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Noncollapsibility definition of confounding

Dear All,

To make it clear at the beginning: I prefer to use DAGs for thinking about confounding nowadays.

In his great paper entitled "Commonalities in the classical, collapsibility and counterfactual concepts of confounding" (S.C. Newman, J Clin Epi 2004;57:325-3299), Newman states:

"According to the collapsibility definition of confounding, F is a confounder of a given measure of effect if and only if both of the following conditions are satisfied: (1) the measure of effect is homogeneous across the strate of F, and (2) the crude and common stratum-specific values of the measure of effect are equal".

Newman quotes:

Kupper et al. 1981

Yanagawa, 1984

Boivin & Wacholder, 1985

From these papers, I cannot see why homogeneity across strata is a necessary factor for the definition of a confounder.

If according to this Definition, a factor F is not a confounder, what is then?

i) neither a confounder nor a effect measure modificator

ii) an effect measure modificator

Maybe, Newman actually meant:

Given that homogeneity across strata of F is present: if noncollapsibility is present, F is a confounder. If the analysis is collapsible, confounding is absent. Isn't that a better Definition here?

Best wishes

Andreas Stang