The growing interest in integrating causal inference and Design Theory

Stephen I wanted to follow up with you to discuss the difference between HTE and the gate induced loss of causal coherence now that I have completed the third paper in my analysis of RCT structure. If you note the above discussion for Elias, HTE exists asafunction of a covariate vector within the second layer estimand and here it is manageable. At the third layer HTE induced by a covariate vector of each included causal system becomes a function of a “covariate mass”. In such a mass, a covariate may be a severity indication in one disease, normal compensation in another and irrelevant in a third, all in one trial. So here you see the comparison DAG at estimand Layer 2 vs Layer 3. (This is from the linked article above). Yet many of these trials where S is synthetic can include 10 or more diseases (parallel causal systems) each with their own parallel covariate vector. Questions like yours were the reason I formulated the third estimand proof. Teaching the difference between a covariate vector and a covariate mass is quite difficult without the formula layers. A 3rd Layer estimand is not tied to a biological DGP, it is tied to the gate and can reverse polarity when the disease mix changes with the next trial. Let me know your thoughts.