I follow a number of statisticians on Linkedin; one of them is Professor P. Richard Hahn at Arizona State. He posted a preprint on causal inference and regression adjustment that I’m sure will interest participants in this forum.
Hahn, Richard P. Herran, Andrew (2025), Regression adjustment for Causal Inference: A Primer with examples. PDF
From the paper:
Three distinct formalisms for causal inference are presented: potential outcomes, causal diagrams, and structural equations. It is shown that the key condition licensing valid causal inference from observational data can be expressed equivalently in each of the three distinct frameworks: conditional unconfoundedness, the back- door criterion, and additive errors that are independent of treatment assignment. While this equivalence is know to experts, it seems to be not well-known among rank-and-file data analysts and is rarely spelled out in any detail in expository texts; we do so here.