Ultra-High-Dimensional Mediation Analysis via Latent Factor Models with Interaction Effects

Music City Center 

Causal mediation analysis provides a framework to understand the causal pathways through which an independent variable affects an outcome via intermediary mediators. However, in high-dimensional settings — where the number of covariates and mediators far exceeds number of observations, traditional methods often fail to capture the complexity of the data. To address this, we propose a novel approach that leverages latent factor models to estimate the mediation functional via modified diversified projection method where one is not required to know the true dimension of the latent factors. We present a √n-consistent and asymptotically normal estimator that allows the interaction between covariates and treatment in generating mediators, as well as the interactions between covariates and treatment and mediators and treatment in generating the response. To demonstrate the practical relevance of our approach, we conduct an analysis on ADNI (Alzheimer's Disease Neuroimaging Initiative) study, investigating how DNA methylation mediates the progress of Alzheimer's Disease (AD). Moveover, our findings supported by extensive simulations and an investigation of geriatric depression scale effect on Alzheimer's Disease Assessment Scale – Cognitive Subscale (ADAS-Cog), mediated via DNA methylation.

Latent Factors

Mediation Analysis

High-Dimensional Models

Factor Model

Diversified Projection Method 

Section on Statistical Learning and Data Science