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Inference for quantile mediation effects in the presence of complex confounding
Journal article   Open access   Peer reviewed

Inference for quantile mediation effects in the presence of complex confounding

Shuoyang Wang and Yuan Huang
Electronic journal of statistics, Vol.20(2), pp.3190-3224
01/01/2026
DOI: 10.1214/26-EJS2560
url
https://doi.org/10.1214/26-EJS2560View
Published (Version of record) Open Access

Abstract

Traditional mediation analysis methods face challenges when dealing with a large number of mediators. In practice, these challenges can be compounded by outliers and the complex relationships introduced by confounders. To address these issues, we propose a quantile-based partially linear mediation analysis method that can handle high-dimensional mediators and introduce the fully-connected-deep-neural-network techniques to model intricate relationships in confounders. Unlike most existing works that focus on mediator selection, we emphasize inference on mediation effects. Theoretical analysis establishes asymptotic validity of the proposed tests, including control of type I error under the null and explicit power characterization under local alternatives. When the dimension of candidate mediators is high, the proposed method consistently selects important features in the outcome model. Numerical studies show that the proposed method outperforms existing approaches under a variety of settings, demonstrating its versatility and reliability as a modeling tool for complex data. We demonstrate the proposed method by examining the mediating role of DNA methylation in the relationship between childhood trauma and cortisol stress reactivity.

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