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If a variable is normally expressed relative to body weight and then I want to include that variable in a regression model that also includes body weight among other variables as covariates, do I have do "un-normalize" that variable to include it in the regression model?

For example, our laboratory studies different metabolic markers in human subjects and we frequently express metabolic variables normalized to total body weight. This is because many of these variables are greatly dependent on the total body weight of an individual.

One variable in particular might be how much glucose is released by the liver during periods of fasting, which is typically expressed as mg of glucose per kg of body weight per minute (mg/kg/min). However, if we are interested in how this particular variables changes over time with other dependent variables (including body weight) in a regression model, then must the mg of glucose per min (mg/min) be used instead of the body weight adjusted (mg/kg/min)?

It seems incorrect to try and adjust for a variable that is already adjusted for in a regression model. The reason I ask is that this issue comes up in our scientific literature and I'm trying to figure out what spurious results or conclusions would this practice lead to?

I appreciate the community's insight into this question!

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No, you should not "unnormalize"! When body weight is already in your model, including other (metabolic) variables as a total, will, in a sense, represent body weight multiple times in the model (and this could well lead to problems with multicollinearity, as one might well expect that different (imperfect) measures of body weight will be highly correlated.

So, when body weight is in the model, all other such variables should be expressed relative to body weight.

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  • $\begingroup$ maybe I'm misunderstanding... but if variables are already being normalized to body weight AND body weight is also included as a variable in the model, wouldn't that be like having body weight represented multiple times? Thanks for your answer above - I'm still trying to follow what you're saying $\endgroup$
    – Vance L Albaugh
    Commented Jun 2, 2016 at 16:33
  • $\begingroup$ I use some similar reasoning in my answer here: stats.stackexchange.com/questions/142338/… you could have a look at it. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jun 3, 2016 at 7:31

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