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?



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