Collider in RCT Subgroup Analysis

llynn: > I like your pathway analysis but the question remains. How does one enrich for the biologic treatment target and at the same time mitigate the potential for generating a synthetic pathway partition? Well, the pathway was the presumed answer, failing something better comes along or someone points out a flaw. What I am not sure about is if comparable weights through randomization would be better than equal weights for the control group given that pathway imposes equal weights on the treated. A general conclusion also emerges regarding effect modification and subgroup analysis that was started in this thread. The standard defense of subgroup analysis in RCTs rests on the assumption that the subgroup-defining variable modifies the treatment effect from outside the causal pathway, that is that it is exogenous to the treatment mechanism. This is the implicit foundation of precision medicine approaches to treatment heterogeneity. What this discussion has demonstrated is that this assumption is self-defeating: for a variable to be a strong effect modifier it must interact with the biological pathway through which treatment operates, but that interaction is precisely what makes it a mediator proxy rather than a causally exogenous modifier. A variable that is truly exogenous is unlikely to be a strong effect modifier; a variable that is a strong effect modifier is unlikely to be truly exogenous. Conditioning on such a variable in the outcome model therefore introduces the risk of collider bias, potentially distorting rather than clarifying the picture of who benefits from treatment. This means that the standard subgroup analysis approach cannot safely identify treatment effect heterogeneity in biological systems, and alternative strategies, such as the treatment pathway approach, are needed to assess effect modification in clinical trials without conditioning on causally entangled variables. Finally to the question of the DAG by Attia that started this thread: Is it a correct representation of effect modification? The answer is likely to be no.