On the Causal Interpretation of Randomized Interventional Indirect Effects

Identification of standard mediated effects such as the natural indirect effect relies on heavy causal assumptions. By circumventing such assumptions, so-called randomized interventional indirect effects have gained popularity in the mediation literature. Here, I introduce properties one might demand of an indirect effect measure in order for it to have a true mediational interpretation. For instance, the sharp null criterion requires an indirect effect measure to be null whenever no individual-level indirect effect exists. I show that without stronger assumptions, randomized interventional indirect effects do not satisfy such criteria. I additionally discuss alternative causal interpretations of such effects.