Mediation analysis is an important statistical tool in many research fields. Particularly, the Sobel test and joint significance test are two popular statistical test methods for mediation effects when we perform mediation analysis in practice. However, the drawback of both mediation testing methods is arising from the conservative type I error, which has reduced their powers and imposed restrictions on their popularity and usefulness. As a matter of fact, this limitation is long-standing for both methods in the medation analysis literature. To deal with this issue, we propose the adaptive Sobel test and adaptive joint significance test for mediation effects, which have significant improvements over the traditional Sobel and joint significance test methods. Meanwhile, our method is user-friendly and intelligible without involving more complicated procedures. The explicit expressions for sizes and powers are derived, which ensure the theoretical rationality of our method. Furthermore, we extend the proposed adaptive Sobel and joint significance tests for multiple mediators with family-wise error rate control. Extensive simulations are conducted to evaluate the performance of our mediation testing procedure. Finally, we illustrate the usefulness of our method by analysing three real-world datasets with continuous, binary and time-to-event outcomes, respectively.

翻译：中介分析是许多研究领域中的一项重要统计工具。特别地，Sobel检验和联合显著性检验是实践中进行中介效应分析时两种常用的统计检验方法。然而，这两种中介检验方法的缺陷源于其保守的第一类错误，这降低了它们的检验效能，并限制了其普及性和实用性。事实上，这一局限性在中介分析文献中对这两种方法而言长期存在。为解决此问题，我们提出了用于中介效应的自适应Sobel检验和自适应联合显著性检验，相较于传统的Sobel检验和联合显著性检验方法有显著改进。同时，我们的方法无需涉及更复杂的程序，具有用户友好和易于理解的特点。我们推导出了检验尺度和检验效能的显式表达式，确保了方法的理论合理性。此外，我们将所提出的自适应Sobel检验和自适应联合显著性检验扩展到具有族系错误率控制的多重中介变量情形。通过大量模拟实验评估了中介检验流程的性能。最后，通过分别分析三个包含连续型、二值型和生存时间结局的实际数据集，展示了我们方法的实用性。