This is a textbook problem I've been trying to understand I wanted to check if my thinking is correct (unfortunately there is no solution manual) I have a case-control study where I'm looking at exposure and a disease stratified by a confounder.
My ORs and associated CIs are:
Overall Pooled: OR =1.05, 95% CI:(0.65,1.75)
Stratified on the confounder:
With confounder: OR = 2.08, 95% CI: (0.84,3.60)
Without confounder: OR = 2.00, 95% CI:(1.60,2.16)
How would I decide if there is confounding or interaction/effect measure modification?
It looks to me that since the pooled is different from the stratum, which are similar to each other, that would mean there is confounding but no interaction/EMM. Is my thinking correct? How do the confidence intervals affect the interpretation? Since the stratum-specific CIs overlap does that mean they are not significantly different?