Counterpoint: Mediation Formulas With Binary Mediators and Outcomes and the "Rare Outcome Assumption"

In their accompanying article, Samoilenko and Lefebvre (Am J Epidemiol. 2019;188(7):1203-1205) correctly note 2 typographical errors in the formulas presented in a 2011 paper on placental abruption by Ananth and VanderWeele (Am J Epidemiol. 2011;174(1):99-108). Fortunately, to the best of our knowledge, researchers are using our methods papers and Dr. VanderWeele's 2015 book on mediation analysis (Explanation in Causal Inference; Oxford University Press, New York, New York), rather than the paper on placental abruption, to carry out their direct and indirect effect analyses; and in our methods papers and the book, the formulas are correct. The formulas discussed by Samoilenko and Lefebvre and in our work make reference to a "rare outcome assumption." In evaluating this assumption, it is important to note that the outcome is to be relatively rare across all strata defined by the exposure and the mediator-a point that is often neglected.