How to compare IRRs of two different groups?

Hello all, thanks in advance for your help. This is my question:

I have a structured panel data for repeated measure over time per single person

I have two groups stratified by whether they had an education level at least equal to secondary level or not.

I am looking at adherence to treatment using two outcome variables:
1) a binary variable reflecting whether they quit the treatment of not (Cox regression model)

2)a count variable expressing the number of pills they forget to take every month (Poisson regression model)

my covariates are age sex and income (the latter as quintiles)

My main variable of interest is whether the persons at baseline are smoker, non smoker or former smoker with smoking as ref group.

My research question is whether the smoking status as an impact on both groups (high or low education level) on the adherence

Therefore I have two main groups (education - binary) stratified by the categorical smoking status

Running the panel cox and poisson is pretty much straightforward and therefore I have IRRs and HRs as compared to ref categories in both groups

My question is: how to compare the variation in the risk between groups?
In very simple model I used to apply the MH test (stratified chi square) but considering these are results from panel data analyses I would have no clue how to deal with it...

I forgot to mention that groups are not matched as both sub-groups of a dataset but there is no difference for the covariates at the baseline
Hi Ralph84,

Are you trying to compare the IRR and HR for non-smoker (vs. smoker as the reference level) between education groups? And then also compare former smoker between education groups? If so, I believe adding an interaction term for smoking status and education (smoking*education) will allow you to do just that. In SAS, these types of comparisons are typically done through contrast statements. Otherwise I do not completely follow your question.
Hello, thanks for the reply!
I stratified the sample in two different groups (high education vs low education) and then I ran the analyses separately (using smoking status as main variable of interest). I use Stata but the commands are pretty much the same in this case. I thought about using the interaction term as well (education level##smokingstatus) but in this case the result appeared to be complicated to interpret to me, that is why I kept the two groups separate.
To compare the 2 groups you will have to combine the results together somehow. I suggest you try modeling the interaction and see how hard it is to interpret the results. I suspect it will be easier than you think. Sounds like you have a pretty good handle on these types of analyses. IRRs and HRs should be very similar to what you are getting when you stratify the groups (in fact identical, I believe). Plus you may actually see smaller confidence intervals because of the increase in sample size.