Abstract
The causal inference literature has provided definitions of direct and indirect effects based on counterfactuals that generalize the approach found in the social science literature. However, these definitions presuppose well-defined hypothetical interventions on the mediator. In many settings, there may be multiple ways to fix the mediator to a particular value, and these various hypothetical interventions may have very different implications for the outcome of interest. In this paper, we consider mediation analysis when multiple versions of the mediator are present. Specifically, we consider the problem of attempting to decompose a total effect of an exposure on an outcome into the portion through the intermediate and the portion through other pathways. We consider the setting in which there are multiple versions of the mediator but the investigator has access only to data on the particular measurement, not information on which version of the mediator may have brought that value about. We show that the quantity that is estimated as a natural indirect effect using only the available data does indeed have an interpretation as a particular type of mediated effect; however, the quantity estimated as a natural direct effect, in fact, captures both a true direct effect and an effect of the exposure on the outcome mediated through the effect of the version of the mediator that is not captured by the mediator measurement. The results are illustrated using 2 examples from the literature, one in which the versions of the mediator are unknown and another in which the mediator itself has been dichotomized.