# Should one derive risk difference from the odds ratio?

**URL:** <https://discourse.datamethods.org/t/should-one-derive-risk-difference-from-the-odds-ratio/4403>\
**Category:** bayes\
**Tags:** absolute-risk\
**Created:** [May 13, 2021, 11:49pm UTC](https://discourse.datamethods.org/t/should-one-derive-risk-difference-from-the-odds-ratio/4403 "2021-05-13T23:49:41Z")\
**Posts on this page:** 1\
**Showing post:** 221

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**Author:** ![Sander](https://discourse.datamethods.org/letter_avatar_proxy/v4/letter/s/90ced4/32.png) [@Sander](https://discourse.datamethods.org/u/Sander)\
**Post date:** [July 6, 2021, 3:46pm UTC](https://discourse.datamethods.org/t/should-one-derive-risk-difference-from-the-odds-ratio/4403/221 "2021-07-06T15:46:41Z")

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> [@AndersHuitfeldt](#):
>
> if there exists a common cause of V and Y, which we will call U, then even if there are no interaction response types between V and A, there is no guarantee that there will be no additive effective modification.

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?

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