A complete graphical criterion for the adjustment formula in mediation analysis

Ilya Shpitser, Tyler J. Vanderweele

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Article number16
JournalInternational Journal of Biostatistics
Issue number1
StatePublished - 2011
Externally publishedYes


  • adjustment
  • causal diagrams
  • confounding
  • covariate adjustment
  • mediation
  • natural direct and indirect effects

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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