I have been working with logistic regression, and I have used it to test an association between an outcome and exposure in a random cohort group. The outcome is cancer and the exposure is smoking.
cancer ~ smoking
The OR I get from this is 20.
Then I add more cases to the model (adjusting for more cases), to see a stronger association and more narrow CI. I know that this will lead to an ascertainment bias. Meaning I will have a bigger proportion of cases (more smokers), so it will no longer be a random cohort group. I did this:
cancer ~ smoking + more_smokers
I was expecting that the OR will increase a bit, but it did the opposite. So I got an OR of 17 instead, but I also got much narrow CI as expected.
What would be the interpretation for the decreasing OR?
