Open Access
2023 Causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects
Trang Quynh Nguyen, Elizabeth L. Ogburn, Ian Schmid, Elizabeth B. Sarker, Noah Greifer, Ina M. Koning, Elizabeth A. Stuart
Author Affiliations +
Statist. Surv. 17: 1-41 (2023). DOI: 10.1214/22-SS140


This paper aims to provide practitioners of causal mediation analysis with a better understanding of estimation options. We take as inputs two familiar strategies (weighting and model-based prediction) and a simple way of combining them (weighted models), and show how a range of estimators can be generated, with different modeling requirements and robustness properties. The primary goal is to help build intuitive appreciation for robust estimation that is conducive to sound practice. We do this by visualizing the target estimand and the estimation strategies. A second goal is to provide a “menu” of estimators that practitioners can choose from for the estimation of marginal natural (in)direct effects. The estimators generated from this exercise include some that coincide or are similar to existing estimators and others that have not previously appeared in the literature. We note several different ways to estimate the weights for cross-world weighting based on three expressions of the weighting function, including one that is novel; and show how to check the resulting covariate and mediator balance. We use a random continuous weights bootstrap to obtain confidence intervals, and also derive general asymptotic variance formulas for the estimators. The estimators are illustrated using data from an adolescent alcohol use prevention study. R-code is provided.

Funding Statement

This work is supported by NIMH grants R01MH115487 and T32MH122357 (PI Stuart).


The authors appreciate Drs. Guanglei Hong and Fan Yang for helpful feedback on an earlier draft; Drs. Ilya Shpitser and Eric Tchetgen Tchetgen for insightful discussions on robust estimation and their seminal article [43]; participants of our summer institute mediation course from 2021 and 2022 and participants of the second term 2021 seminar on statistical methods for mental health research at Johns Hopkins Bloomberg School of Public Health for fruitful discussion; and two anonymous Referees, the Associate Editor and the Editor Dr. Richard Lockhart for their thoughtful and constructive comments. The authors thank the participants, staff and investigators of the PAS trial.


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Trang Quynh Nguyen. Elizabeth L. Ogburn. Ian Schmid. Elizabeth B. Sarker. Noah Greifer. Ina M. Koning. Elizabeth A. Stuart. "Causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects." Statist. Surv. 17 1 - 41, 2023.


Received: 1 March 2022; Published: 2023
First available in Project Euclid: 17 January 2023

arXiv: 2102.06048
MathSciNet: MR4535404
zbMATH: 07649352
Digital Object Identifier: 10.1214/22-SS140

Primary: 62D20

Keywords: causal mediation analysis , method visualization , natural (in)direct effects , robust estimation

Vol.17 • 2023
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