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Bias Formulas for Sensitivity Analysis for Direct and Indirect Effects
Open accessAbstract
A key question in many studies is how to divide the total effect of an exposure into a component that acts directly on the outcome and a component that acts indirectly, ie, through some intermediate. For example, one might be interested in the extent to which the effect of diet on blood pressure is mediated through sodium intake and the extent to which it operates through other pathways. In the context of such mediation analysis, even if the effect of the exposure on the outcome is unconfounded, estimates of direct and indirect effects will be biased if control is not made for confounders of the mediator-outcome relationship. Often data are not collected on such mediator-outcome confounding variables; the results in this paper allow researchers to assess the sensitivity of their estimates of direct and indirect effects to the biases from such confounding. Specifically, the paper provides formulas for the bias in estimates of direct and indirect effects due to confounding of the exposure-mediator relationship and of the mediator-outcome relationship. Under some simplifying assumptions, the formulas are particularly easy to use in sensitivity analysis. The bias formulas are illustrated by examples in the literature concerning direct and indirect effects in which mediator-outcome confounding may be present.
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Citations
Cites
Baron, R. M., & Kenny, D. A. (1986) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.51.6.1173 · Cited by 91,532
Introduction to Statistical Mediation Analysis
MacKinnon, D. P. (2012) · doi:10.4324/9780203809556 · Cited by 5,618
A general approach to causal mediation analysis.
Imai, K., Keele, L., & Tingley, D. (2010) · Psychological Methods · doi:10.1037/a0020761 · Cited by 4,143
A structural approach to selection bias
Hernán, M. A., Hernández-Díaz, S., & Robins, J. M. (2004) · Epidemiology · doi:10.1097/01.ede.0000135174.63482.43 · Cited by 2,844
Robins, J. (1986) · Mathematical Modelling · doi:10.1016/0270-0255(86)90088-6 · Cited by 2,451
Process Analysis: Estimating Mediation in Treatment Evaluations
Judd, C. M., & Kenny, D. A. (1981) · Evaluation Review · doi:10.1177/0193841x8100500502 · Cited by 2,442
Causal diagrams for empirical research
PEARL, J. (1995) · Biometrika · doi:10.1093/biomet/82.4.669 · Cited by 2,355
Identifiability and exchangeability for direct and indirect effects
Robins, J. M., & Greenland, S. (1992) · Epidemiology · doi:10.1097/00001648-199203000-00013 · Cited by 1,793
On the importance—and the unimportance— of birthweight
Wilcox, A. J. (2001) · International Journal of Epidemiology · doi:10.1093/ije/30.6.1233 · Cited by 889
Conceptual issues concerning mediation, interventions and composition
VanderWeele, T. J., & Vansteelandt, S. (2009) · Statistics and Its Interface · doi:10.4310/sii.2009.v2.n4.a7 · Cited by 758
Self-citationMarginal Structural Models for the Estimation of Direct and Indirect Effects
VanderWeele, T. J. (2009) · Epidemiology · doi:10.1097/ede.0b013e31818f69ce · Cited by 583
Self-citationVanderWeele, T. J., & Arah, O. A. (2010) · Epidemiology · doi:10.1097/ede.0b013e3181f74493 · Cited by 455
Self-citationAssociation, Causation, And Marginal Structural Models
Robins, J. M. (1999) · Synthese · doi:10.1023/a:1005285815569 · Cited by 404
Concerning the Consistency Assumption in Causal Inference
VanderWeele, T. J. (2009) · Epidemiology · doi:10.1097/ede.0b013e3181bd5638 · Cited by 368
Self-citationEstimation of Direct Causal Effects
Petersen, M. L., Sinisi, S. E., & van der Laan, M. J. (2006) · Epidemiology · doi:10.1097/01.ede.0000208475.99429.2d · Cited by 362
The Birth Weight "Paradox" Uncovered?
Hernández–Dı́az, S., Schisterman, E. F., & Hernán, M. Á. (2006) · American Journal of Epidemiology · doi:10.1093/aje/kwj275 · Cited by 357
Computation, Causation, and Discovery
(1999) · AAAI Press eBooks · doi:10.7551/mitpress/2006.001.0001 · Cited by 353
Highly Structured Stochastic Systems
Green, P. J. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 332
Direct and Indirect Causal Effects via Potential Outcomes*
Rubin, D. B. (2004) · Scandinavian Journal of Statistics · doi:10.1111/j.1467-9469.2004.02-123.x · Cited by 324
Past adult lead exposure is associated with longitudinal decline in cognitive function
Schwartz, B. S., Stewart, W. F., Bolla, K. I., Simon, D., Bandeen‐Roche, K., Gordon, B., Links, J. M., & Todd, A. C. (2000) · Neurology · doi:10.1212/wnl.55.8.1144 · Cited by 243
Opening the Black Box: a motivation for the assessment of mediation
Hafeman, D., & Schwartz, S. (2009) · International Journal of Epidemiology · doi:10.1093/ije/dyn372 · Cited by 226
Robins, J. M. (1987) · Computers & Mathematics with Applications · doi:10.1016/0898-1221(87)90238-0 · Cited by 213
Kaufman, J. S., MacLehose, R. F., & Kaufman, S. (2004) · Epidemiologic Perspectives & Innovations · doi:10.1186/1742-5573-1-4 · Cited by 207
Directed Acyclic Graphs, Sufficient Causes, and the Properties of Conditioning on a Common Effect
VanderWeele, T. J., & Robins, J. M. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwm179 · Cited by 198
Self-citationPast adult lead exposure is linked to neurodegeneration measured by brain MRI
Stewart, W. F., Schwartz, B. S., Davatzikos, C. A., Shen, D. G., Liu, D., Wu, X., Todd, A. C., Shi, W., Bassett, S. S., & Youssem, D. (2006) · Neurology · doi:10.1212/01.wnl.0000216138.69777.15 · Cited by 184
Estimating Direct Effects in Cohort and Case–Control Studies
Vansteelandt, S. (2009) · Epidemiology · doi:10.1097/ede.0b013e3181b6f4c9 · Cited by 159
Causal Mediation Analyses with Rank Preserving Models
Have, T. R. T., Joffe, M. M., Lynch, K. G., Brown, G. K., Maisto, S. A., & Beck, A. T. (2007) · Biometrics · doi:10.1111/j.1541-0420.2007.00766.x · Cited by 157
VanderWeele, T. J. (2009) · European Journal of Epidemiology · doi:10.1007/s10654-009-9331-1 · Cited by 146
Self-citationQuantification of collider‐stratification bias and the birthweight paradox
Whitcomb, B. W., Schisterman, E. F., Perkins, N. J., & Platt, R. W. (2009) · Paediatric and Perinatal Epidemiology · doi:10.1111/j.1365-3016.2009.01053.x · Cited by 120
Computation, Causation and Discovery
MTW, Glymour, C., & Copper, G. F. (2000) · Journal of the American Statistical Association · doi:10.2307/2669507 · Cited by 109
Identifying Direct and Indirect Effects in a Non-Counterfactual Framework
Geneletti, S. (2007) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2007.00584.x · Cited by 108
Estimation of Controlled Direct Effects
Goetgeluk, S., Vansteelandt, S., & Goetghebeur, E. (2008) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00673.x · Cited by 104
van der Laan, M. J., & Petersen, M. L. (2008) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1064 · Cited by 100
Mediation analysis with principal stratification
Gallop, R., Small, D. S., Lin, J. Y.-C., Elliott, M. R., Joffe, M. M., & Have, T. R. T. (2009) · Statistics in Medicine · doi:10.1002/sim.3533 · Cited by 94
Simple relations between principal stratification and direct and indirect effects
VanderWeele, T. J. (2008) · Statistics & Probability Letters · doi:10.1016/j.spl.2008.05.029 · Cited by 92
Self-citationDirect and Indirect Effects for Neighborhood-Based Clustered and Longitudinal Data
VanderWeele, T. J. (2010) · Sociological Methods & Research · doi:10.1177/0049124110366236 · Cited by 84
Self-citationJoffe, M. M., Small, D. S., & Hsu, C. (2007) · Cited by 71
Defining and Estimating Intervention Effects for Groups that will Develop an Auxiliary Outcome
Joffe, M. M., Small, D., & Hsu, C.-Y. (2007) · Statistical Science · doi:10.1214/088342306000000655 · Cited by 67
Alternative Assumptions for the Identification of Direct and Indirect Effects
Hafeman, D., & VanderWeele, T. J. (2010) · Epidemiology · doi:10.1097/ede.0b013e3181c311b2 · Cited by 61
Self-citationMinimal sufficient causation and directed acyclic graphs
VanderWeele, T. J., & Robins, J. M. (2009) · The Annals of Statistics · doi:10.1214/08-aos613 · Cited by 52
Self-citationMINIMAL SUFFICIENT CAUSATION AND DIRECTED ACYCLIC GRAPHSPreprint
VanderWeele, T. J., & Robins, J. M. (2009) · Cited by 51
Self-citationCommentary: Estimating direct and indirect effects—fallible in theory, but in the real world?
Blakely, T. A. (2002) · International Journal of Epidemiology · doi:10.1093/ije/31.1.166 · Cited by 45
Sjölander, A., Humphreys, K., Vansteelandt, S., Bellocco, R., & Palmgren, J. (2008) · Biometrics · doi:10.1111/j.1541-0420.2008.01108.x · Cited by 39
Sensitivity Analysis: Distributional Assumptions and Confounding Assumptions
VanderWeele, T. J. (2008) · Biometrics · doi:10.1111/j.1541-0420.2008.01024.x · Cited by 37
Self-citationCaffo, B. S., Chen, S., Stewart, W. F., Bolla, K. I., Yousem, D. M., Davatzikos, C. A., & Schwartz, B. S. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwm326 · Cited by 26
Flagged first, then by citations
Research works printed but not linked: 3
- Pearl, 2001, Proceedings of the Seventeenth Conference on Uncertainty and Artificial Intelligence., 411
- Hafeman, 2008, Opening the Black Box: A Reassessment of Mediation From a Counterfactual Perspective [dissertation].
- Avin, 2005, Proceedings of the International Joint Conferences on Artificial Intelligence., 357
Cited by
Sorted by citations
A general approach to causal mediation analysis.
Imai, K., Keele, L., & Tingley, D. (2010) · Psychological Methods · doi:10.1037/a0020761 · Cited by 4,143
Mediation Analysis: A Practitioner's Guide
VanderWeele, T. J. (2016) · Annual Review of Public Health · doi:10.1146/annurev-publhealth-032315-021402 · Cited by 1,985
Self-citationValeri, L., & VanderWeele, T. J. (2013) · Psychological Methods · doi:10.1037/a0031034 · Cited by 2,132
“If there are confounders of the exposure–outcome, mediator–outcome, or exposure–mediator relationship then, to the extent possible, these should be controlled for in the models; otherwise sensitivity analysis techniques (VanderWeele, 2010; Imai, Keele, & Tingley, 2010) can be used.”
BackgroundMethodInfluentialSelf-citationIdentification, Inference and Sensitivity Analysis for Causal Mediation Effects
Imai, K., Keele, L., & Yamamoto, T. (2010) · Statistical Science · doi:10.1214/10-sts321 · Cited by 1,628
Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable
Elwert, F., & Winship, C. (2014) · Annual Review of Sociology · doi:10.1146/annurev-soc-071913-043455 · Cited by 1,168
Metadata
- Authors
- VanderWeele, T. J.
- Affiliations
- Harvard University (US)
- Corresponding author
- VanderWeele, Tyler J.
- Venue
- Epidemiology
- Published
- 2010-07
- Volume
- 21
- Issue
- 4
- Pages
- 540-551
- ISSN
- 1044-3983 (ISSN-L)
- PMC
- PMC4231822
- OpenAlex
- W2075031358
- Cited by
- 435
- References
- 42
- Citations by year
- 2026: 20 · 2025: 16 · 2024: 15 · 2023: 25 · 2022: 32 · 2021: 28 · 2020: 29 · 2019: 38 · 2018: 21 · 2017: 23 · 2016: 34 · 2015: 32 · 2014: 33 · 2013: 27 · 2012: 34
- FWCI
- 23.96
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of Environmental Health Sciences (R01ES017876)
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (R03HD060696)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- direct and indirect effects, mediation analysis, sensitivity analysis, confounding, bias correction
- MeSH terms
- Brain, Cognition Disorders, Humans, Lead Poisoning, Organ Size, Regression Analysis, Risk Factors, Sensitivity and Specificity, Statistics as Topic, Models, Statistical, Bias
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