Mediation analysis is an important statistical tool in many research fields. Its aim is to investigate the mechanism along the causal pathway between an exposure and an outcome. Particularly, the Sobel test and joint significance test are two popular statistical methods for testing mediation effects 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 some restrictions on their popularity and usefulness. As a matter of fact, this limitation is long-standing for the two methods in the literature. To fill this gap, we propose two novel data-adaptive tests for mediation effects, namely the adaptive Sobel test and the adaptive joint significance test, which have significant improvements over traditional Sobel and joint significance tests. Meanwhile, the proposed method is user-friendly without involving complicated procedures. The explicit expressions for size and power are derived, which ensure the theoretical rationality of our method. Furthermore, we extend the proposed adaptive Sobel and adaptive joint significance tests for multiple mediators with family-wise error rate (FWER) 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：中介分析是众多研究领域中的重要统计工具，旨在探究暴露与结局之间因果路径的作用机制。在实践中，Sobel检验和联合显著性检验是检验中介效应的两种常用统计方法。然而，这两种中介检验方法均存在因I类错误保守性导致的效能降低问题，这对其普及性和应用价值造成了长期制约。事实上，这一局限性在文献中已困扰这两种方法多年。为弥补这一不足，本文提出两种新型数据适应性中介效应检验方法——适应性Sobel检验与适应性联合显著性检验，其效能显著优于传统Sobel检验和联合显著性检验。同时，所提方法无需复杂操作，用户友好。我们推导了检验水平与检验效能的显式表达式，确保了方法的理论合理性。进一步地，我们将所提出的适应性Sobel检验与适应性联合显著性检验扩展至多重中介变量场景，并实现了族系错误率控制。通过大量模拟实验评估了中介检验流程的性能。最后，我们分别采用连续型、二值型和生存时间结局的三个真实数据集验证了方法的实用性。