Testing for the indirect effect under the null for genome-wide mediation analyses

Abstract

Mediation analysis helps researchers assess whether part or all of an exposure's effect on an outcome is due to an intermediate variable. The indirect effect can help in designing interventions on the mediator as opposed to the exposure and better understanding the outcome's mechanisms. Mediation analysis has seen increased use in genome-wide epidemiological studies to test for an exposure of interest being mediated through a genomic measure such as gene expression or DNA methylation (DNAm). Testing for the indirect effect is challenged by the fact that the null hypothesis is composite. We examined the performance of commonly used mediation testing methods for the indirect effect in genome-wide mediation studies. When there is no association between the exposure and the mediator and no association between the mediator and the outcome, we show that these common tests are overly conservative. This is a case that will arise frequently in genome-wide mediation studies. Caution is hence needed when applying the commonly used mediation tests in genome-wide mediation studies. We evaluated the performance of these methods using simulation studies, and performed an epigenome-wide mediation association study in the Normative Aging Study, analyzing DNAm as a mediator of the effect of pack-years on FEV₁ .

Keywords: DNA methylation, epigenetics, hypothesis testing, type I error; composite null.

Figure 1. Directed Acyclic Graphs for the continuous mediator and outcome model

The Natural Indirect Effect (NIE) is the effect of A on Y through M conditional on confounders X, therefore ${\beta }_1{\theta }_2$. This is the path through M. The Natural Direct Effect (NDE) is the effect of A on Y not through M conditional on X, therefore ${\theta }_1$.. Finally, the Total Effect is the total effect of A on Y either through or not through M, therefore ${\theta }_1+{\beta }_1{\theta }_2$. This is equal to ${\varphi }_1$ from the reduced model without M included.

Figure 2. QQ-plots of individual p-values for various associations in Normative Aging genome-wide Study

A) P-values from pack-years to DNAm B) P-values from DNAm to FEV₁ adjusting for pack-years C) Testing DNA methylation as a mediator for the association between pack years and lung function using the joint significance approach D) Testing DNA methylation as a mediator for the association between pack years and lung function using product p-value with Sobel variance estimate.