A mediation analysis for a nonrare dichotomous outcome with sequentially ordered multiple mediators

Mediation analyses can help us to understand the biological mechanism in which an exposure or treatment affects an outcome. Single mediator analyses have been used in various applications, but may not be appropriate for analyzing intricate mechanisms involving multiple mediators that affect each other. Thus, in this article, we studied multiple sequentially ordered mediators for a dichotomous outcome and presented the identifiability assumptions for the path-specific effects on the outcome, that is, the effect of an exposure on the outcome mediated by a specific set of mediators. We proposed a closed-form estimator for the path-specific effects by modeling the dichotomous outcome using a probit model. Asymptotic variance of the proposed estimator is derived and can be approximated via delta method or bootstrapping. Simulations under a finite sample showed the validity of our method in capturing the path-specific effects when the probability of each potential counterfactual outcome is not small and demonstrated the utility of a computationally efficient alternative to bootstrapping for calculating variance. The method is applied to investigate the effects of polycystic ovarian syndrome on live birth rates mediated by estradiol levels and the number of oocytes retrieved in a large electronic in vitro fertilization database. We implemented the method into an R package SOMM, which is available at https://github.com/roqe/SOMM.