[R] odds ratio: how to create reference

[Eik Vettorazzi]

You notice that your reference is for the SAS-procedure glm?!

To play around and since you provided no data example I've created some 
data (by an idea from Frank Harrell jr. 
http://www.biostat.wustl.edu/archives/html/s-news/2002-04/msg00103.html)

n <- 30
treat <- rep(c('a','b','c'), length.out=n)
lg<- log(1.2)*(treat=='b')+log(1.5)*(treat=='c')   # here the intercept 
is assumed to be 0 which means that there is an even chance of having 
y=1 or y=0 when treat is 'a'.
y <- ifelse(runif(n) <= plogis(lg), 1, 0)
trf<-as.factor(treat)

To have a first look at the data you can do
table(y,treat)

and you can fit your model via
mm<-glm(y~trf,family=binomial(link="logit"))

and to get your odds ratios
exp(coef(mm))

you may look at the model matrix to see that treatment contrasts 
correspond to use two dummies for "b" and "c" and an intercept term 
(which here refers to the reference level "a")
model.matrix(mm)

hth again.



Bunny, lautloscrew.com schrieb:
> Hi,
>
> i found something interesting to me:
> http://www.otago.ac.nz/sas/stat/chap39/sect27.htm
>
>  and  i am about to get an idea of the reference thing ( -1 ) , but 
> couldn´t connect on the following example:
>
> For the GLM parameterization scheme (PARAM=GLM), the design variables 
> are as follows.
>
> Maybe you´ll find some time, to take another look.
>
> thanks in advance
>
>
>
> Am 23.09.2008 um 11:36 schrieb Eik Vettorazzi:
>
>> Hi,
>> You can state a probability p as odds p/(1-p) and vice versa. To get 
>> an odds ratio you need actually two odds. Then you can get the odds 
>> ration of being/having "a" instead of "b" by odds(a)/odds(b), where 
>> "b" is the reference level.
>> If you fit a logistic regression model (which means that your outcome 
>> is dichotomous) then the estimated coefficients are actually 
>> log(oddsratios) - which you can transform to odds by exp() .
>> You can use a factor-variable with three levels for race and 
>> treatment-contrasts to get odds ratios for not being white against 
>> being white - make sure, that either your factor has "white" as first 
>> level or specify the contrast with the "base" argument.
>> If you create 3 dummy variables and involve an intercept in your 
>> model your model will be perfectly collinear - the so called "dummy 
>> variable trap" - you can use an intercept and create two dummies for 
>> the covariate levels you are actually interested in and put this in 
>> your logistic model - the result will be the same as with the 
>> treatment contrasts.
>>
>> hth.
>>
>> Bunny, lautloscrew.com schrieb:
>>> HI there,
>>>
>>> i know this is a basic question, though i need some help because 
>>> this is somewhat away from my current issue, but nevertheless 
>>> interesting to me... Lets assume i have some estimated 
>>> probabilities, say estimated by a logit model. i know i can also 
>>> state them as an odds ratio.
>>>
>>> Now i´d like to state these odds ratios as a reference to a specific 
>>> outcome of my investigated variable.
>>>
>>> for example, if my covariate of interest is race and possible 
>>> outcomes are white, black and hispanic, whereas the latter are 
>>> minorities in my case - how can i state the odds ratio in such a way 
>>> that white is the reference (always 1) and other races' odds ratio 
>>> are relative to the reference. e.g. hispanics are 1.5 times more 
>>> likely to ...
>>>
>>> Is creating 3 binary dummies for race the right way  ? And if so how 
>>> can i go on.
>>> As i said, i know this is rather basic, i am thankful for any links 
>>> / references...
>>>
>>> thanks in advance !
>>>
>>> ______________________________________________
>>> 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.
>>
>> -- 
>> Eik Vettorazzi
>> Institut für Medizinische Biometrie und Epidemiologie
>> Universitätsklinikum Hamburg-Eppendorf
>>
>> Martinistr. 52
>> 20246 Hamburg
>>
>> T ++49/40/42803-8243
>> F ++49/40/42803-7790
>>
>

-- 
Eik Vettorazzi
Institut für Medizinische Biometrie und Epidemiologie
Universitätsklinikum Hamburg-Eppendorf

Martinistr. 52
20246 Hamburg

T ++49/40/42803-8243
F ++49/40/42803-7790