Confounder or Effect modifier based of Odds ratio

#1
Hi,

So we have been given odds ratio for males and females in four different scenarios to find out if sex is a confounder or effect modifier in a study looking at the association between lung cancer and smoking.

The Ratios are something like this

OR(Male) OR(Female) Crude OR Adjusted OR
2.51 2.15 2.32 2.35
1.06 0.95 2.02 1.01
4.40 3.41 4.02 2.63
2.15 0.65 1.42 1.29

I'm not sure as to how to interpret these ratios in order to say if sex is a confounder or effect modifier.
 

hlsmith

Omega Contributor
#2
I will think about this more, but effect modifiers are usually examined via a multiplicative or additive interaction term, not just controlling for a variable. Let us see if I am following:

in a sample of just males, smokers have a 2.51 times higher odds of cancer
in a sample of just females, smokers have a 2.15 times higher odds of cancer
in a sample of males and females not controlling for sex, smokers have a 2.32 times higher odds of cancer
in a sample of males and females controlling for sex, smokers have a 2.35 times higher odds of cancer

This one seems like no confounding or modification. What do the different rows represent? Are these supposed be four examples, which you are to determine which example may have confounding, etc.?