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A Comparison of Potential Outcome Approaches for Assessing Causal Mediation

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Book cover Statistical Causal Inferences and Their Applications in Public Health Research

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

Abstract

Mediation occurs as part of a hypothesized causal chain of events: An intervention or treatment, T, has an effect on the mediator, M, which then affects an outcome variable, Y. Within the potential outcomes framework for causal inference, three different definitions of the mediation effects have been proposed: principal strata effects (e.g., Rubin, Scand. J. Stat. 31:161–170, 2004; Jo, Psychol. Methods 13:314–336, 2008), natural effects (e.g., Pearl, Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 2001; Imai et al., Psychol. Methods 15:309–334, 2010), and controlled effects (e.g., Robins and Greenland, Epidemiology 3:143–155, 1992; VanderWeele, Epidemiology 20:18–26, 2009). We illustrate that each of these definitions answers a different scientific question. We examine five different estimators of the various definitions and discuss identifying assumptions about unmeasured confounding, the existence of direct effects (i.e., the effect of T on Y that is not due to M), iatrogenic effects of T on M, the existence of post-treatment confounders, and the existence of interactions. We assess the robustness of each of the estimators to violations of the assumptions using a simulation study that systematically challenges different aspects of these assumptions. We found that when no assumptions were violated, as may be expected, each approach was unbiased for its respective population value and 95 % confidence interval (CI) coverage was maintained. However, when assumptions are violated, the effects may be severely biased and 95 % CI coverage is not maintained. We suggest that researchers choose the appropriate definition based on the scientific question to be addressed and the identifying assumptions that are plausible given their data.

Authors’ note: Preparation of this article was supported by NIDA Center Grant P50 DA100075-15 and NIDA R01 DA09757. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute on Drug Abuse (NIDA) or the National Institutes of Health (NIH).

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Notes

  1. 1.

    Gallop [59] proposed Bayesian estimation of direct effects when the mediator is continuous.

References

  1. MacKinnon, D.P.: Introduction to Statistical Mediation Analysis. LEA, New York (2008)

    Google Scholar 

  2. Coffman, D.L.: Estimating causal effects in mediation analysis using propensity scores. Struct. Equ. Model. 18, 357–369 (2011)

    Article  MathSciNet  Google Scholar 

  3. Coffman, D.L., Zhong, W.: Assessing mediation using marginal structural models in the presence of confounding and moderation. Psychol. Methods (2012). doi:10.1037/a0029311

    Google Scholar 

  4. Imai, K., Keele, L., Tingley, D.: A general approach to causal mediation analysis. Psychol. Methods 15, 309–334 (2010)

    Article  Google Scholar 

  5. Jo, B.: Causal inference in randomized experiments with mediational processes. Psychol. Methods 13, 314–336 (2008)

    Article  Google Scholar 

  6. Pearl, J.: The causal mediation formula – a guide to the assessment of pathways and mechanisms. Prev. Sci. 13, 426–436 (2012)

    Article  Google Scholar 

  7. Holland, P.W.: Causal inference, path analysis, and recursive structural equations models. Sociol. Methodol. 18, 449–484 (1988)

    Article  Google Scholar 

  8. Holland, P.W.: Statistics and causal inference. J. Am. Stat. Assoc. 81, 945–970 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rubin, D.B.: Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol. 66, 688–701 (1974)

    Article  Google Scholar 

  10. Rubin, D.B.: Causal inference using potential outcomes: design, modeling, decisions. J. Am. Stat. Assoc. 100, 322–331 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Little, R.J.A., Rubin, D.B.: Causal effects in clinical and epidemiological studies via potential outcomes: concepts and analytical approaches. Annu. Rev. Public Health 21, 121–145 (2000)

    Article  Google Scholar 

  12. Schafer, J.L., Kang, J.D.Y.: Average causal effects from non-randomized studies: a practical guide and simulated example. Psychol. Methods 13, 279–313 (2008)

    Article  Google Scholar 

  13. Winship, C., Morgan, S.L.: The estimation of causal effects from observational data. Annu. Rev. Sociol. 25, 659–706 (1999)

    Article  Google Scholar 

  14. VanderWeele, T.J.: Concerning the consistency assumption in causal inference. Epidemiology 20(6), 880–883 (2009)

    Article  Google Scholar 

  15. Westreich, D., Cole, S.R.: Invited commentary: positivity in practice. Am. J. Epidemiol. 171, 674–677 (2010)

    Article  Google Scholar 

  16. Frangakis, C.E.: Principal stratification. In: Gelman, A., Meng, X.L. (eds.) Applied Bayesian Modeling and Causal Inference from Incomplete Data Perspectives, pp. 97–108. Wiley, New York (2004)

    Google Scholar 

  17. Frangakis, C.E., Rubin, D.B.: Principal stratification in causal inference. Biometrics 58, 21–29 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rubin, D.B.: Direct and indirect causal effects via potential outcomes. Scand. J. Stat. 31, 161–170 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pearl, J.: Direct and indirect effects. In: Besnard, P., Hanks, S. (eds.) Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufman, San Francisco (2001)

    Google Scholar 

  20. Robins, J.M., Greenland, S.: Identifiability and exchangeability for direct and indirect effects. Epidemiology 3, 143–155 (1992)

    Article  Google Scholar 

  21. VanderWeele, T.J., Vansteelandt, S.: Conceptual issues concerning mediation, interventions and composition. Stat. Interface 2, 457–468 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Imai, K., Keele, L., Yamamoto, T.: Identification, inference, and sensitivity analysis for causal mediation effects. Stat. Med. 25, 51–71 (2010)

    MathSciNet  MATH  Google Scholar 

  23. VanderWeele, T.J.: Simple relations between principal stratification and direct and indirect effects. Stat. Probab. Lett. 78, 2957–2962 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sobel, M.E.: Identification of causal parameters in randomized studies with mediating variables. J. Educ. Behav. Stat. 33, 230–251 (2008)

    Article  Google Scholar 

  25. Gallop, R., Small, D.S., Lin, J.Y., Elliott, M.R., Joffe, M.M., Ten Have, T.R.: Mediation analysis with principal stratification. Stat. Med. 28, 1108–1130 (2009)

    Article  MathSciNet  Google Scholar 

  26. VanderWeele, T.J.: Marginal structural models for the estimation of direct and indirect effects. Epidemiology 20, 18–26 (2009)

    Article  Google Scholar 

  27. Pearl, J.: Interpretation and identification of Causal Mediation. Psychol. Meth. 19(4), 459–481 (2014)

    Article  Google Scholar 

  28. VanderWeele, T.J.: Bias formulas for sensitivity analysis for direct and indirect effects. Epidemiology 21, 1–12 (2010)

    Article  MathSciNet  Google Scholar 

  29. Baron, R.M., Kenny, D.A.: The moderator–mediator variable distinction in social psychological research: conceptual, strategic and statistical considerations. J. Person. Soc. Psychol. 51, 1173–1182 (1986)

    Article  Google Scholar 

  30. Avin, C., Shipster, I., Pearl, J.: Identifiability of path-specific effects. In: Proceedings of the International Joint Conferences on Artificial Intelligence, pp. 357–363. Department of Statistics, UCLA, Los Angeles (2005)

    Google Scholar 

  31. Hafeman, D.M., VanderWeele, T.J.: Alternative assumptions for identification of direct and indirect effects. Epidemiology 22, 753–764 (2011). doi:10.1097/EDE.0b013e3181c311b2

    Article  Google Scholar 

  32. Vansteelandt, S., VanderWeele, T.J.: Natural direct and indirect effects on the exposed: effect decomposition under weaker assumptions. Biometrics 68(4), 1019–1027 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  33. Ten Have, T.R., Joffe, M.M.: A review of causal estimation of effects in mediation analysis. Stat. Meth. Med. Res. 21, 77–107 (2012)

    Article  Google Scholar 

  34. Ten Have, T.R., Joffe, M.M., Lynch, K.G., Brown, G.K., Maisto, S.A., Beck, A.T.: Causal mediation analyses with rank preserving models. Biometrics 36, 926–934 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. Lynch, K.G., Kerry, M., Gallop, R., Ten Have, T.R.: Causal mediation analyses for randomized trials. Health Serv. Outcome Res. Methodol. 8, 57–76 (2008)

    Article  Google Scholar 

  36. Angrist, J.D., Imbens, G.W., Rubin, D.B.: Identification of causal effects using instrumental variables. J. Am. Stat. Assoc. 91, 444–472 (1996)

    Article  MATH  Google Scholar 

  37. Elliott, M.R., Raghunathan, T.E., Li, Y.: Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes. Biostatistics 11, 353–372 (2010)

    Article  Google Scholar 

  38. Daniels, M.J., Roy, J., Kim, C., Hogan, J.W., Perri, M.: Bayesian inference for the causal effect of mediation. Biometrics 68(4), 1028–1036 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Hogan, J.W.: Imputation-based inference for natural direct and indirect effects. Presented at the Workshop on Causal Inference in Health Research, Montreal, Canada, May 2011

    Google Scholar 

  40. Keele, L., Tingley, D., Yamamoto, T., Imai, K.: Mediation: R package for causal mediation analysis [Computer software manual] (2009). Available from http://CRAN.R-project.org/package=mediation (R package version 2.1)

  41. Robins, J.M., Hernan, M.A., Brumback, B.A.: Marginal structural models and causal inference in epidemiology. Epidemiology 11, 550–560 (2000)

    Article  Google Scholar 

  42. MacKinnon, D.P., Lockwood, C.M., Hoffman, J.M., West, S.G., Sheets, V.: A comparison of methods to test mediation and other intervening variable effects. Psychol. Methods 7, 83–104 (2002)

    Article  Google Scholar 

  43. Bound, J., Jaeger, D.A., Baker, R.M.: Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. J. Am. Stat. Assoc. 90, 443–450 (1995)

    Google Scholar 

  44. Hernan, M.A., Robins, J.M.: Instruments for causal inference: an epidemiologist’s dream? Epidemiology 17(4), 360–371 (2006)

    Article  Google Scholar 

  45. Pearl, J.: On a class of bias-amplifying covariates that endanger effect estimates. UCLA Cognitive Systems Laboratory, Technical Report (R-356). In: Grunwald, P., Spirtes, P. (eds.) Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, pp. 417–424. Corvallis, OR (2010)

    Google Scholar 

  46. Imai, K., Yamamoto, T.: Identification and sensitivity analysis for multiple causal mechanisms: revisiting evidence from framing experiments. Polit. Anal. 1, 1–31 (2013). doi:10.1093/pan/mps040

    Google Scholar 

  47. Wang, W., Nelson, S., Albert, J.M.: Estimation of causal mediation effects for a dichotomous outcome in multiple-mediator models using the mediation formula. Stat. Med. 32(24), 4211–4228 (2013)

    Article  MathSciNet  Google Scholar 

  48. Lange, T., Vansteelandt, S., Bekaert, M.: A simple unified approach for estimating natural direct and indirect effects. Am. J. Epidemiol. 176, 190–195 (2012)

    Article  MATH  Google Scholar 

  49. Jo, B., Stuart, E.A., MacKinnon, D.P., Vinokur, A.D.: The use of propensity scores in mediation analysis. Multivar. Behav. Res. 46, 1–28 (2011). doi:10.1080/00273171.2011.576624

    Article  Google Scholar 

  50. Vansteelandt, S., Bekaert, M., Lange, T.: Imputation strategies for the estimation of natural direct and indirect effects. Epidemiol. Methods 1, 131–158 (2012)

    Article  MATH  Google Scholar 

  51. VanderWeele, T.J., Vansteelandt, S.: Odds ratios for mediation analysis for a dichotomous outcome. Am. J. Epidemiol. 172, 1339–1348 (2010)

    Article  Google Scholar 

  52. Valeri, L., VanderWeele, T.J.: Mediation analysis allowing for exposure-mediator interactions and causal interpretation: theoretical assumptions and implementation with SAS and SPSS macros. Psychol. Methods (2013)

    Google Scholar 

  53. Pearl, J.: Interpretable conditions for identifying direct and indirect effects. UCLA Cognitive Systems Laboratory Technical Report (R-389) (2012)

    Google Scholar 

  54. Vansteelandt, S.: Estimating direct effects in cohort and case-control studies. Epidemiology 20(6), 851–860 (2009)

    Article  Google Scholar 

  55. Emsley, R., Dunn, G., White, I.R.: Mediation and moderation of treatment effects in randomised controlled trials of complex treatments. Stat. Methods Med. Res. 19(3), 237–270 (2010)

    Article  MathSciNet  Google Scholar 

  56. Albert, J.M.: Mediation analysis via potential outcomes models. Stat. Med. 27, 1282–1304 (2008)

    Article  MathSciNet  Google Scholar 

  57. Dunn, G., Bentall, R.: Modelling treatment-effect heterogeneity in randomized controlled trials of complex interventions (psychological treatments). Stat. Med. 26, 4719–4745 (2007)

    Article  MathSciNet  Google Scholar 

  58. Joffe, M.M., Greene, T.: Related causal frameworks for surrogate outcomes. Biometrics 65, 530–538 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  59. Gallop, R.: Principal stratification for assessing mediation with a continuous mediator. Paper presented at the Eastern North American Region of the International Biometric Society, Washington, April 2012

    Google Scholar 

  60. Cole, S.R., Frangakis, C.: The consistency statement in causal inference: a definition or an assumption. Epidemiology 20(1), 3–5 (2009)

    Article  Google Scholar 

  61. MacCallum, R.C., Zhang, S., Preacher, K.J., Rucker, D.D.: On the practice of dichotomization of quantitative variables. Psychol. Methods 7(1), 19–40 (2002). doi:10.1037/1082-989X.7.1.19

    Article  Google Scholar 

  62. Rosenbaum, P.R.: The consequences of adjustment for a concomitant variable that has been affected by the treatment. J. R. Stat. Soc. Ser. A (General) 147, 656–666 (1984)

    Article  Google Scholar 

  63. West, S.G., Biesanz, J.C., Pitts, S.C.: Causal inference and generalization in field settings: experimental and quasi-experimental designs. In: Reis, H.T.J., Judd, C. (eds.) Handbook of Research Methods in Social and Personality Psychology, pp. 40–84. Cambridge University Press, New York (2000)

    Google Scholar 

  64. Cox, M.G., Kisbu-Sakarya, Y., Miočević, M., MacKinnon, D.P.: Sensitivity plots for confounder bias in the single mediator model. Eval. Rev. 37(5), 405–431 (2014)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. The Methodology Center, Pennsylvania State University, 404 Health and Human Development Building, University Park, PA, 16802, USA

    Donna L. Coffman

  2. Department of Psychology, Arizona State University, Tempe, AZ, 85281, USA

    David P. MacKinnon

  3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Yeying Zhu

  4. Department of Biostatistics and Informatics, University of Colorado, Aurora, CO, 80045, USA

    Debashis Ghosh

Authors
  1. Donna L. Coffman
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  2. David P. MacKinnon
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  3. Yeying Zhu
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  4. Debashis Ghosh
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Corresponding author

Correspondence to Donna L. Coffman .

Editor information

Editors and Affiliations

  1. Department of Epidemiology School of Public Health and Tropical Medicine, Tulane University, New Orleans, Louisiana, USA

    Hua He

  2. Christiana Care Health System, Value Institute, Newark, Delaware, USA

    Pan Wu

  3. School of Social Work and Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina, USA

    Ding-Geng (Din) Chen

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Coffman, D.L., MacKinnon, D.P., Zhu, Y., Ghosh, D. (2016). A Comparison of Potential Outcome Approaches for Assessing Causal Mediation. In: He, H., Wu, P., Chen, DG. (eds) Statistical Causal Inferences and Their Applications in Public Health Research. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-41259-7_14

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