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 adjusted 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 adjusted joint significance tests for small-scale mediation hypotheses with family-wise error rate (FWER) control. Additionally, a novel adjusted 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作检验中介效应的主流统计方法。然而，该方法存在局限性：由于第一类错误率偏保守，导致统计检验力降低，一定程度上限制了其应用普适性与实用性。为弥补这一不足，本研究提出针对单一中介变量的调整联合显著性检验——一种新型数据自适应中介效应检验方法，较传统联合显著性检验具有显著改进。该方法设计简便，无需复杂操作流程。我们推导出了检验尺度与检验力的显式表达式，确保了方法的理论有效性。进一步地，我们将所提出的调整联合显著性检验扩展至小规模中介假设检验场景，并实现了对族系错误率（FWER）的控制。此外，我们还提出了一种新型调整Sobel型方法，用于估计中介效应的置信区间，在实现理想覆盖率方面较传统Sobel置信区间有显著提升。通过大量模拟实验，我们将所提出的中介检验与置信区间程序与多种现有方法进行了比较评估。最后，通过分别包含连续型、二值型及时间事件型结局变量的三个真实世界数据集分析，验证了本方法的实用价值。