Kai Wang - Colloquium Speaker
Mediation analysis is becoming increasingly popular in social, behavioral, and biological sciences. It studies the direct effect and the indirect effect of a treatment on an outcome. However, there are some concerning observations regarding these fundamental concepts with their current definitions. In this talk, I will introduce various effects the treatment has on the joint likelihood of the mediator and the outcome under a general model setting. By considering parameter configurations under which the total effect, the direct effect, and the indirect effects are absent, the likelihood ratio tests (LRTs) for each effect are introduced. The LRT for the indirect effect is an intersection union test (IUT), which is also known as the joint significance test (JST). This connection explains the power superiority of the JST observed repeatedly in previous simulation studies. The LRT for the total effect is novel. It is also an IUT. These LRTs lead to new measures of the size of the indirect effect and the direct effect that have desired properties. Two examples are given to demonstrate these concepts. This novel approach complements the current methods for mediation analysis.