Collider in RCT Subgroup Analysis

Because both are post intervention variables and therefore the only difference between mediators and effect modifiers are that with a mediator we have the structure for example:

Statin-> LDL reduction → CVD event

With the effect modifier we have the same structure with the following condition added on:

Receptor status ----> LDL reduction

So I believe that we can gate all mediators and once gated it is not induced by the treatment but remains associated with it through the post-treatment effect it induces. The gating variable is thus a conditional mediator and as I said above, every patient who enters the conditional analysis has now been selected into a cell (Receptor status x statin treatment cells) by the joint realization of their treatment and their response to such treatment, even if such response is replaced by the gating variable (the receptor status) and the response to treatment is not visible as that is a proxy for the gate. The distortion is not a general property of all post-treatment variables. It is specific to post-treatment variables that are simultaneously treatment-associated and outcome-prognostic. This selection bias seems to me to be irrecoverable if the receptor status enters the analysis, even though it is pre-treatment.

Of course if you have other thoughts about this, I would be keen to hear this.