>>>>>>>>> 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.>>>>>>>>>>>>>>>>>> I appreciate your help very much in advance.>>>>>>>>>>>>>>>>>> -->>>>>>>>> KH>>>>>>>>>>>>>>>>>> ______________________________________________>>>>>>>>> R-help_at_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_at_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-tp3462416p3473354.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>>> PLEASE do read the posting guide>>> http://www.R-project.org/posting-guide.html>>> 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>> E-mail address>> Office: khosoda_at_med.kobe-u.ac.jp>> Home : khosoda_at_venus.dti.ne.jp>> *************************************************>>>> ______________________________________________>> R-help_at_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-tp3462416p3483634.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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> 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 E-mail address Office: khosoda_at_med.kobe-u.ac.jp Home : khosoda_at_venus.dti.ne.jp ______________________________________________ R-help_at_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.

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