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odds ratio: how to create reference

4 messages · Bunny, lautloscrew.com, Eik Vettorazzi, Philip Twumasi-Ankrah +1 more

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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 !
#
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:

  
    
#
Philip Twumasi-Ankrah wrote:
These calculations are automatic using the Design package, e.g.

dd <- datadist(d); options(datadist='d')
f <- lrm(y ~ pol(age,2)*sex+rcs(weight,4), data=d)
summary(f, sex='m')   # makes 'm' the reference cell if you don't like 
the default; gives odds ratios

For the sex OR age is set to the median (default; easily changed; 
doesn't matter if interaction term omitted).

Bunny in your original post it would be less confusing if you did not 
call levels of an independent variable the outcomes.  Many people refer 
to the dependent variable as the outcome variable.

Frank