Offset parameter observation time adjustment in logistic regression?

[Elliot Sprecher]

Hello all,

I'm trying to understand the interpretation of odds ratios in logistic
regression when an offset parameter is used to account for different
observation durations.

For a single dichotomous predictor (A vs. B) of a binary outcome
(event vs. non-event), the odds ratio is just the odds of an event
given predictor A vs the odds of an even given predictor B. These are
implicitly understood to be under the same conditions, including the
length of time observed.

How does the use of the offset parameter change how this is
expressed? Do you explicitly add “during a single unit time of
observation” to the description? (And if so, how does using different
units, say, days, months, or years, affect the OR?) I've seen at
least one explanation indicate that the interpretation changes to a
comparison of rates of events for each predictor, but how would this
be stated in terms of the OR?

If we were measuring event counts, then applying Poisson or negative
binomial regression with an offset parameter, the interpretation would
be pretty straightforward. It's just a little frustrating, but I seem
to be misunderstanding something basic here.

As usual, thanks in advance,
Elliot

[David Duffy]

Elliot Sprecher <elliots...@gmail.com> wrote:

> I'm trying to understand the interpretation of odds ratios in logistic
> regression when an offset parameter is used to account for different
> observation durations.

Look up incidence ratio, hazard ratio etc.

[elliots...@gmail.com]

Hi David,

I checked them out, but I haven't been able to get the explanations to *click* just yet. As I understand it, hazard and incidence ratios and the like are derived from risk ratios, whereas the use of logistic regression yields odds ratios. I suppose I could determine an RR and its statistical derivations from an OR. But that doesn't seem to be in the spirit of doing logistic regression in the first place. Is there some standard, accepted terminology which allows me to describe the results of an offset-adjusted logistic regression in terms of the derived OR rates?

Thanks, and again for your patience,
Elliot

[David Duffy]

elliots...@gmail.com wrote:
> On Friday, June 22, 2012 11:45:10 AM UTC+3, David Duffy wrote:
>> Elliot Sprecher <elliots...@gmail.com> wrote:
>>
>> > I'm trying to understand the interpretation of odds ratios in logistic
>> > regression when an offset parameter is used to account for different
>> > observation durations.

Google "binomial regression time offset" gives:

http://memorias.ioc.fiocruz.br/106%285%29/106_5_3114.pdf

[Elliot]

Hi David,

Of course, I ran the search using "logistic" rather than "binomial", and missed it -- nice little writeup.

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?

Again, my thanks, almost there I think,
Elliot

[David Duffy]

Elliot <elliots...@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())))

[Elliot]

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