Should one derive risk difference from the odds ratio?

[Sander]

@AndersHuitfeldt

why it doesn’t lead to a paradox in situations where effect stability would lead to risks above 100%. I think the answer to that, is that it is set up for causal interaction instead of effect modification. That setup factors out the possibility that risk due to background factors varies between groups; any baseline risk difference is due to the causal effect of one of the interacting factors. I am therefore not convinced that this result would allow you to establish stability of an additive parameter between groups whose baseline risk differs due to background factors.

Well how about you try and convince yourself one way or another by plugging some numbers in for the proportions of noninteraction types allowed (which have only one constraint: they must to sum to 1) to get the risks from the formulas on p. 77 of ME3 and see if you can vary the baseline risk (I presume you mean R00) while holding the RDs constant? I think you will find that yes the RDs can be constant while R00 varies, limited only by the fact that the RDs must sum to equal or less than 1-R00; if as typical R00 is not very large then in RD terms this is a vast range for additive effects to live in. In other words, your original claim is wrong…

You can research it if you want, but I seem to recall this was known in the bioassay literature in the 1920s and is one of the reasons product terms in linear models came to be called “interactions” (much later, statisticians in their unbounded carelessness began calling all product terms “interactions” regardless of the link function for the linear predictor, even though a connection of those terms to actual biologic interactions is absent from all but a few models).

P.S. Added belatedly: For those with a historical bent, in a paper invited by an engineering toxicology journal (“Elementary models for biological interaction”, Journal of Hazardous Materials 1985;10:449-454) I attempted to provide a connection between bioassay and epidemiologic models for interaction.