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Message from discussion Offset parameter observation time adjustment in logistic regression?

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More options Jul 2 2012, 3:07 am
Newsgroups: sci.stat.math
From: Elliot <elliotsprec...@gmail.com>
Date: Mon, 2 Jul 2012 00:07:44 -0700 (PDT)
Local: Mon, Jul 2 2012 3:07 am
Subject: Re: Offset parameter observation time adjustment in logistic regression?

On Thursday, June 28, 2012 4:15:27 AM UTC+3, David Duffy wrote:
> Elliot <elliotsprec...@gmail.com> wrote:
> > I think the only thing I'm unclear on is what to call the resulting
> > odds ratio per unit time, using the correct, accepted terminology.  It
> > isn't a hazard ratio or incidence ratio, unless I'm misunderstanding the
> > terms or messing up the algebra -- it is related to them like odds
> > ratios are related to risk ratios, but they aren't the same thing.

> > So say you had a study where, for a cohort of subjects, the odds
> > ratio, offset adjusted for unequal observation times, for understanding
> > a statistical point was 1.96 for those who read helpful forum messages
> > vs. those who didn't.  What is the term for this adjusted OR for the
> > predictor, and how would you state it formally?

> Why don't you plug some numbers in and see.  There is such a thing as
> an incidence odds ratio.

> exp(coef(glm(cbind(a,b) ~ x + offset(log(e)), family=binomial())))
> exp(coef(glm(a ~ x + offset(log(b*e)), family=poisson())))

I didn't make myself clear, I was looking for the terminology, not the model term, but you've given me my answer -- "incidence odds ratio".  Didn't know there was such a thing.  Now to search for and read up on it to further reduce my ignorance.

Thanks for all the help,
Elliot