Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators

Causal mediation modeling has become a popular approach for studying the effect of an exposure on an outcome through a mediator. However, current methods are not applicable to the setting with a large number of mediators. We propose a testing procedure for mediation effects of high dimensional continuous mediators. We characterize the marginal mediation effect, the multivariate component-wise mediation effects, and the L2 norm of the component-wise effects, and develop a Monte-Carlo procedure for evaluating their statistical significance. To accommodate the setting with a large number of mediators and a small sample size, we further propose a transformation model using the spectral decomposition. Under the transformation model, mediation effects can be estimated using a series of regression models with a univariate transformed mediator, and examined by our proposed testing procedure. Extensive simulation studies are conducted to assess the performance of our methods for continuous and dichotomous outcomes. We apply the methods to analyze genomic data investigating the effect of microRNA miR-223 on a dichotomous survival status of patients with glioblastoma multiforme (GBM). We identify nine gene ontology sets with expression values that significantly mediate the effect of miR-223 on GBM survival.