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Re: st: How to test the significance of a ratio of two correlated odds ratios in Stata


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How to test the significance of a ratio of two correlated odds ratios in Stata
Date   Mon, 5 Sep 2011 09:50:08 +0200

On Mon, Sep 5, 2011 at 1:18 AM, Tiago V. Pereira wrote:
> I would like to obtain the ratio of two odds ratios from a simple logistic
> regression model. <snip>
> Specifically, what I looking for is the ratio of  OR2 to OR1 (i.e. test if
> this ratio is statistically significant from 1), where:
>
> OR2 = odds ratio for covariate ==2 vs covariate ==0
> OR1 = odds ratio for covariate ==1 vs covariate ==0

I would do this by creating my own dummy variables. Lets say that 0 is
a placebo, and 1 and 2 are different treatments. I would create one
dummy that is 0 when placebo and 1 when any treatment and one dummy
that is 0 when placebo or treatment 1 and is 1 when treatment 2. If
you add those two dummies to your model than the "odds ratio" reported
by -logit- is actually the ratio of odds ratios you are looking for.

*---------------------- begin example -------------------
clear
set obs 5000
set seed 7654321
*generates a categorical covariate 0,1,2
gene covariate = round(runiform()*2)
gen byte treated = covariate > 0 & covariate < .
gen byte group2 = covariate == 2 if covariate < .

* generates a 1/0 disease status, 1 = disease,0=healthy
* baseline odds is .10 diseased per healthy individual
* getting any treatment decreases that odds by (1-.6)*100) = -60%
* this decrease is (1-.8)*100% = -20% stronger is you get treatment2
gene status = runiform() < invlogit(ln(.10) + ln(.6)*treated + ln(.8)*group2)

* estimate that model
gen byte baseline = 1
logit status treated group2 baseline, or nocons
*---------------- end example ------------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

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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