Hypothesis test of causal mediation

Abstract

For statistical inference, hypothesis testing and estimation enjoy duality in most problems, but not in mediation analyses. Causal mediation analysis has been a popular approach to investigate whether an exposure or intervention has an effect on an outcome mediated through an intermediary factor termed mediator. A mediation effect involves two parameters: one for the exposure-mediator association, and the other for the mediator-outcome association conditional on the exposure. A hypothesis test for mediation is conducted under the null hypothesis where either one of the two associations is zero or both are zeros. I study various existing testing procedures for mediation and demonstrate two methodological challenges: 1) the null hypothesis of mediation is a composite null hypothesis, and 2) the test statistics does not necessarily converge to Gaussian. To address these issues, I propose two classes of methods: one for the setting where the null composition is not available (Huang 2018 AoAS), and the other for the setting where the null composition may be inferred from the data (Huang 2019 AoAS; Huang 2019 Biometrics). The proposed methods are size alpha tests and are applicable to single- and multi-mediator analyses. The utility will be demonstrated in simulation and genome-wide studies.