Variance component tests of multivariate mediation effects under composite null hypotheses

Mediation effects of multiple mediators are determined by two associations: one between an exposure and mediators ( S ‐ M ) and the other between the mediators and an outcome conditional on the exposure ( M ‐ Y ). The test for mediation effects is conducted under a composite null hypothesis, that is, either one of the S ‐ M and M ‐ Y associations is zero or both are zeros. Without accounting for the composite null, the type 1 error rate within a study containing a large number of multimediator tests may be much less than the expected. We propose a novel test to address the issue. For each mediation test j , j = 1 , … , J , we examine the S ‐ M and M ‐ Y associations using two separate variance component tests. Assuming a zero‐mean working distribution with a common variance for the element‐wise S ‐ M (and M ‐ Y ) associations, score tests for the variance components are constructed. We transform the test statistics into two normally distributed statistics under the null. Using a recently developed result, we conduct J hypothesis tests accounting for the composite null hypothesis by adjusting for the variances of the normally distributed statistics for the S ‐ M and M ‐ Y associations. Advantages of the proposed test over other methods are illustrated in simulation studies and a data application where we analyze lung cancer data from The Cancer Genome Atlas to investigate the smoking effect on gene expression through DNA methylation in 15 114 genes.