Thanks Anders for the concession and clarifications. I certainly agree that there is no guarantee of observing additivity if there exists a common cause U of V and Y, because we now have confounding of the V effect on Y by U. To be more precise, we should not expect additivity of the observed RD(AY|V) and RD(VY|A) even if the causal AY and VY RDs do add, because in your set-up the observed RD(VY|A) is confounded by U.
It appears that you want to use V to guide decisions about treatment A without concern about confounding of V effects; that’s fine. But as far as I can see, all you are saying is that you are concerned with a case in which we think RD(AY|V) is unbiased enough for the AY effect to provide to clinicians, but we may have failed to control enough confounding of RD(VY|A) to make valid inferences about the V effect on Y. In that case it should be no surprise that we cannot make valid inferences about the interaction of A and V effects.
In sum, the one point I see coming out of your arguments is that if you want to study the causal interactions of A and V on Y, you have to control confounding of both A and V. More precisely and generally: To study causal interactions among components Xj of a vector of exposures X = (X1,…,XJ), you have to control confounding of X, e.g., by blocking all back-door paths from X to Y. A corollary is that to ease correct deductions about confounding control for studying causal interactions from a DAG, we ought to examine the graph that replaces the potentially interacting exposures with a single vector of them.
Given that your concern translates into a higher-order confounding problem, my answer to your query would be Yes: I can easily formalize a biological story for the data generating process that leads to absence of RD modification (i.e. stability of the causal risk difference across groups constructed from observational variables, with baseline risks differing arbitrarily within logical constraints): All I need for that is (1) no AV-interaction response types and (2) sufficient control of confounding of effects of the exposure vector (A,V) on Y; then there will be no modification of the observed RD(AY|V) across V within confounder levels and also after marginal adjustment (or after averaging using any shared weighting scheme). Note that (2) is no more stringent a requirement than that for mediation analysis, in which we replace the baseline variable V with an mediator M between A and Y.
Do you agree (in which case this subthread should be done) or can you exhibit a mistake in my reasoning?