A different perspective of cross-world independence assumption and the utility of natural effects versus controlled effects.

The pure effects described by Robins and Greenland, and later called natural effects by Pearl, have been criticized because they require a cross-world independence assumption. In this paper, we use potential outcomes and sufficient causal sets to present a conceptual perspective of the cross-world independence assumption that explains why the clinical utility of natural effects is sometimes greater than that of controlled effects. Our perspective is consistent with recent work on mediation of natural effects, path specific effects and separable effects.