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. The joint significance test is widely utilized as a prominent statistical approach for examining mediation effects in practical applications. Nevertheless, the limitation of this mediation testing method stems from its conservative Type I error, which reduces its statistical power and imposes certain constraints on its popularity and utility. The proposed solution to address this gap is the adaptive joint significance test for one mediator, a novel data-adaptive test for mediation effect that exhibits significant advancements compared to traditional joint significance test. The proposed method is designed to be user-friendly, eliminating the need for complicated procedures. We have derived explicit expressions for size and power, ensuring the theoretical validity of our approach. Furthermore, we extend the proposed adaptive joint significance tests for small-scale mediation hypotheses with family-wise error rate (FWER) control. Additionally, a novel adaptive Sobel-type approach is proposed for the estimation of confidence intervals for the mediation effects, demonstrating significant advancements over conventional Sobel's confidence intervals in terms of achieving desirable coverage probabilities. Our mediation testing and confidence intervals procedure is evaluated through comprehensive simulations, and compared with numerous existing approaches. 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，旨在探究暴露变量与结局变量之间因果路径的作用机制。在实际应用中，联合显著性检验被广泛用于检验中介效应这一重要统计方法。然而，该中介检验方法的局限性在于其保守的第一类错误率，这降低了统计功效，并对其普及性和实用性产生了一定约束。为解决这一不足，本文提出了针对单一中介变量的自适应联合显著性检验，这是一种新颖的数据自适应中介效应检验方法，相比传统联合显著性检验具有显著改进。所提方法设计简便易用，无需复杂流程。我们推导出了检验规模和功效的显式表达式，确保了方法的理论有效性。此外，我们将所提出的自适应联合显著性检验扩展至控制族系错误率的小规模中介假设场景。同时，提出了一种新型自适应Sobel型方法以估计中介效应的置信区间，在实现理想覆盖概率方面相比传统Sobel置信区间取得了显著进展。通过全面仿真评估并与多种现有方法对比，验证了本中介检验及置信区间方法的性能。最后，分别使用具有连续型、二值型和时间-事件型结局的三个真实数据集，阐明了本方法的实用性。