Count models - how to handle denominator (as offset) when granularity varies

Question

Say I want to do a Poisson Regression to examine how an incidence rate changes over time adjusting for gender. I aggregate the data into the covariate patterns of interest with the count in each category and use the population data for that specific pattern as an offset.

Now I want to add in another factor - for example smoking status. But the national statistics data doesn't provide population data for that specific combination of factors (i.e males in 2005 who smoked). What do I use as the population offset in this case? Is it reasonable to simply apply the most granular level of population data available to the categories that don't have all available information (e.g. same offset for smokers and non-smokers in each year?)

Alternatively, is it ever appropriate to just aggregate to the top level (in this case year) and apply the same offset to all covariate combinations? Looking for some general guidelines. I presume this won't be as accurate because you are not specifying population numbers corresponding to at-risk people for that particular combination.

Answer 1

I aggregate the data into the covariate patterns of interest with the count in each category and use the population data for that specific pattern as an offset.

Yes, that is a good approach. You could equally well use binomial logistic regression with Popn as the number of trails, which will give virtually the same results as Poisson log-linear regression with log(Popn) as the offset.

Is it reasonable to simply apply the most granular level of population data available to the categories that don't have all available information (e.g. same offset for smokers and non-smokers in each year?)

No, that will give incorrect results if the numbers of smokers and non-smokers in the population are not equal.

is it ever appropriate to just aggregate to the top level (in this case year) and apply the same offset to all covariate combinations? Looking for some general guidelines. I presume this won't be as accurate because you are not specifying population numbers corresponding to at-risk people for that particular combination.

You've answered your own question really. Applying the same offset to all covariate combinations isn't just inaccurate, it's just plain wrong if the population numbers are very unequal.