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Individualized Dynamic Mediation Analysis Using Latent Factor Models

Yijiao Zhang, Yubai Yuan, Yuexia Zhang, Zhongyi Zhu, Annie Qu

Abstract

Mediation analysis plays a crucial role in causal inference as it can investigate the pathways through which treatment influences outcome. Most existing mediation analysis assumes that mediation effects are static and homogeneous within populations. However, mediation effects usually change over time and exhibit significant heterogeneity among individuals in many real-world applications. Additionally, the mediation mechanism can be complicated and involves non-sparse, making mediator selection particularly challenging. To address these issues, we propose an individualized dynamic mediation analysis method for mediator selection. Our approach can identify the significant mediators at the population level while capturing the time-varying and heterogeneous mediation effects at the individual level via varying-coefficient structural equation models. Another advantage of our method is that we allow the presence of unmeasured time-varying confounders that induce the heterogeneous mediation effects. We provide asymptotic results for the proposed estimator and selection consistency for significant mediators. Extensive simulation studies and an application to a DNA methylation study demonstrate the effectiveness and advantages of our method.

Individualized Dynamic Mediation Analysis Using Latent Factor Models

Abstract

Mediation analysis plays a crucial role in causal inference as it can investigate the pathways through which treatment influences outcome. Most existing mediation analysis assumes that mediation effects are static and homogeneous within populations. However, mediation effects usually change over time and exhibit significant heterogeneity among individuals in many real-world applications. Additionally, the mediation mechanism can be complicated and involves non-sparse, making mediator selection particularly challenging. To address these issues, we propose an individualized dynamic mediation analysis method for mediator selection. Our approach can identify the significant mediators at the population level while capturing the time-varying and heterogeneous mediation effects at the individual level via varying-coefficient structural equation models. Another advantage of our method is that we allow the presence of unmeasured time-varying confounders that induce the heterogeneous mediation effects. We provide asymptotic results for the proposed estimator and selection consistency for significant mediators. Extensive simulation studies and an application to a DNA methylation study demonstrate the effectiveness and advantages of our method.
Paper Structure (17 sections, 4 theorems, 20 equations, 4 figures, 3 tables)

This paper contains 17 sections, 4 theorems, 20 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Motivation and Setup
  4. Individualized Dynamic Mediation Analysis
  5. Mediation Selection with Latent Dynamics
  6. Estimation
  7. Theoretical Properties
  8. Simulation
  9. Heterogeneous setting with counteractive effects
  10. Homogeneous setting
  11. Application to ADNI methylation data
  12. Prediction results
  13. Confidence intervals for individualized mediation effects
  14. Identified dynamic latent factors
  15. Discussion
  16. ...and 2 more sections

Key Result

Proposition 1

Under Assumption assump:identification(i), the individualized mediation effects $\operatorname{IDE}$ and $\operatorname{IIE}$ are identifiable through $\operatorname{IDE}_{it}(x,x^{\prime})=\theta_{it}(x-x^{\prime}), \operatorname{IIE}_{it}(x,x^{\prime})=\boldsymbol{\alpha}_{it}^{\top}\boldsymbol{\b

Figures (4)

  • Figure 1: Estimated effects for mediator $M_1$ (cg12682382) in two latent groups with sample sizes larger than 50 and the combined data. Numbers in parentheses represent the regression $p$-values for testing each effect against zero. $X$ denotes depression level and $Y$ denotes cognitive dysfunction. The results are based on the data in year 2010.
  • Figure 2: Heterogeneous mediation structure when $p=3, n=3, T=2$, and $r=2$.
  • Figure 3: Estimated individualized mediation effects of GDS on the degree of cognitive dysfunction in AD via CpG site "cg01343084" in 2010, 2011, and 2012, with corresponding 95% confidence intervals.
  • Figure 4: Recovered individual dynamic latent factor with group membership as well as membership patterns from 2010 to 2012. "Dynamic" indicates that the membership changes over time and "Static" indicates that the membership remains invariant over time.

Theorems & Definitions (5)

  • Proposition 1
  • Remark 1
  • Theorem 1
  • Theorem 2
  • Corollary 1