The natural indirect effect (NIE) and mediation proportion (MP) are two measures of primary interest in mediation analysis. The standard approach for estimating NIE and MP is through the product method, which involves a model for the outcome conditional on the mediator and exposure and another model describing the exposure-mediator relationship. The purpose of this article is to comprehensively develop and investigate the finite-sample performance of NIE and MP estimators via the product method. With four common data types, we propose closed-form interval estimators via the theory of estimating equations and multivariate delta method, and evaluate its empirical performance relative to the bootstrap approach. In addition, we have observed that the rare outcome assumption is frequently invoked to approximate the NIE and MP with a binary outcome, although this approximation may lead to non-negligible bias when the outcome is common. We therefore introduce the exact expressions for NIE and MP with a binary outcome without the rare outcome assumption and compare its performance with the approximate estimators. Based upon these theoretical developments and empirical studies, we offer several practical recommendations to inform practice. An R package mediateP is developed to implement the methods for point and variance estimation discussed in this paper.

翻译：自然间接效应(NIE)和调解比例(MP)是调解分析中主要关注的两种衡量标准。估算NIE和MP的标准方法是产品方法,其中涉及一个以调解人和接触为条件的结果模型和另一个描述暴露-调解关系的模型,本条的目的是全面发展和调查NIE和MP估计器通过产品方法的有限抽样性表现。有四种共同的数据类型,我们通过估计方程和多变量三角形方法的理论提出封闭式间隔估计器,并评价其相对于靴子捕捉方法的经验性表现。此外,我们注意到,稀有的结果假设经常被援引为将NIE和MP的二元结果接近,尽管这种近似可能会导致在结果常见时出现非明显偏差。我们因此,在没有罕见的结果假设的情况下,对NIE和MP的二进制结果作了精确表达,并将其业绩与近似估计器作比较。根据这些理论发展和经验研究,我们提出了几项实用的建议,以告知实践。我们讨论的是,一份R组合介质估算,以落实该论文中的差异。