Parametric-Regression–Based Causal Mediation Analysis of Binary Outcomes and Binary Mediators: Moving Beyond the Rareness or Commonness of the Outcome

In the causal mediation framework, several parametric-regression–based approaches have been introduced in the last decade for estimating natural direct and indirect effects. For a binary outcome, a number of proposed estimators use a logistic model and rely on specific assumptions or approximations that may be delicate or not easy to verify in practice. To circumvent the challenges prompted by the rare outcome assumption in this context, an exact closed-form natural-effects estimator on the odds ratio scale was recently introduced for a binary mediator. In this work, we further push this exact approach and extend it for the estimation of natural effects on the risk ratio and risk difference scales. Explicit formulas for the delta method standard errors are provided. The performance of our proposed exact estimators is demonstrated in simulation scenarios featuring various levels of outcome rareness/commonness. The total effect decomposition property on the multiplicative scales is also examined. Using a SAS macro (SAS Institute, Inc., Cary, North Carolina) we developed, our approach is illustrated to assess the separate effects of exposure to inhaled corticosteroids and placental abruption on low birth weight mediated by prematurity. Our exact natural-effects estimators are found to work properly in both simulations and the real data example.