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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).

Many thanks!

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You cannot use these variables in this model.

HbA1c is used to diagnose diabetes, which is your dependent variable. So all HbA1c levels below threshold are not diabetes, all above threshold are diabetes, so you have perfect prediction of diabetes (by definition, as the threshold defines diabetes) so your logistic regression will not run.

Insulin resistance "is a condition that will eventually lead to diabetes", so it is not diabetes, so if this is recorded then you know the diagnosis is not diabetes -- perfect prediction. Similarly for "pre-diabetes".

You could use these variables recorded in the past to predict current diabetes. Eg, if someone was diagnosed with insulin resistance 12 months ago, what is probability they have diabetes now.

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  • $\begingroup$ Thank you for your answer. I have a follow up question: There is an additional variable "diabetic drug usage (yes/ no)". If the person used any diabetic drug, it will be classified as having diabetes. On the other hand, not all people actually know they have diabetes during the cross-sectional study, thus they are not in the treatment (i.e. the drug usage is not 100% predict present of diabetes). Do you think I should include this in the model? $\endgroup$ May 19, 2018 at 11:02
  • $\begingroup$ I think you're saying if someone reports using the drug then they are classed as diabetic (deterministic, nothing to model), but if they do not take the drug they may or may not have diabetes (so the drug tells you nothing about this group). So it does not help in the model. $\endgroup$
    – timbp
    May 25, 2018 at 12:49

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