Mediation Analysis using Semi-parametric Shape-Restricted Regression with Applications.

Often linear regression is used to estimate mediation effects. In many instances the underlying relationships may not be linear. Although, the exact functional form of the relationship may be unknown, based on the underlying science, one may hypothesize the shape of the relationship. For these reasons, we develop a novel shape-restricted inference-based methodology for conducting mediation analysis. This work is motivated by an application in fetal endocrinology where researchers are interested in understanding the effects of pesticide application on birth weight, with human chorionic gonadotropin (hCG) as the mediator. Using the proposed methodology on a population-level prenatal screening program data, with hCG as the mediator, we discovered that while the natural direct effects suggest a positive association between pesticide application and birth weight, the natural indirect effects were negative.