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Causal mediation analysis is a useful tool for epidemiological research, butit has been criticized for relying on a "cross-world" independence assumptionthat is empirically difficult to verify and problematic to justify based onbackground knowledge. In the present article we aim to assist the appliedresearcher in understanding this assumption. Synthesizing what is known aboutthe cross-world independence assumption, we discuss the relationship betweenassumptions for causal mediation analyses, causal models, and non-parametricidentification of natural direct and indirect effects. In particular we give apractical example of an applied setting where the cross-world independenceassumption is violated even without any post-treatment confounding. Further, wereview possible alternatives to the cross-world independence assumption,including the use of computation of bounds that avoid the assumptionaltogether. Finally, we carry out a numerical study in which the cross-worldindependence assumption is violated to assess the ensuing bias in estimatingnatural direct and indirect effects. We conclude with recommendations forcarrying out causal mediation analyses.

Insights into the "cross-world" independence assumption of causal mediation analysis