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But what if the relationship with obesity has nonlinearities, how good is this control?

There are studies with millions of participants and by controlling for smoking, obesity, they still find increased risk and associations that are still very probably noise.fitting.

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I’m not disagreeing with you that proper statistical research especially in a clinical setting is hard. It was the “tricks” and hint of non-physics : no-science I was responding to. I do think we should give doctors the benefit of the doubt. Just imagine the work involved in research with 100 real patients, let alone larger numbers. Then the next point is: where to get your research subjects. If you want to study non-linearities you’d want both patients and healthy subjects (and ideally people who switch categories). That’s several orders of magnitude more complex to get going. Not every subject gets funding for that scale.

Do you mean that the GLM wouldn't properly account for obesity's relationship with testosterone if the two have a nonlinear relationship? Is this something that could be accounted for by splines? I'm still trying to learn this stuff.

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