How to interpret OR confidence intervals for interaction or confounding?

Question

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?

Answer 1

Generally speaking, you would make the most informed decision based on the variables on hand to see whether the confounding variable falls in the causal pathway of the disease or not. Since your question is to try and verify what the variable could be based on just the Odds Ratios, I found a source that might be useful:

"This is an example of confounding - the stratified results are both on the same side of the crude odds ratio. This is positive confounding because the unstratified estimate is biased away from the null hypothesis." - Source (STAT 507, PSU)

Answer 2

The noncollapsibility effect cannot be distinguished from that due to confounding in this case and calls into question the change-in-effect criterion for confounding when using odds ratios. See this paper (updated published version Aug 2023)