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，其目的在于探究暴露与结局之间因果路径上的作用机制。在实际应用中，联合显著性检验被广泛用作检验中介效应的主要统计方法。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，并在一定程度上限制了其普及性和实用性。针对这一不足，所提出的解决方案是单中介变量的自适应联合显著性检验，这是一种新型的数据自适应中介效应检验方法，相较于传统联合显著性检验展现出显著改进。该方法设计便捷易用，无需复杂程序。我们推导了检验尺度与功效的显式表达式，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需控制族系错误率的小规模中介假设检验中。同时，我们提出了一种新型自适应Sobel型方法用于估计中介效应的置信区间，在实现理想覆盖概率方面相较于传统Sobel置信区间展现出显著优势。通过综合模拟实验，我们将所提出的中介检验与置信区间方法与多种现有方法进行了比较评估。最后，我们分别通过分析三个包含连续型、二值型及时间事件结局的实测数据集，展示了本方法的实用价值。