Odds Ratio yielding an error

[Zhianni Yang]

Hula.

I am so sorry if this one is an elementary question, please inform me and I will delete it right away.

In sum, I want to know whether sex is a potential confounder in the association of asthma and respiratory infection.

the unadjusted odds ratio yield 1.12. Moreover, I try to adjust it for sex using 0 (female) as the baseline and 1 (male) as the baseline.

therefore, the adjusted for male will be 1.316748 and the adjusted for female will be 0.8284719*1.316748

Moreover, if we take a look at the differences for female odds ratio, the percentage changes will just be around 3% (<10%, not huge enough to be considered as confounder). However for male, it will be 16% (>10%)

I am in a dilemma because of this.
Please let me know.

[Maarten Buis]

Confounding variables and modifying variables are two very different beasts. By adding an interaction you looked at modifying instead of confounding, i.e. you assumed that asthma symptoms work differently for males and females (gender modifies the effect of asthma symptoms). With a confounding variable you think that gender influences respiratory infections and asthma symptoms, e.g. there are more males with asthma symptoms. If you don't control for gender, than part of the "asthma effect" is actually a "gender effect".

If you had a continuous variable and could use a linear model, you would just have two models one with gender and one without (both without the interaction effect) and compared the coefficients for asthma symptoms. Unfortunately, everything is (a lot) harder in non-linear models like logistic regression. Doing this kind of analysis right is an area of active research. You could look here: https://sociologicalscience.com/articles-v10-10-332/ and here: https://boris.unibe.ch/176998/8/jann...n-2023-mor.pdf for some tools that could be used for this problem.