Collider in RCT Subgroup Analysis

Yes, that is correct, the subgroup has to be based on a post-treatment variable or its proxy (the proxy could be a pre-treatment variable but must impact a post -treatment variable). For this scheme to hold, the subgroup must be based on a conditional mediator. The reason why we call the conditional mediator an effect modifier is detailed in the preprint.

Where this would not apply are prognostic or clearly pre-treatment variables. For example in the RECOVERY trial of dexamethasone for survival in COVID there were subgroups based on mechanical ventilation (MV), on oxygen only (O2) and not on oxygen (no-O2). Here these are clearly prognostic and pre-treatment subgroups so applying this would fail completely. That said, I personally don’t believe in stratification for subgroup effects (meaning adding a product term to regression) and believe that adding the subgroup as a covariate suffices because these represent risk magnification if pre-treatment rather than effect modification. Of course, I may have missed something, so please correct me if you have any other thoughts about this