Mediation misgivings: ambiguous clinical and public health interpretations of natural direct and indirect effects

Recent methodological innovation is giving rise to an increasing number of applied papers in medical and epidemiological journals in which natural direct and indirect effects are estimated. However, there is a longstanding debate on whether such effects are relevant targets of inference in population health. In light of the repeated calls for a more pragmatic and consequential epidemiology, we review three issues often raised in this debate: (i) the use of composite cross-world counterfactuals and the need for cross-world independence assumptions; (ii) interventional vs non-interventional identifiability; and (iii) the interpretational ambiguity of natural direct and indirect effect estimates. We use potential outcomes notation and directed acyclic graphs to explain 'cross-world' assumptions, illustrate implications of this assumption via regression models and discuss ensuing issues of interpretation. We argue that the debate on the relevance of natural direct and indirect effects rests on whether one takes as a target of inference the mathematical object per se, or the change in the world that the mathematical object represents. We further note that public health questions may be better served by estimating controlled direct effects.