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On Efficient Inference of Causal Effects with Multiple Mediators

Haoyu Wei, Hengrui Cai, Chengchun Shi, Rui Song

TL;DR

This work develops a semiparametric framework for estimating causal effects with multiple interacting mediators under unknown causal graphs. It defines direct and indirect interventional effects for individual mediators and derives quadruply robust estimators that remain consistent under broad misspecification by combining four identification strategies and averaging over MECs. The authors establish asymptotic normality and semiparametric efficiency of both OLS-based direct strategies and the proposed quadruply robust estimators, with practical fast implementations and bootstrap-based uncertainty quantification. Through extensive simulations and an empirical study on trauma survivors, the method demonstrates robustness and improved inference for complex mediation structures. The approach is dimension-free under mild convergence conditions and offers tools for reliable causal mediation analysis across diverse data types and graph configurations.

Abstract

This paper provides robust estimators and efficient inference of causal effects involving multiple interacting mediators. Most existing works either impose a linear model assumption among the mediators or are restricted to handle conditionally independent mediators given the exposure. To overcome these limitations, we define causal and individual mediation effects in a general setting, and employ a semiparametric framework to develop quadruply robust estimators for these causal effects. We further establish the asymptotic normality of the proposed estimators and prove their local semiparametric efficiencies. The proposed method is empirically validated via simulated and real datasets concerning psychiatric disorders in trauma survivors.

On Efficient Inference of Causal Effects with Multiple Mediators

TL;DR

This work develops a semiparametric framework for estimating causal effects with multiple interacting mediators under unknown causal graphs. It defines direct and indirect interventional effects for individual mediators and derives quadruply robust estimators that remain consistent under broad misspecification by combining four identification strategies and averaging over MECs. The authors establish asymptotic normality and semiparametric efficiency of both OLS-based direct strategies and the proposed quadruply robust estimators, with practical fast implementations and bootstrap-based uncertainty quantification. Through extensive simulations and an empirical study on trauma survivors, the method demonstrates robustness and improved inference for complex mediation structures. The approach is dimension-free under mild convergence conditions and offers tools for reliable causal mediation analysis across diverse data types and graph configurations.

Abstract

This paper provides robust estimators and efficient inference of causal effects involving multiple interacting mediators. Most existing works either impose a linear model assumption among the mediators or are restricted to handle conditionally independent mediators given the exposure. To overcome these limitations, we define causal and individual mediation effects in a general setting, and employ a semiparametric framework to develop quadruply robust estimators for these causal effects. We further establish the asymptotic normality of the proposed estimators and prove their local semiparametric efficiencies. The proposed method is empirically validated via simulated and real datasets concerning psychiatric disorders in trauma survivors.
Paper Structure (31 sections, 15 theorems, 238 equations, 2 figures, 2 tables, 2 algorithms)

This paper contains 31 sections, 15 theorems, 238 equations, 2 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph Terminology
  4. Causal Graph Structural Assumption
  5. Markov Equivalence Class
  6. Definition of Causal Effects
  7. Semiparametric Efficient Scores
  8. Direct Strategy and Ordinary Least Squares (OLS) Estimations
  9. OLS estimator under semi-linear model
  10. Multiple Robust Estimators
  11. Several Alternative Strategies
  12. Alternative Strategy 1
  13. Alternative Strategy 2
  14. Alternative Strategy 3
  15. Quadruply Robust Estimator
  16. ...and 16 more sections

Key Result

Theorem 4.1

Suppose Assumption ass_structure holds, then for any $j \in [p]$, and for any fixed $\mathcal{G}_M$

Figures (2)

  • Figure 1: Simulation results for both continuous (top row) and discrete (bottom row) scenarios, showcasing the estimated average causal direct mediation effect (left column) and indirect mediation effect (right column) over $N = 100$ replications. The dots represent estimated averages, error bars detail the standard error derived from the replications, and the red line represents the true average value, calculated via numeric integrals according to Definition \ref{['def_med']}.
  • Figure 2: Estimated DAG of mediators

Theorems & Definitions (31)

  • Definition 3.1: pearl2009causal
  • Definition 3.2
  • Theorem 4.1
  • Theorem 4.3
  • Corollary 4.4
  • Proposition 5.2: Identification
  • Proposition 5.3: Interpretation
  • Proposition 5.4
  • Proposition 6.1
  • Theorem 7.3
  • ...and 21 more