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，其目的是探究暴露因素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的主要统计方法。然而，该中介检验方法的局限性源于其保守的第一类错误率，这降低了统计检验力，并对其推广性和实用性造成一定限制。为弥补这一不足，本文针对单中介变量提出自适应联合显著性检验——一种新型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具有显著改进。该方法设计简便易用，无需复杂操作流程。我们推导了检验水平和统计功效的显式表达式，确保了方法的理论有效性。进一步地，我们将所提自适应联合显著性检验拓展至控制族系错误率的小规模中介假设检验场景。此外，本文提出一种新型自适应Sobel型方法用于估计中介效应的置信区间，在达到理想覆盖概率方面相较传统Sobel置信区间取得显著进步。通过系统仿真评估并与多种现有方法比较，验证了所提中介检验与置信区间方法的性能。最后，通过分别分析连续型、二分类及时间事件结局的三个实际数据集，展示了本文方法的实用性。