[Paper Review] Bayesian Sparse Mediation Analysis with Targeted Penalization of Natural Indirect Effects

Yanyi Song, Xiang Zhou+10 more|arXiv (Cornell University)|Aug 14, 2020

Advanced Causal Inference Techniques12 references4 citations

TL;DR

This paper proposes two novel Bayesian methods—GMM and PTG—for high-dimensional mediation analysis that directly penalize natural indirect effects (NIEs) to identify active mediators. By modeling exposure-mediator and mediator-outcome effects jointly with structured priors, the methods improve selection and estimation accuracy, achieving up to 30% power gain over existing methods in simulations and identifying biologically relevant mediators in MESA and LIFECODES cohorts.

ABSTRACT

Causal mediation analysis aims to characterize an exposure's effect on an outcome and quantify the indirect effect that acts through a given mediator or a group of mediators of interest. With the increasing availability of measurements on a large number of potential mediators, like the epigenome or the microbiome, new statistical methods are needed to simultaneously accommodate high-dimensional mediators while directly target penalization of the natural indirect effect (NIE) for active mediator identification. Here, we develop two novel prior models for identification of active mediators in high-dimensional mediation analysis through penalizing NIEs in a Bayesian paradigm. Both methods specify a joint prior distribution on the exposure-mediator effect and mediator-outcome effect with either (a) a four-component Gaussian mixture prior or (b) a product threshold Gaussian prior. By jointly modeling the two parameters that contribute to the NIE, the proposed methods enable penalization on their product in a targeted way. Resultant inference can take into account the four-component composite structure underlying the NIE. We show through simulations that the proposed methods improve both selection and estimation accuracy compared to other competing methods. We applied our methods for an in-depth analysis of two ongoing epidemiologic studies: the Multi-Ethnic Study of Atherosclerosis (MESA) and the LIFECODES birth cohort. The identified active mediators in both studies reveal important biological pathways for understanding disease mechanisms.

Motivation & Objective

• Address the challenge of identifying active mediators in high-dimensional settings where thousands of potential mediators (e.g., DNAm, biomarkers) are measured.
• Overcome limitations of univariate mediation analysis and standard regularization that penalize path coefficients separately without targeting the indirect effect.
• Develop a Bayesian framework that jointly models exposure-mediator and mediator-outcome effects to enable direct penalization of the product (NIE) for improved mediator selection.
• Improve statistical power and reduce estimation bias in identifying mediators with strong indirect effects in complex, high-dimensional omics data.

Proposed method

• Propose two joint prior models: a four-component Gaussian mixture prior (GMM) and a product threshold Gaussian prior (PTG) to model exposure-mediator and mediator-outcome effects jointly.
• Implement targeted penalization on the natural indirect effect (NIE), defined as the product of the exposure-mediator and mediator-outcome path coefficients, through structured priors that reflect the composite four-group structure of mediators.
• Use median inclusion probabilities (PIPs) at 0.5 as a selection criterion for identifying active mediators, validated via simulations to control false discovery rate.
• Incorporate shrinkage and variable selection via hierarchical priors that allow for simultaneous estimation and selection of active mediators in high-dimensional settings.
• Apply the methods to real data from the MESA and LIFECODES cohorts, analyzing DNAm and biomarker mediators in relation to health outcomes.
• Use simulation studies to compare performance against competing methods, including Lasso, SCAD, and Bayesian variable selection, focusing on selection and estimation accuracy of NIEs.

Experimental results

Research questions

• RQ1 Can Bayesian joint modeling with targeted penalization of the natural indirect effect improve identification of active mediators in high-dimensional mediation analysis?
• RQ2 How does the proposed method compare to existing penalized and Bayesian methods in terms of power and accuracy for selecting true non-null mediators?
• RQ3 What biological pathways are uncovered when applying the method to real high-dimensional omics data from MESA and LIFECODES?
• RQ4 How effective is the median inclusion probability (PIP = 0.5) as a selection criterion for controlling false discovery rate in this context?
• RQ5 To what extent do correlations among mediators affect the performance of the proposed methods, and how can they be better incorporated in future models?

Key findings

• The proposed GMM and PTG methods achieve up to 30% higher statistical power in identifying true non-null mediators compared to competing methods in simulation studies.
• In the MESA cohort, the methods identified 8–10 key DNAm sites and nearby genes—such as NFE2L1, PTK2, and CREB1—mediating the effect of neighborhood socioeconomic status on BMI.
• In the LIFECODES cohort, the methods detected 12(13)-EpoME and 9-oxoODE as significant mediators linking prenatal phthalate exposure to gestational age, suggesting roles in oxidative stress and inflammation pathways.
• The methods outperformed existing Bayesian and frequentist approaches in both selection accuracy and estimation bias reduction, particularly when indirect effects were moderate to strong.
• The use of median inclusion probability (PIP = 0.5) as a selection threshold provided effective false discovery rate control, validated through simulation experiments.
• The methods revealed biologically plausible mediation pathways, such as DNAm-mediated effects on metabolic and inflammatory traits, supporting their utility in biosocial and epidemiological research.