OR vs RR when the outcome is common

Question

I have a dichotomous outcome (life satisfaction). The proportion of people in my sample who are satisfied is fairly high (about 85%). I know that from my Chi-squared analysis that both income and age are significantly associated with being satisfied (both are categorical variables).

I want to run logistic regression with life satisfaction as my outcome and adjust for both income and age to see if they both remain associated with life satisfaction (after adjusting for each other). I'm not interested in the OR estimations per se, only whether they remain associated. I also want to run contrasts to determine differences between groups, post hoc.

My main question is: because the outcome is common in the population, should I worry too much about logistic regression inflating the OR compared to the RR? Or should I really be using Poisson regression?

My second question is: when I am running contrasts after running logistic regression, should these be on the beta coefficients (the ORs themselves) or should this be between the predicted margins, and will the contrasts be incorrect if the outcome is common?

Maybe this doesn't even matter as I don't have a time component ... I think I am worrying for nothing

Answer 1

Any time you're trying to decide between using an OR or a RR, the solution is to ask yourself, as the scientist constructing the model, which measure is more meaningful in this context. Do you think that an increase from 80% to 90% has the same relevance as an increase from 60% to 67.5%? Then you should use the RR. If you think that an increase from 80% to 90% is more akin to an increase from 60% to 77%, then you should use the OR.

It's not that one is right and one is wrong. It's a matter of choosing which is more appropriate.