Invited commentary: boundless science--putting natural direct and indirect effects in a clearer empirical context

Epidemiologists are increasingly using natural effects for applied mediation analyses, yet 1 key identifying assumption is unintuitive and subject to some controversy. In this issue of the Journal, Jiang and VanderWeele (Am J Epidemiol. 2015;182(2):105-108) formalize the conditions under which the difference method can be used to estimate natural indirect effects. In this commentary, I discuss implications of the controversial "cross-worlds" independence assumption needed to identify natural effects. I argue that with a binary mediator, a simple modification of the authors' approach will provide bounds for natural direct and indirect effect estimates that better reflect the capacity of the available data to support empirical statements on the presence of mediated effects. I discuss complications encountered when odds ratios are used to decompose effects, as well as the implications of incorrectly assuming the absence of exposure-induced mediator-outcome confounders. I note that the former problem can be entirely resolved using collapsible measures of effect, such as risk ratios. In the Appendix, I use previous derivations for natural direct effect bounds on the risk difference scale to provide bounds on the odds ratio scale that accommodate 1) uncertainty due to the cross-world independence assumption and 2) uncertainty due to the cross-world independence assumption and the presence of exposure-induced mediator-outcome confounders.