Collider in RCT Subgroup Analysis
I came across this interesting article: A proposal for capturing interaction and effect modification using DAGs
Interaction : they propose that this term should be used specifically when both treatment and “subgroup” have a direct causal effect on the outcome
Effect modifier : they suggest reserving this strictly for situations where the second factor (the modifier) does not have a direct causal effect on the outcome itself.
I want to extend this framework to subgroup analysis in randomized trials, where one would focus on the parameter related to T \times S to answer the question:
Is the treatment effect different between subgroups?
I noticed that stratifying by subgroup and including the T \times S parameter could open a backdoor path in both interaction or effect modifier frameworks if an unobserved variable influences both T \times S and the outcome:
ie T \times S would act as a collider.
Has this phenomenon in subgroup analyses been described before in RCTs? How should one interpret such analyses if there is a risk of opening backdoor paths through unobserved variables?
Discussion in the ATmosphere