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Mediation analysis is an important statistical tool in many research fields.Its aim is to investigate the mechanism along the causal pathway between anexposure and an outcome. The joint significance test is widely utilized as aprominent statistical approach for examining mediation effects in practicalapplications. Nevertheless, the limitation of this mediation testing methodstems from its conservative Type I error, which reduces its statistical powerand imposes certain constraints on its popularity and utility. The proposedsolution to address this gap is the adaptive joint significance test for onemediator, a novel data-adaptive test for mediation effect that exhibitssignificant advancements compared to traditional joint significance test. Theproposed method is designed to be user-friendly, eliminating the need forcomplicated procedures. We have derived explicit expressions for size andpower, ensuring the theoretical validity of our approach. Furthermore, weextend the proposed adaptive joint significance tests for small-scale mediationhypotheses with family-wise error rate (FWER) control. Additionally, a noveladaptive Sobel-type approach is proposed for the estimation of confidenceintervals for the mediation effects, demonstrating significant advancementsover conventional Sobel's confidence intervals in terms of achieving desirablecoverage probabilities. Our mediation testing and confidence intervalsprocedure is evaluated through comprehensive simulations, and compared withnumerous existing approaches. Finally, we illustrate the usefulness of ourmethod by analysing three real-world datasets with continuous, binary andtime-to-event outcomes, respectively.

Efficient Adaptive Joint Significance Tests and Sobel-Type Confidence Intervals for Mediation Effects