A note on “Simple graphical rules to assess selection bias in general-population and selected-sample treatment effects" by M. B. Mathur and I. Shpitser

This short note is a commentary on the paper by Mathur and Shpitser (2024), with the aim to enlarge the class of graphs for which the conditional Average Treatment Effect is nonparametrically identified, by allowing the outcome to be on the pathway between the treatment and the selection indicator. A first straightforward generalization is possible when (i) the outcome Y is binary, and (ii) the population prevalence of Y is known a priori, or can be made the object of a sensitivity analysis. Furthermore, identification of the effect is possible also for Y having any nature, provided that a selection bias breaking node  V exists and the population prevalence of V is known.