Efficient Adaptive Sobel and Joint Significance Tests for Mediation Effects

Mediation analysis is an important statistical tool in many research fields. Particularly, the Sobel test and joint significance test are two popular statistical test methods for mediation effects when we perform mediation analysis in practice. However, the drawback of both mediation testing methods is arising from the conservative type I error, which has reduced their powers and imposed restrictions on their popularity and usefulness. As a matter of fact, this limitation is long-standing for both methods in the medation analysis literature. To deal with this issue, we propose the adaptive Sobel test and adaptive joint significance test for mediation effects, which have significant improvements over the traditional Sobel and joint significance test methods. Meanwhile, our method is user-friendly and intelligible without involving more complicated procedures. The explicit expressions for sizes and powers are derived, which ensure the theoretical rationality of our method. Furthermore, we extend the proposed adaptive Sobel and joint significance tests for multiple mediators with family-wise error rate control. Extensive simulations are conducted to evaluate the performance of our mediation testing procedure. Finally, we illustrate the usefulness of our method by analysing three real-world datasets with continuous, binary and time-to-event outcomes, respectively.