Efficient Adaptive Sobel and Joint Significance Tests for Mediation Effects

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. Particularly, the Sobel test and joint significance test are two popular statistical methods for testing mediation effects 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 some restrictions on their popularity and usefulness. As a matter of fact, this limitation is long-standing for the two methods in the literature. To fill this gap, we propose two novel data-adaptive tests for mediation effects, namely the adaptive Sobel test and the adaptive joint significance test, which have significant improvements over traditional Sobel and joint significance tests. Meanwhile, the proposed method is user-friendly without involving complicated procedures. The explicit expressions for size and power are derived, which ensure the theoretical rationality of our method. Furthermore, we extend the proposed adaptive Sobel and adaptive joint significance tests for multiple mediators with family-wise error rate (FWER) 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.