Problems in high-dimensional mediation analysis

Abstract

A mediation model seeks to identify and explain the mechanism of the direct and indirect effects of an exposure variable on an outcome variable, potentially mediated through several intervening variables. Statistical methods for mediation analysis are well-developed when the number of mediator variables is relatively small, but problems arise when the number of potential mediators exceeds the sample size. In this thesis, we address three problems in linear mediation models in the presence of high-dimensional mediators: estimating and inference for the indirect effect, power analysis for testing total effect, and estimation for the proportion of indirect effect.