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5/05/2021 05:57:00 PM
You are absolutely right on the first part. Good point, we'd actually be formulating it with an IPTW weighted average. I figured I'd just leave that out of this for simplicity in this question, but you are right that it doesn't make sense just as an average. But for your second point, yes getting the expected difference in outcome conditional on X is a good way to frame it too. Would there be a name for fitting two completely different regression functions and taking the difference? u/[ExcelsiorStatistics](https://www.reddit.com/user/ExcelsiorStatistics/) answer made sense to me, in both the linear case as well as fitting an arbitrary function. If you include terms for X and A\*X in any function f(X,A\*X) (linear or nonlinear) then I'd think the model should benefit from joint fitting if there is any useful information and there is limited data.