  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.
