I have discussed in an article that perhaps the time has come when we need to reconsider if there can be such a thing as additive versus multiplicative effect modification for binary outcomes.
The argument is quite simple:
a) It has long been thought that effect modification on the RD scale denotes additive effect modification
b) It has been also thought that effect modification on the RR scale denotes multiplicative effect modification
c) It is known that for a third variable which is prognostic for the outcome, the absence of additive means there will be multiplicative effect modification and vice versa.
In a recent lecture I was giving to medical students on effect modification, a student stood up and asked me "if either one must be present shouldn't one of them be wrong?". This set me thinking and the conclusion was startling - both were incorrect. The reason is quite simple: Working with risks means that a product term is required to keep risks bounded between zero and 1 and therefore effect modification is not the only reason for the product term. Secondly, relative risks tend towards 1 as baseline risk increases [1] and this also leads to spurious product terms. My conclusions have been written up [2] and were that neither the risk difference nor the risk ratio scale is appropriate for demonstrating effect modification. There is thus only one type of effect modification for binary outcomes - that on the OR scale - and there is likely to be no such thing as additive versus multiplicative effect modification.
It would be good to have the thoughts of researchers in this area
References [1; article] and [2; preprint] are linked below
Article Questionable utility of the relative risk in clinical resear...
Preprint Redefining effect modification
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