Charles McAlindin Just to be precise and clear here let us say that confidence intervals can be overlapping and the difference still statistically significant?

So would you employ overlapping or non-overlapping confidence intervals as a criteria for statistically significant differences?  That does not give you a guide to how different or similar the ORs are. Use standard statistical tests on the logarithms of the ORs.

Employ Mc Nemar's test if all else fails and be careful with the overlapping (or not) of CI - that can be misleading. Further

## a model where the OR are equal

Res1

Do you know which cases are overlapping, or do you just have an estimate, like 13% filled out both, but not know which cases did?

Use panel regression and adjust time series in the very model.

If you are using R please refer to Pradeep Paraman comment. If you are using Stata:

xtset id time

xtlogistic response covariate1 covariate2 covariate3 i.time, re

How you do you choose your respondents for the first and for the second period of time?

Please read the following question and answers:

https://www.researchgate.net/post/How-can-I-perform-a-statistical-test-for-the-difference-between-two-odds-ratiosfor-the-purpose-of-impact-evaluation-of-a-public-health-project