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Re: st: Logistic regression interpretation


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Logistic regression interpretation
Date   Wed, 22 Sep 2010 09:06:15 +0000 (GMT)

--- On Tue, Sep 21, Dr. Bill Westman  wrote:
> > A simple logistic regression was run - outcome - Survived/Non Survived
> > (1/0), with Group(Treatmeant/Control -- 1/0) & Risk(High/Low -- 1/0)
> >
> > The results
> >
> > ---------+-------------
> > Survived | Odds Ratio  
> > ---------+-------------
> >     Risk |   4.790295  
> >    group |   2.111181 
> > ---------+-------------
> >
> > Can I assume that odds of treatment survival were 2.1 times higher in
> > the treatment Group for LOW risk patients?
> > And for High Risk patients in the treatment group is the adds 4. 8 +
> > 2.1 (or 7 times higher)?

There are no interactions so the odds increases with a factor 2.1 when 
one receives the treatment regardless of whether one is in the high or
low risk group (the baseline odds differs between the high and low risk
group, but does not change our result).

You can see this in the example below. The -margins- command is used in
this example to get the odds (exp(linear predictor)) for each of the 
four groups. The -coefl- option is added to show how -margins stores 
each of these odds. The -di- commands use those odds to calculate the
odds ratios again. Lets assume that group in your example is collgrad
in mine, and that risk in your example is married in mine. You can see
that without adding the interaction terms the odds ratio is the same
for both married and unmarried people.

*-------------------- begin example ---------------------
sysuse nlsw88, clear
gen byte baseline = 1
logit union i.married i.collgrad baseline, or nocons

margins, exp(exp(xb())) over(married collgrad) post coefl
di _b[0bn.married#1.collgrad]/_b[0bn.married#0bn.collgrad]
di _b[1.married#1.collgrad]/_b[1.married#0bn.collgrad]
*-------------------- end example ------------------------
(For more on examples I sent to the Statalist see: 
http://www.maartenbuis.nl/example_faq )

> - Also - Is the command
> 
> listcoef, help percent
> 
> indicating that the odds of survival are 111% higher for
> Treatment group?  

Yes, and you could have seen that directly from the output of
your -logit- command. If something changes by a factor 2 it
increases 100%, and if something changes by a factor .7 then it
decreases 30%. The general rule to move from a ratio to a percentage
is (ratio - 1) * 100%. You found an odds ratio of 2.11, so the
odds changes (2.11 - 1)*100% = 111%

> and if so - is that 111% at both High/Low risk Levels?

Yes, as I explained above.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


      

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