Should we do adjustment for "closely related" variable in logistic regression?
For example: I want to know the whether smoking status can predict the present of diabetes, such that Diabetes ~ smoking
I know that I could (and should) including some covariates/ confounding factors, such as age, sex... However, I would like to know whether it is appropriate to include closely related variables such as "glucose level", "HbA1c level", "HOMAR-IR", "present of pre-diabetes"?
In case you are not familiar the diagnosis of diabetes: diabetes is usually diagnosis by elevated level of glucose and/ or HbA1c. HOMAR-IR is an index for insulin resistance, which is a condition will eventually lead to diabetes. People have mild elevated glucose (but not as high as the diagnostic threshold) will be classify as pre-diabetes.
It would be great if someone can explain on why or why not to include those variables. Are there any differences if I am using linear regression but not logistic regression?
In case we should include them:
I know that there is a term called multicollinearity, but I am not sure whether it is related to my question. Furthermore, I guess these terms have strong multicollinearity if I include them all in the model. Please correct me if I am wrong. Otherwise, please also advise how to pick some of them into the model (if we should include some).