Date:         Mon, 19 Jan 1998 14:24:39 -0700
Reply-To:     Mike Dean <Mike.Dean@HSC.UTAH.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         Mike Dean <Mike.Dean@HSC.UTAH.EDU>
Subject:      Interpreting odds ratios
Content-type: text/plain

>Andrew D. Graham wrote:
>>
> >Hi all.  Suppose I fit a logistic regression model with several
> >explanatory variables, one of which is AGE.  I get an estimated
> >Odds Ratio of 0.95 for AGE.
>>.....
>.>....
> >Say I'm interested in the effect of aging 5 years.
> >I take exp(5*coeff on AGE) = 0.80, and say that my odds
> >decrease by 20% for every 5 year increase in age?
 
> Michael Mao replied:
 
>If the odds decrease by 5% for every year increase in age, then for
>every 5 year increase in age the odds decrease by 22.6%, not 20%.
> 1-(.95)**5 = 0.226
 
I am pretty sure that Andrew Graham is right with his approach.  You need to
multiply the parameter estimate (not the odds ratio) by the number of units
(in this case years) and then exponentiate the result to get the odds ratio
associated with the number of years.  See Hosmer and Lemeshow page 57.  It is
incorrect to use Michael Mao's approach, and the results are dramatically
different.  Consider, if the OR is 0.95 for a continuous variable like age,
it is very unsensible for the odds ratio associated with 5 years to be 0.226.