Does non-linearity matter when testing interactions in a logistic regression?


I have been thinking a lot about testing for the interaction effect these past few days and have been reading up a lot on it. But I will really appreciate if you can help clarify a few things.

I will be running logistic regression because my dependent variable is disease and no disease. I have a couple of exposure variables. Exposure 1 has a U shaped relationship to disease, sort of like the relationship between BMI and health. Exposure 2 has a linear relationship with the dependent variable.

From what I have read so far about it, it seems ok to test for the interaction effect between exposure 1 and exposure 2 in a logistic regression. Is that a wrong assumption? If it is ok to test for the interaction effect, should I still centre the exposure variables?

Thank you so much!!!!
That's a good question.

I did the usual U shaped testing by including a quadratic term and the quadratic term was significant. This model does not include the interaction term or the other exposure variable. I did that because when I looked at the data descriptively, the proportion of people with disease by level of exposure, it shows a U shaped pattern.