I am working on a project where typical approach in the field has been to calculate treatment effect on a quality of life scale conditional on being classified a responder (I know) on another scale. These are all randomized trials, but I am concerned because the target trial would be 2X2 including randomization to response which we obviously do not have here. That is enough for me to recommend different approaches but I am wondering if anyone is aware of a good paper (simulation would be great) that shows these comparisons are not randomized and offers a plausible example of how bias can creep in (I am thinking either via a collider or third variable but am not confident in drawing up a sim from scratch).
My gut is that a better alternative is to measure correlation between the outcomes (since I think this is really the goal) with e.g. a copula but then just use marginal treatment effects.
I will add some additional thoughts a little later but just about to get in the car to head to the countryside!