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A Complete Graphical Criterion for the Adjustment Formula in Mediation Analysis

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  • Shpitser Ilya
  • VanderWeele Tyler J

Abstract

Various assumptions have been used in the literature to identify natural direct and indirect effects in mediation analysis. These effects are of interest because they allow for effect decomposition of a total effect into a direct and indirect effect even in the presence of interactions or non-linear models. In this paper, we consider the relation and interpretation of various identification assumptions in terms of causal diagrams interpreted as a set of non-parametric structural equations. We show that for such causal diagrams, two sets of assumptions for identification that have been described in the literature are in fact equivalent in the sense that if either set of assumptions holds for all models inducing a particular causal diagram, then the other set of assumptions will also hold for all models inducing that diagram. We moreover build on prior work concerning a complete graphical identification criterion for covariate adjustment for total effects to provide a complete graphical criterion for using covariate adjustment to identify natural direct and indirect effects. Finally, we show that this criterion is equivalent to the two sets of independence assumptions used previously for mediation analysis.

Suggested Citation

  • Shpitser Ilya & VanderWeele Tyler J, 2011. "A Complete Graphical Criterion for the Adjustment Formula in Mediation Analysis," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-24, March.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:16
    DOI: 10.2202/1557-4679.1297
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    References listed on IDEAS

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    1. van der Laan Mark J. & Petersen Maya L, 2008. "Direct Effect Models," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-29, October.
    2. Stephen J. Chanock & David J. Hunter, 2008. "When the smoke clears ..," Nature, Nature, vol. 452(7187), pages 537-538, April.
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    Cited by:

    1. Gambelli, Danilo & Alberti, Francesca & Solfanelli, Francesco & Vairo, Daniela & Zanoli, Raffaele, 2017. "Third generation algae biofuels in Italy by 2030: A scenario analysis using Bayesian networks," Energy Policy, Elsevier, vol. 103(C), pages 165-178.
    2. Tyler J. VanderWeele & Eric J. Tchetgen Tchetgen, 2017. "Mediation analysis with time varying exposures and mediators," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 917-938, June.
    3. Christoph Dworschak, 2024. "Bias mitigation in empirical peace and conflict studies: A short primer on posttreatment variables," Journal of Peace Research, Peace Research Institute Oslo, vol. 61(3), pages 462-476, May.
    4. Rahul Singh & Liyuan Xu & Arthur Gretton, 2021. "Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves," Papers 2111.03950, arXiv.org, revised Jul 2023.

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