Often linear regression is used to perform mediation analysis. However, in many instances, the underlying relationships may not be linear, as in the case of placental-fetal hormones and fetal development. Although, the exact functional form of the relationship may be unknown, one may hypothesize the general 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. We assume a practically plausible set of nonlinear effects of hCG on the birth weight and a linear relationship between pesticide exposure and hCG, with both exposure-outcome and exposure-mediator models being linear in the confounding factors. 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.

翻译：中介效应分析常采用线性回归方法。然而在许多情况下，如胎盘-胎儿激素与胎儿发育的关系中，潜在变量间可能并非线性关系。尽管关系的确切函数形式未知，但可对关系的总体形态提出假设。基于此，我们开发了一种新颖的基于形状约束推断的中介效应分析方法。本研究受胎儿内分泌学领域应用启发——研究人员以人绒毛膜促性腺激素（hCG）为中介变量，旨在探究农药施用对出生体重的影响。我们假设hCG对出生体重存在实际可行的非线性效应集，且农药暴露与hCG呈线性关系，同时暴露-结局模型和暴露-中介模型在混杂因素层面均为线性。通过将所提方法应用于以hCG为中介变量的人群产前筛查项目数据，我们发现：自然直接效应表明农药施用与出生体重呈正相关，而自然间接效应呈现负相关。