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：中介分析是许多研究领域中一种重要的统计工具，其目的在于探究暴露因素与结局之间因果通路的作用机制。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，该中介检验方法的局限性在于其过于保守的I类错误，这降低了统计检验力，并在一定程度上限制了其推广与应用。针对这一不足，我们提出了面向单个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，相较于传统联合显著性检验有显著改进。所提方法设计简洁，无需复杂流程。我们推导出了检验尺度与检验功效的显式表达式，从而保证了该方法的理论有效性。此外，我们将所提自适应联合显著性检验扩展至小规模中介假设问题，并实现了对家系错误率（FWER）的控制。同时，我们提出了一种新颖的自适应Sobel型方法用于估计中介效应的置信区间，该方法在实现理想覆盖概率方面相较于传统Sobel置信区间有显著提升。我们通过大量模拟实验对所提中介检验与置信区间程序进行了评估，并与多种现有方法进行了对比。最后，我们分别通过分析三个包含连续型、二值型和时间至事件型结局变量的真实数据集，展示了所提方法的实用性。