Collider in RCT Subgroup Analysis

Thank you both for the comments. I agree it is confusing so let me try to make things clearer using the RECOVERY data.

a) If I assume that ventilation status is a pre-randomization prognostic variable then I add it to regression as an adjustment and get a benefit across all three groups:

b) If I consider ventilation status an effect modifier, then I get the effects that the authors reported which was benefit mainly for those on MV:

c) If I consider the ventilation status as a pathway variable (newly introduced in the preprint) then we get the following that means that the pathways differ from the no-intervention in different ways as follows and also assumes no pathway without intervention:

What we infer clearly depends on where we position the third variable structurally meaning that we need to be certain what we are dealing with here. I would go for a) with RECOVERY but the authors went with b) and all I am saying is that b) just represents overfitting because there is no clear indication in my mind that ventilation status represents a variable associated with dexamethasone in a post-randomization sense nor is there any indication that c) is correct which is that it serves as a pathway only for the intervention. Even had the modifier criteria been accepted, a further argument I make is that a subgroup or product term for ventilation status would be wrong because its entry into the outcome model would lead to collider (selection) bias.

The RECOVERY data nicely summarizes the preprint so you can now decide if this sits with you or not.