Skip to main content
Log in

Mediation and mechanism

  • Commentary
  • Published:
European Journal of Epidemiology Aims and scope Submit manuscript

Abstract

The concepts of mediation and mechanism are contrasted and logical implications holding between theses two concepts are described. The concept of mediation can be formalized using counterfactual definitions of indirect effects; the concept of mechanism can be formalized within the sufficient cause framework. It is shown that both concepts can be illustrated using a single causal diagram. It is also shown that mediation implies mechanism but mechanism need not imply mediation. Discussion is given regarding how the distinction between “statistical causality” and “mechanistic causality” is blurred by recent work in causal inference concerning methods for testing for mediation and mechanism.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

References

  1. Hafeman D. A sufficient cause based approach to the assessment of mediation. Eur J Epidemiol. 2008;23:711–21. doi:10.1007/s10654-008-9286-7.

    Article  PubMed  Google Scholar 

  2. Judd CM, Kenny DA. Estimating mediation in treatment evaluations. Process Anal. 1981;5:602–19.

    Google Scholar 

  3. Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J Pers Soc Psychol. 1986;51:1173–82. doi:10.1037/0022-3514.51.6.1173.

    Article  PubMed  CAS  Google Scholar 

  4. Bollen KA. Total, direct and indirect effects in structural equation models. In: Clogg CC, editor. Sociological methodology. Washington, DC: American Sociological Association; 1987. p. 37–69.

    Google Scholar 

  5. Holland PW. Causal inference, path analysis, and recursive structural equations models. In: Clogg CC, editor. Sociological methodology. Washington, DC: American Sociological Association; 1988. p. 449–84.

    Google Scholar 

  6. Sobel ME. Effect analysis and causation in linear structural equation models. Psychometrika. 1990;55:495–515. doi:10.1007/BF02294763.

    Article  Google Scholar 

  7. Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect effects. Epidemiology. 1992;3:143–55. doi:10.1097/00001648-199203000-00013.

    Article  PubMed  CAS  Google Scholar 

  8. Pearl J. Direct and indirect effects. In: Proceedings of the seventeenth conference on uncertainty and artificial intelligence. San Francisco: Morgan Kaufmann; 2001:411-420.

  9. Kaufman JS, MacLehose RF, Kaufman S. A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation. Epidemiol Perspect Innov. 2004;1:4. doi:10.1186/1742-5573-1-4.

    Article  PubMed  Google Scholar 

  10. Peterson ML, Sinisi SE, van der Laan MJ. Estimation of direct causal effects. Epidemiology. 2006;17:276–84. doi:10.1097/01.ede.0000208475.99429.2d.

    Article  Google Scholar 

  11. VanderWeele TJ. Marginal structural models for the estimation of direct and indirect effects. Epidemiology. 2009;20:18–26. doi:10.1097/EDE.0b013e31818f69ce.

    Article  PubMed  Google Scholar 

  12. Frangakis CE, Rubin DB. Principal stratification in causal inference. Biometrics. 2002;58:21–9. doi:10.1111/j.0006-341X.2002.00021.x.

    Article  PubMed  Google Scholar 

  13. Rubin DB. Direct and indirect effects via potential outcomes. Scand J Stat. 2004;31:161–70. doi:10.1111/j.1467-9469.2004.02-123.x.

    Article  Google Scholar 

  14. VanderWeele TJ. Simple relations between principal stratification and direct and indirect effects. Stat Probab Lett. 2008;78:2957–62. doi:10.1016/j.spl.2008.05.029.

    Article  Google Scholar 

  15. Rothman KJ. Causes. Am J Epidemiol. 1976;104:587–92.

    PubMed  CAS  Google Scholar 

  16. VanderWeele TJ, Robins JM. The identification of synergism in the sufficient-component cause framework. Epidemiol. 2007;18:329–39. doi:10.1097/01.ede.0000260218.66432.88.

    Article  Google Scholar 

  17. VanderWeele TJ, Robins JM. Empirical and counterfactual conditions for sufficient cause interactions. Biometrika. 2008;95:49–61. doi:10.1093/biomet/asm090.

    Article  Google Scholar 

  18. Cayley A. On a question in the theory of probabilities. Philos Mag. 1853;6:259.

    Google Scholar 

  19. Mackie JL. Causes and conditions. Am Philos Q. 1965;2:245–55.

    Google Scholar 

  20. MacMahon B, Pugh TF. Causes and entities of disease. In: Clark DW, MacMahon B, editors. Preventive medicine. Boston: Little, Brown, and Company; 1967. p. 11–8.

    Google Scholar 

  21. VanderWeele TJ, Robins JM. Directed acyclic graphs, sufficient causes and the properties of conditioning on a common effect. Am J Epidemiol. 2007;166:1096–104. doi:10.1093/aje/kwm179.

    Article  PubMed  Google Scholar 

  22. VanderWeele TJ, Robins JM. Minimal sufficient causation and directed acyclic graphs. Ann Stat. 2009. (in press).

  23. Hall N, Paul LA. Causation and preemption. In: Clark P, Hawley K, editors. Philosophy of science today. Oxford: Oxford University Press; 2003. p. 100–29.

    Google Scholar 

  24. Greenland S, Robins JM. Conceptual problems in the definition and interpretation of attributable fractions. Am J Epidemiol. 1988;128:1185–97.

    PubMed  CAS  Google Scholar 

  25. Greenland S, Brumback B. An overview of relations among causal modeling methods. Int J Epidemiol. 2002;31:1030–7. doi:10.1093/ije/31.5.1030.

    Article  PubMed  Google Scholar 

  26. Hoffmann K, Heidemann C, Weikert C, Schulze MB, Boeing H. Estimating the proportion of disease due to classes of sufficient causes. Am J Epidemiol. 2006;163:76–83. doi:10.1093/aje/kwj011.

    Article  PubMed  Google Scholar 

  27. Aalen OO, Frigessi A. What can statistics contribute to a causal understanding? Scand J Stat. 2007;34:155–68. doi:10.1111/j.1467-9469.2006.00549.x.

    Article  Google Scholar 

  28. Heckman JJ. The scientific model of causality. Sociol Methodol. 2005;1:1–98. doi:10.1111/j.0081-1750.2006.00163.x.

    Article  Google Scholar 

  29. Heckman JJ. Econometric causality. Int Stat Rev. 2007;76:1–27. doi:10.1111/j.1751-5823.2007.00024.x.

    Article  Google Scholar 

  30. Machamer P, Darden L, Craver CF. Thinking about mechanisms. Philos Sci. 2000;67:1–25. doi:10.1086/392759.

    Article  Google Scholar 

  31. Pearl J. Casual diagrams for empirical research (with discussion). Biometrika. 1995;82:669–710. doi:10.1093/biomet/82.4.669.

    Article  Google Scholar 

  32. Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology. 1999;10:37–48. doi:10.1097/00001648-199901000-00008.

    Article  PubMed  CAS  Google Scholar 

  33. Glymour MM, Greenland S. Causal diagrams. In: Rothman KJ, Greenland S, Lash TL, editors. Modern epidemiology. 3rd ed. Philadelphia: Lippincott Williams and Wilkins; 2008. p. 183–209.

    Google Scholar 

  34. Robins JM. Testing and estimation of direct effects by reparameterizing directed acyclic graphs with structural nested models. In: Glymour C, Cooper GF, editors. Computation, causation, and discovery. Menlo Park, CA, Cambridge, MA: AAAI Press/The MIT Press; 1999. p. 349–405.

    Google Scholar 

  35. Robins JM. Semantics of causal DAG models and the identification of direct and indirect effects. In: Green P, Hjort NL, Richardson S, editors. Highly structured stochastic systems. New York: Oxford University Press; 2003. p. 70–81.

    Google Scholar 

  36. Joffe M, Small D, Hsu CY. Defining and estimating intervention effects for groups that will develop an auxiliary outcome. Stat Sci. 2007;22:74–97. doi:10.1214/088342306000000655.

    Article  Google Scholar 

  37. VanderWeele TJ. Sufficient cause interactions and statistical interactions. Epidemiology. 2009;20:6–13. doi:10.1097/EDE.0b013e31818f69e7.

    Article  PubMed  Google Scholar 

  38. Cox DR, Wenmuth N. Causality: a statistical view. Int Stat Rev. 2004;72:285–305.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tyler J. VanderWeele.

Technical appendix

Technical appendix

Mediation, controlled direct effects, and natural direct and indirect effects

Note that the total effect Y1−Y0 decomposes as the sum of a total direct effect and a pure indirect effect, Y1−Y0 = \({\rm{(Y_{1M_{1}}}}\!-\!{\rm{Y_{0M_{1}})}}+{\rm{(Y_{0M_{1}}}}\!-\!{\rm{Y_{0M_{0}})}}\), or as the sum of a total indirect effect and a pure direct effect, Y1−Y0 = \({\rm{(Y_{1M_{1}}}}\!-\!{\rm{Y_{1M_{0}})}}+{\rm{(Y_{1M_{0}}}}\!-\!{\rm{Y_{0M_{0}})}}\). If both the pure indirect effect and the total indirect effect are zero, i.e., if both \({\rm{Y_{0M_{1}}}}\!-\!{\rm{Y_{0M_{0}}}=0}\) and \({\rm{Y_{1M_{1}}}}\!-\!{\rm{Y_{0M_{1}}}=0}\), then we will have that Y1−Y0 = \({\rm{Y_{1M_{1}}}}\!-\!{\rm{Y_{0M_{1}}}}\) and that Y1−Y0 = \({\rm{Y_{1M_{0}}}}\!-\!{\rm{Y_{0M_{0}}}}\) so that the total effect, the total direct effect and the pure direct effect all coincide. We thus say that “M mediates the effect of X on Y” whenever one of the natural indirect effects is non-zero since, if they are both zero then the total effect and the natural direct effects coincide.

Note that it is more difficult to use the controlled direct effect to draw conclusions about mediation. The controlled direct effect takes the form Y1m−Y0m. Even if X has no effect on M so that there is no mediation, the controlled direct effect Y1m−Y0m may differ from the total effect. For example, suppose that X has no effect on M so that there is no mediation of the effect of X on Y by M but suppose there is interaction between X and M. If there is interaction between the effects of X and M on Y, then Y1m−Y0m will differ for different values of m and thus one of the controlled direct effects Y11−Y01 or Y10−Y00 will differ from Y1−Y0. Obtaining a controlled direct effect that is different than the total effect is thus not evidence that mediation is present. If there is no interaction between the effects of X and M on Y then Robins [35] has shown that the controlled direct, the total direct effect and the pure direct effect all coincide; furthermore all of these quantities will be equal to the total effect if there are no natural indirect effects; in this case one can compare total effects and controlled direct effects to assess mediation. Thus only under the assumption of no interaction can one use controlled direct effects to assess mediation. See the work of Robins and Greenland [7] and Kaufman et al. [9] for further critique of using controlled direct effects to assess mediation and indirect effects.

Relationship between direct and indirect effects, with a sufficient cause taken as the mediator, and the probabilities of the background component causes

Here we express controlled direct effects, with some sufficient cause S taken as the mediator, in terms of the probabilities of the background components of the sufficient causes in Fig. 1. Note that if S were set to 1 then Y would be 1 since S is a sufficient cause for Y; it thus does not make sense to discuss controlled direct effects of the form Yx=1,s=1−Yx=0,s=1 since this controlled direct effect is zero for any sufficient cause and we report only the controlled direct effects of the form Yx=1,s=0−Yx=0,s=0. Note that a binary variable Z can be treated as an event and so we will let P(Z) denote P(Z = 1).

For S = BM:

$$ \begin{aligned} {\text{E}}\left[ {{\text{Y}}_{{{\text{x}} =\,1,{\text{s}} =\,0}} - {\text{Y}}_{{{\text{x}} =\,0,{\text{s}} =\,0}} } \right] & =\,{\text{P}}({\text{L or C}}\,{\text{or FM}}_{{{\text{x}} =\,1}} ) - {\text{ P}}({\text{L}}) \\ & =\,{\text{ P}}\left[ {{\text{L}}^{\text{c}} ({\text{C\,or\,FM}}_{{{\text{x}} =\,1}} )} \right] \\ & =\,{\text{ P}}\left[ {{\text{L}}^{\text{c}} {\text{C\,or\,L}}^{\text{c}} {\text{F}}({\text{A\,or\,K}})} \right] \\ \end{aligned} $$

For S = CX:

$$ \begin{aligned} {\text{E}}\left[ {{\text{Y}}_{\text{x = 1,s = 0}} - {\text{Y}}_{{{\text{x}} = 0,{\text{s}} = 0}} } \right] & =\,{\text{P}}({\text{L}}\;{\text{or\;BM}}_{{{\text{x}} = 1}} {\text{ \;or \;FM}}_{{{\text{x}} = 1}} ) - {\text{P}}({\text{L\;or\;BM}}_{{{\text{x}} = 0}} ) \\ & = {\text{ P}}\left[ {{\text{L\;or\;B}}({\text{A\;or\;K}}){\text{ or\;F}}({\text{A\;or\;K}})} \right] - {\text{P}}({\text{L\;or\;BK}}) \\ & = {\text{ P}}\left[ {{\text{L}}^{\text{c}} {\text{K}}^{\text{c}} {\text{BA\;or\;L}}^{\text{c}} {\text{K}}^{\text{c}} {\text{FA}}\,{\text{or\;L}}^{\text{c}} {\text{B}}^{\text{c}} {\text{F}}({\text{A}}\,{\text{or\;K}})} \right] \\ \end{aligned} $$

For S = FXM:

$$ \begin{aligned} {\text{E}}\left[ {{\text{Y}}_{{{\text{x}} = 1,{\text{s}} = 0}} - {\text{Y}}_{{{\text{x}} = 0,{\text{s}} = 0}} } \right] & = {\text{P}}({\text{L}}\,{\text{ or\;BM}}_{{{\text{x}} = 1}} {\text{\;or\;C}}) - {\text{P}}({\text{L\;or\;BM}}_{{{\text{x}} = 0}} ) \\ & = {\text{ P}}\left[ {{\text{L\;or\;B}}({\text{A\;or\;K}}){\text{ or\;C}}} \right] - {\text{P}}({\text{L\;or\;BK}}) \\ & = {\text{ P}}\left[ {{\text{L}}^{\text{c}} {\text{K}}^{\text{c}} {\text{BA\;or\;L}}^{\text{c}} ({\text{B}}^{\text{c}}\;{\text{or \;K}}^{\text{c}} ){\text{C}}} \right] \\ \end{aligned} $$

Rights and permissions

Reprints and permissions

About this article

Cite this article

VanderWeele, T.J. Mediation and mechanism. Eur J Epidemiol 24, 217–224 (2009). https://doi.org/10.1007/s10654-009-9331-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10654-009-9331-1

Keywords

Navigation