Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of mediation effects) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients (PoC) test and the joint significance (JS) test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed.

翻译：中介分析旨在评估某一暴露因素是否以及如何通过中间变量影响感兴趣的结果。由于科学领域对此类分析的需求巨大，该问题近期引起了广泛关注。中介效应的检验面临重大挑战，因为其基础零假设（即不存在中介效应）是复合型的。现有的大多数中介检验方法过于保守，导致统计功效不足。为克服这一重要方法论障碍，我们开发了一种自适应Bootstrap检验框架，能够适用于中介路径分析中不同类型的复合零假设。将该框架应用于系数乘积检验和联合显著性检验后，我们的自适应检验程序在复合零假设下控制了第一类错误率，与现有检验相比显著提升了统计功效。本文从理论性质和数值实例两方面对所提出的方法进行了讨论。