Hypothesis Test of Mediation Effect in Causal Mediation Model With High-Dimensional Continuous Mediators

Abstract

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.

Causal Mediation Analysis of Survival Outcome with Multiple Mediators

“…Variances and confidence intervals for ${\mathrm{\Delta }}^{\mathit{Aalen}}$ and ${\mathrm{\Delta }}^{\mathit{Cox}}$ can be calculated using a resampling method that takes random draws from multivariate normal distribution of estimates for $({\delta }_S, {\alpha }_S, {\alpha }_M, {\lambda }_S, {\lambda }_{M1}, {\lambda }_{M2})$ or $({\delta }_S, {\alpha }_S, {\alpha }_M, {\gamma }_S, {\gamma }_{M1}, {\gamma }_{M2})$ 13,28 with detail provided in the eAppendix (Sections A4 and A5).…”

“…The path-specific effect approach has also been proposed as a method to adjust for exposure-induced confounding for the mediator-outcome association 26 , similar to our problem in the hepatitis study. Causal mediation models have been generalized to incorporate mixed variable types such as a combination of continuous and dichotomous mediators 27 or a set of high-dimensional continuous mediators 28 . However, these methods focus on non-censored outcomes.…”

Multiscale regression modeling in mouse supraspinatus tendons reveals that dynamic processes act as mediators in structure–function relationships

“…Mediator models have recently been used in a variety of fields to explain the relationship between correlated parameters (Baron and Kenny, 1986; Huang and Pan, 2015; Tripp et al, 2015; Wright and DeKemper, 2015). Traditional mediator models make several assumptions in addition to all of the standard assumptions of the general linear model, such as the independence of measured parameters and the lack of significant correlation between the independent variable and the mediator.…”

A multiple mediator analysis approach to quantify the effects of the ADH1B and ALDH2 genes on hepatocellular carcinoma risk

“…In order to assess the effect of multiple sequential mediators of interest, the concept of path-specific effects can be applied to address potential confounders of the mediator-outcome relationship (Huang & Pan, 2016; VanderWeele & Vansteelandt, 2014; Vanderweele, Vansteelandt, & Robins, 2014). However, having two sequential mediators still introduces the so called “recanting witness assumption”, where the mediator’s effect may vary dependent on the specific pathway leading to the outcome of interest (Avin, Shpitser, & Pearl, 2005; Vanderweele et al, 2014).…”