Controlled Direct and Mediated Effects: Definition, Identification and Bounds

Scandinavian Journal of Statistics

Volumn 38, Issue 3, 2011, Pages 551-563

  Vanderweele, Tyler J ^a  

^a HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Bounds; Causal inference; Direct and indirect effects; Mediation; Unmeasured confounding

Indexed keywords

EID: 80051892522     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2010.00722.x     Document Type: Article

References (46)

1. Avin, C., Shpitser, I. & Pearl, J. (2005). Identifiability of path-specific effects. In Proceedings of International Joint Conferences on Artificial Intelligence, 357-363. The International Joint Conferences on Artificial Intelligence, Inc. Morgan Kaufmann Publishers, Inc. San Francisco, CA, USA.
2. Baron, R. M. & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J. Pers. Soc. Psychol. 51, 1173-1182.
3. Bennet, W. D., Brown, J. S., Zeman, K. L., Hu, S.-C., Scheuch, G. & Sommerer, K. (2002). Targeting delivery of aerosols to different lung regions. J. Aerosol Med. 15, 179-188.
4. Cai, Z., Kuroki, M., Pearl, J. & Tian, J. (2008). Bounds on direct effects in the presence of confounded intermediate variables. Biometrics 64, 695-701.
5. Cox, D. R. (1958). The planning of experiments. Wiley, New York.
6. Didelez, V., Dawid, A. P. & Geneletti, S. G. (2006). Direct and indirect effects of sequential treatments. In Proceedings of the Twenty-Second Annual Conference on University in Artificial Intelligence (UAI-06) (eds R. Dechter & T. Richardson ), 138-146. AUAI Press, Virginia.
7. Esary, J. D., Proschan, F. & Walkup, D. W. (1967). Association of random variables, with applications. Ann. Math. Statist. 38, 1466-1474.
8. Gallop, R., Small, D. S., Lin, J. Y., Elliott, M. R., Joffe, M. & Ten Have, T. R. (2009). Mediation analysis with principal stratification. Stat. Med. 28, 1108-1130.
9. Geneletti, S. (2007). Identifying direct and indirect effects in a non-counterfactual framework. J. Roy. Statist. Soc. Ser. B 69, 199-216.
10. Goetgeluk, S., Vansteelandt, S. & Goetghebeur, E. (2008). Estimation of controlled direct effects. J. Roy. Statist. Soc. Ser. B 70, 1049-1066.
11. Hafeman, D. M. & Schwartz, S. (2009). Opening the black box: a motivation for the assessment of mediation. Int. J. Epidemiol. 38, 838-845.
12. Hafeman, D. M. & VanderWeele, T. J. (2010). Alternative assumptions for the identification of direct and indirect effects. Epidemiology. Available at doi: (accessed May 24, 2010).
13. Imai, K., Keele, L. & Yamamoto, T. (2010). Identification, inference, and sensitivity analysis for causal mediation effects. Statist. Sci. 25, 51-71.
14. Joffe, M., Small, D. & Hsu, C.-Y. (2007). Defining and estimating intervention effects for groups that will develop an auxiliary outcome. Statist. Sci. 22, 74-97.
15. Judd, C. M. & Kenny, D. A. (1981). Estimating mediation in treatment evaluations. Process Anal. 5, 602-619.
16. Kaufman, J. S., MacLehose, R. F. & Kaufman, S. (2004). A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation. Epidemiol. Perspect. Innov. 1, 1-13.
17. Kaufman, S., Kaufman, J. S., MacLehose, R. F., Greenland, S. & Poole, C. (2005). Improved estimation of controlled direct effects in the presence of unmeasured confounding of intermediate variables. Stat. Med. 24, 1683-1702.
18. Kaufman, S., Kaufman, J. S. & MacLehose, R. F. (2009). Analytic bounds on causal risk differences in directed acyclic graphs involving three observed binary variables. J. Statist. Plann. Inference 139, 3473-3487.
19. Kuroki, M. & Miyakawa, M. (1999). Identifiability criteria for causal effects of joint interventions. J. Japan Statist. Soc. 29, 105-117.
20. MacKinnon, D. P. (2008). An introduction to statistical mediation analysis. Lawrence Erlbaum Associates, New York.
21. Neyman, J. (1923). Sur les applications de la theorie des probabilites aux experiences agricoles: Essay des principles. Excerpts reprinted (1990) in English. (eds D. Dabrowska and T. Speed, Trans.). Statist. Sci. 5, 463-472.
22. Pearl, J. (1995). Casual diagrams for empirical research (with discussion). Biometrika 82, 669-710.
23. Pearl, J. (2001). Direct and indirect effects. In Proceedings of the Seventeenth Conference on Uncertainty and Artificial Intelligence, 411-420. San Francisco: Morgan Kaufmann, San Francisco.
24. Pearl, J. (2009). Causality: models, reasoning, and inference, 2nd edn. Cambridge University Press, Cambridge.
25. Pearl, J. & Robins, J. M. (1995). Probabilistic evaluation of sequential plans from causal models with hidden variables. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (eds P. Besnard & S. Hanks ), 444-453. Morgan Kaufmann Publishers, Inc. San Francisco, CA, USA.
26. Petersen, M. L., Sinisi, S. E. & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology 17, 276-284.
27. Robins, J. M. (1986). A new approach to causal inference in mortality studies with sustained exposure period - application to control of the healthy worker survivor effect. Math. Model. 7, 1393-1512.
28. Robins, J. M. (1987). Addendum to a new approach to causal inference in mortality studies with sustained exposure period - application to control of the healthy worker survivor effect. Comput. Math. Appl. 14, 923-945.
29. Robins, J. M. (1999). Testing and estimation of direct effects by reparameterizing directed acyclic graphs with structural nested models. In Computation, causation, and discovery. (eds C. Glymou & G. F. Cooper ), 349-405. MenloPark, CA, Cambridge, MA: AAAI Press/The MIT Press, Cambridge, MA.
30. Robins, J. M. (2003). Semantics of causal DAG models and the identification of direct and indirect effects. In Highly structured stochastic systems (eds P. Green, N. L. Hjort & S. Richardson ), 70-81. Oxford University Press, New York.
31. Robins, J. M. & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology 3, 143-155.
32. Rosenbaum, P. R. & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41-55.
33. Rubin, D. (1974). Estimating causal effects of treatments in randomized and non-randomized studies. J. Educ. Psychol. 66, 688-701.
34. Rubin, D. B. (1978). Bayesian inference for causal effects: the role of randomization. Ann. Statist. 6, 34-58.
35. Rubin, D. B. (1990). Formal modes of statistical inference for causal effects. J. Statist. Plann. Inference 25, 279-292.
36. Rubin, D. B. (2004). Direct and indirect effects via potential outcomes. Scand. J. Statist. 31, 161-170.
37. Sobel, M. E. (2008). Identification of causal parameters in randomized studies with mediating variables. J. Educ. Behav. Stat. 33, 230-251.
38. Ten Have, T. R., Joffe, M. M., Lynch, K. G., Brown, G. K., Maisto, S. A. & Beck, A. T. (2007). Causal mediation analyses with rank preserving models. Biometrics 63, 926-934.
39. van der Laan, M. J. & Petersen, M. L. (2008). Direct effect models. Int. J. Biostat. 4, 1-27.
40. VanderWeele, T. J. (2008a). Simple relations between principal stratification and direct and indirect effects. Statist. Probab. Lett. 78, 2957-2962.
41. VanderWeele, T. J. (2008b). The sign of the bias of unmeasured confounding. Biometrics 64, 702-706.
42. VanderWeele, T. J. (2009a). Mediation and mechanism. Eur. J. of Epidemiol. 24, 217-224.
43. VanderWeele, T. J. (2009b). Marginal structural models for the estimation of direct and indirect effects. Epidemiology 20, 18-26.
44. VanderWeele, T. J. (2010). Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology 21, 540-551.
45. VanderWeele, T. J. & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Stat. Interface - Spec. Issue Mental Health Soc. Behav. Sci. 2, 457-468.
46. Vansteelandt, S. (2009). Estimating direct effects in cohort and case-control studies. Epidemiology 20, 851-860.