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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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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-citation
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
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Items 101–200 of 434
Statistical Mediation Analysis
MacKinnon, D. P., & Tofighi, D. (2012) · Wiley eBooks · doi:10.1002/9781118133880.hop202025 · Cited by 58
Who Wants What?: Redistribution Preferences in Comparative Perspective
Rueda, D., & Stegmueller, D. (2019) · Cited by 59
Burrows, S., Auger, N., Gamache, P., St-Laurent, D., & Hamel, D. (2011) · BMC Public Health · doi:10.1186/1471-2458-11-577 · Cited by 57
“We could not adjust for some covariates that could mediate or confound results, such as substance use or psychiatric illness [10,11,14], nor did we test for interaction between exposures and potential mediators [32], hence results from fully adjusted models should not be considered unbiased estimates of direct (unmedi…”
ResultTranslational Epidemiologic Approaches to Understanding the Consequences of Early-Life Exposures
D'Onofrio, B. M., Class, Q. A., Rickert, M. E., Sujan, A. C., Larsson, H., Kuja‐Halkola, R., Sjölander, A., Almqvist, C., Lichtenstein, P., & Öberg, A. S. (2015) · Behavior Genetics · doi:10.1007/s10519-015-9769-8 · Cited by 62
“A structural approach can, however, help identify and avoid erroneous inferences in effect decomposition (VanderWeele 2009, 2010; VanderWeele and Hernandez-Diaz 2011).”
Causal mediation analysis with multiple causally non-ordered mediators
Taguri, M., Featherstone, J. D. B., & Cheng, J. (2015) · Statistical Methods in Medical Research · doi:10.1177/0962280215615899 · Cited by 59
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VanderWeele, T. J., & Hernández–Dı́az, S. (2010) · Paediatric and Perinatal Epidemiology · doi:10.1111/j.1365-3016.2010.01175.x · Cited by 55
Self-citationInterference and Sensitivity Analysis
VanderWeele, T. J., Tchetgen, E. J. T., & Halloran, M. E. (2014) · Statistical Science · doi:10.1214/14-sts479 · Cited by 59
Self-citationKeele, L. J. (2015) · American Journal of Evaluation · doi:10.1177/1098214015594689 · Cited by 55
“Results that become statistically insignificant, or even change signs, with small violations of the assumption are considered to be sensitive and unreliable (see VanderWeele, 2010, for an alternative approach to sensitivity analysis).”
BackgroundDecomposition of the Total Effect in the Presence of Multiple Mediators and Interactions.
Bellavia, A., & Valeri, L. (2018) · American Journal of Epidemiology · doi:10.1093/aje/kwx355 · Cited by 59
“Additional research is also needed to evaluate the robustness of the components to residual confounding, extending current sensitivity-analysis techniques (23, 24) to the specific components of the decomposition.”
BackgroundConcentrated poverty, ambient air pollution, and child cognitive development
Wodtke, G. T., Ard, K. J., Bullock, C., White, K., & Priem, B. (2022) · Science Advances · doi:10.1126/sciadv.add0285 · Cited by 58
“We assess the sensitivity of our results to unobserved confounding by computing bias terms and then using them to construct a set of adjusted point estimates for the NDE and NIE ( 43 , 45 ).”
Nordahl, H., Rod, N. H., Frederiksen, B., Andersen, I., Lange, T., Diderichsen, F., Prescott, E., Overvad, K., & Osler, M. (2012) · European Journal of Epidemiology · doi:10.1007/s10654-012-9745-z · Cited by 53
Tracing Causal Paths from Experimental and Observational Data
Zhou, X., & Yamamoto, T. (2022) · The Journal of Politics · doi:10.1086/720310 · Cited by 57
“This approach can be seen as an extension of the bias formulas developed by VanderWeele (2010) to the setting of multiple causally dependentmediators.”
BackgroundMethodInfluentialA sensitivity analysis for temporal bias in cross-sectional mediation.
Georgeson, A. R., Alvarez-Bartolo, D., & MacKinnon, D. P. (2023) · Psychological Methods · doi:10.1037/met0000628 · Cited by 53
Components of the Indirect Effect in Vaccine Trials
VanderWeele, T. J., Tchetgen, E. J. T., & Halloran, M. E. (2012) · Epidemiology · doi:10.1097/ede.0b013e31825fb7a0 · Cited by 52
Self-citationWeighting-Based Sensitivity Analysis in Causal Mediation Studies
Hong, G., Qin, X., & Yang, F. (2018) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998617749561 · Cited by 51
“The weighting-based bias formula is inherently related to the general form of the bias formula derived by VanderWeele (2010) under treatment randomization.”
BackgroundMethodAttard, S. M., Herring, A. H., Mayer‐Davis, E. J., Popkin, B. M., Meigs, J. B., & Gordon‐Larsen, P. (2012) · Diabetologia · doi:10.1007/s00125-012-2697-8 · Cited by 51
“We did not include BMI in the final models on the basis that it is a causal intermediate on the pathway from urbanisation to diabetes and, as such, could potentially bias results [16].”
BackgroundSchoenaker, D. A. J. M., Soedamah‐Muthu, S. S., & Mishra, G. D. (2016) · American Journal of Clinical Nutrition · doi:10.3945/ajcn.116.133884 · Cited by 50
Glymour, M. M., & Vittinghoff, E. (2013) · Epidemiology · doi:10.1097/ede.0000000000000013 · Cited by 49
Hong, G., Deutsch, J., & Hill, H. D. (2015) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998615583902 · Cited by 49
“If such a posttreatment covariate is unobserved, sensitivity analysis may be employed to assess the consequence of the possible omission (Imai et al., 2010a, 2010b; VanderWeele, 2010).”
Bayesian Inference for the Causal Effect of Mediation
Daniels, M. J., Roy, J. A., Kim, C., Hogan, J. W., & Perri, M. G. (2012) · Biometrics · doi:10.1111/j.1541-0420.2012.01781.x · Cited by 50
“Note that the sequential ignorability assumption is often weakened by including baseline covariates and conducting sensitivity analysis (Imai et al., 2010a; Vanderweele, 2010), which we did not do here.”
BackgroundA Complete Graphical Criterion for the Adjustment Formula in Mediation Analysis
Shpitser, I., & VanderWeele, T. J. (2011) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1297 · Cited by 44
“There are a number of examples in the literature showing this (Imai et al., 2010; Hafeman and VanderWeele, 2010; Robins et al., 2010).”
BackgroundResultInfluentialSelf-citationValeri, L., Reese, S., Zhao, S., Page, C. M., Nystad, W., Coull, B. A., & London, S. J. (2017) · Epigenomics · doi:10.2217/epi-2016-0145 · Cited by 45
Aitken, Z., Simpson, J. A., Gurrin, L. C., Bentley, R., & Kavanagh, A. M. (2017) · International Journal of Epidemiology · doi:10.1093/ije/dyx277 · Cited by 45
Loucks, E. B., Huang, Y., Agha, G., Chu, S. H., Eaton, C. B., Gilman, S. E., Buka, S. L., & Kelsey, K. T. (2016) · Psychosomatic Medicine · doi:10.1097/psy.0000000000000411 · Cited by 44
“Proportion of mediation was calculated as IE / (DE + IE) to indicate the proportion of total effect of SES on BMI mediated through CpG methylation (53); note that the proportion of mediation has plausible interpretation only if both DE and IE are in the same direction.”
MethodAccounting for citizens when explaining open government effectiveness
Porumbescu, G. A., Cucciniello, M., & Gil-García, J. R. (2020) · Government Information Quarterly · doi:10.1016/j.giq.2019.101451 · Cited by 49
“For this reason, sensitivity tests are used (Imai, Keele, Yamamoto 2010; VanderWeele 2010).”
Mumford, S. L., Schisterman, E. F., Siega‐Riz, A. M., Gaskins, A. J., Wactawski‐Wende, J., & VanderWeele, T. J. (2010) · American Journal of Epidemiology · doi:10.1093/aje/kwq388 · Cited by 44
Self-citationZhou, Z., Lin, C., Ma, J., Towne, S. D., Han, Y., & Fang, Y. (2019) · American Journal of Epidemiology · doi:10.1093/aje/kwz099 · Cited by 42
Flexible Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula
Loeys, T., Moerkerke, B., Smet, O. D., Buysse, A., Steen, J., & Vansteelandt, S. (2013) · Multivariate Behavioral Research · doi:10.1080/00273171.2013.832132 · Cited by 44
“VanderWeele and Vansteelandt (2009) relaxed the latter assumption and derived closed-form expressions for the direct and indirect effect in the presence of interactions in linear models.”
BackgroundMethodInfluentialUsing mediation analysis to identify causal mechanisms in disease management interventions
Linden, A., & Karlson, K. B. (2013) · Health Services and Outcomes Research Methodology · doi:10.1007/s10742-013-0106-5 · Cited by 45
Identification of operating mediation and mechanism in the sufficient-component cause framework
Suzuki, E., Yamamoto, E., & Tsuda, T. (2011) · European Journal of Epidemiology · doi:10.1007/s10654-011-9568-3 · Cited by 42
Forastiere, L., Mealli, F., & VanderWeele, T. J. (2015) · Journal of the American Statistical Association · doi:10.1080/01621459.2015.1125788 · Cited by 40
“…different techniques such as © American Statistical Association instrumental variables (Dunn and Bentall 2007; Ten Have et al. 2007; Albert 2008; Small 2012), sensitivity analysis (Imai, Keele, and Yamamoto 2010; VanderWeele 2010a), or Principal Stratification (PS; Frangakis and Rubin 2002).”
BackgroundMethodSelf-citationLiu, S., Ulbricht, C. M., Chrysanthopoulou, S. A., & Lapane, K. L. (2016) · BMC Research Notes · doi:10.1186/s13104-016-2163-7 · Cited by 41
Yu, Y., Liew, Z., Wang, A., Arah, O. A., Li, J., Olsen, J., Cnattingius, S., Qin, G., Obel, C., Fu, B., et al. (2019) · PLoS Medicine · doi:10.1371/journal.pmed.1002831 · Cited by 38
“We performed a sensitivity analysis to assess and adjust for violations of the uncontrolled confounding assumption [23,29].”
BackgroundMethodSensitivity analyses for parametric causal mediation effect estimation
Albert, J. M., & Wang, W. (2014) · Biostatistics · doi:10.1093/biostatistics/kxu048 · Cited by 38
Comparing Alternative Corrections for Bias in the Bias-Corrected Bootstrap Test of Mediation
Chen, D., & Fritz, M. S. (2021) · Evaluation & the Health Professions · doi:10.1177/01632787211024356 · Cited by 37
Leung, B. M. Y., McDonald, S., Kaplan, B. J., Giesbrecht, G. F., & Tough, S. (2013) · BMC Medical Research Methodology · doi:10.1186/1471-2288-13-149 · Cited by 37
“Despite some overrepresentation of higher SES, there was wide variability within the predictors and outcomes, which did not affect each study’s ability to address its research (outcome) questions [13]: in the case of APrON, the relationship between nutrition and maternal mental health, or in the case of AOB, factors r…”
BackgroundParental Smoking and Risk of Childhood-onset Type 1 Diabetes
Magnus, M. C., Tapia, G., Olsen, S. F., Granström, C., Mårild, K., Ueland, P. M., Midttun, Ø., Svensson, J., Johannesen, J., Skrivarhaug, T., et al. (2018) · Epidemiology · doi:10.1097/ede.0000000000000911 · Cited by 38
A Framework for Bayesian Nonparametric Inference for Causal Effects of Mediation
Kim, C., Daniels, M. J., Marcus, B. H., & Roy, J. A. (2016) · Biometrics · doi:10.1111/biom.12575 · Cited by 38
“For example, VanderWeele (2010) reviews assumptions for the identification of natural direct and indirect effects and states that if those assumptions hold and (semi-) parametric regression models are correctly specified (which are part of uncheckable assumptions), then the natural direct and…”
BackgroundBayesGmed: An R-package for Bayesian causal mediation analysis
Yimer, B. B., Lunt, M., Beasley, M., Macfarlane, G. J., & McBeth, J. (2023) · PLoS ONE · doi:10.1371/journal.pone.0287037 · Cited by 36
“Several methods have been proposed in the literature to explore the sensitivity of causal effect estimates to unmeasured confounding [5, 30, 31].”
BackgroundKoshiol, J. E., Castro, F. A., Kemp, T. J., Gao, Y.-T., Roa, J. C., Wang, B., Nogueira, L., Araya, J. C., Shen, M.-C., Rashid, A., et al. (2016) · Cytokine · doi:10.1016/j.cyto.2016.05.003 · Cited by 37
“Similarly, CCL2 and CXCL8 interact synergistically to maximize leukocyte chemotaxis [31], and a recent study found that SAA1 induces a chemotactic cascade, of which CXCL8 is part, leading to prolonged leukocyte attraction [32].”
BackgroundSources of confounding in life course epidemiology
Santos, S., Zugna, D., Pizzi, C., & Richiardi, L. (2018) · Journal of Developmental Origins of Health and Disease · doi:10.1017/s2040174418000582 · Cited by 36
Grätz, M. (2022) · Quality & Quantity · doi:10.1007/s11135-021-01310-8 · Cited by 43
“13 The literature on sensitivity analysis aims to quantify how large the bias through unobserved variables has to be to change conclusions based on selection on observed variables approaches (Hong et al. 2018; Imai et al. 2010; Imbens 2003; VanderWeele 2010; VanderWeele and Chiba 2014).”
BackgroundHow, and For Whom, Does Higher Education Increase Voting?
Ahearn, C. E., Brand, J. E., & Zhou, X. (2022) · Research in Higher Education · doi:10.1007/s11162-022-09717-4 · Cited by 38
“Specifically, we use the bias factor approach developed by VanderWeele (2010) and VanderWeele & Arah (2011) (see Brand et al. (2019) for a recent application).”
MethodThat’s a lot to Process! Pitfalls of Popular Path ModelsPreprint
Rohrer, J. M., Hünermund, P., Arslan, R. C., & Elson, M. (2021) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/paeb7 · Cited by 42
Interventional Approach for Path-Specific Effects
Lin, S., & VanderWeele, T. J. (2017) · Journal of Causal Inference · doi:10.1515/jci-2015-0027 · Cited by 36
Self-citationLiu, X., & Wang, L. (2020) · Psychological Methods · doi:10.1037/met0000345 · Cited by 39
Mediation Analysis With Multiple Versions of the Mediator
VanderWeele, T. J. (2012) · Epidemiology · doi:10.1097/ede.0b013e31824d5fe7 · Cited by 34
Self-citationDevelopmental Origins of Cardiovascular Disease
Yeung, E. H., Robledo, C. A., Boghossian, N. S., Zhang, C., & Mendola, P. (2014) · Current Epidemiology Reports · doi:10.1007/s40471-014-0006-4 · Cited by 37
“Using more current epidemiologic methods [15], a recent analysis demonstrated that the negative association between birth weight and blood pressure after adjustment for current weight is unlikely to be caused by controlling for the possible intermediate of current weight [16].”
MethodCommentary: Resolutions of the birthweight paradox: competing explanations and analytical insights
VanderWeele, T. J. (2014) · International Journal of Epidemiology · doi:10.1093/ije/dyu162 · Cited by 34
“However, we can use sensitivity analysis techniques to assess how such unmeasured confounding might change estimates.(15) If an unmeasured confounder U had: a prevalence of 2% among the smoking and non-smoking mothers with normal birthweight infants; a prevalence of 3% among smoking mothers with low birthweight infant…”
Self-citationOn Partial Versus Full Mediation and the Importance of Effect Sizes
Ledermann, T., Rudaz, M., & Fritz, M. S. (2025) · Advances in Methods and Practices in Psychological Science · doi:10.1177/25152459251355585 · Cited by 48
“Omitting a mediator or a confounder of one of the direct effects violates the no-omitted-variable assumption (e.g., Fritz et al., 2016; Tofighi & Kelley, 2016; VanderWeele, 2010).”
Huang, J. Y., Gavin, A. R., Richardson, T. S., Rowhani‐Rahbar, A., Siscovick, D. S., & Enquobahrie, D. A. (2015) · American Journal of Epidemiology · doi:10.1093/aje/kwv148 · Cited by 32
“To assess the robustness of model 3 to unmeasured confounding, we simulated the influence of a hypothetical binary mediator-outcome confounder (22, 41).”
ResultLee, C., Park, S., & Boylan, J. M. (2020) · The Journals of Gerontology Series B · doi:10.1093/geronb/gbaa208 · Cited by 33
“To assess the robustness of results to potential violations of the conditional ignorability assumption, we examined the extent to which an unmeasured confounder would have to affect both the mediator and the outcome to invalidate our findings (VanderWeele, 2010).”
ResultFujii, R., Sato, S., Tsuboi, Y., Cárdenas, A., & Suzuki, K. A. O. (2021) · Epigenetics · doi:10.1080/15592294.2021.1959736 · Cited by 33
“Sensitivity analyses have been proposed to assess the degree of bias [39,47] from stringent assumptions of mediation analysis.”
BackgroundAfrican American Race and HIV Virological Suppression: Beyond Disparities in Clinic Attendance
Howe, C. J., Napravnik, S., Cole, S. R., Kaufman, J. S., Adimora, A. A., Elston, B., Eron, J. J., & Mugavero, M. J. (2014) · American Journal of Epidemiology · doi:10.1093/aje/kwu069 · Cited by 33
“Although methods are available to assess the sensitivity of estimates for controlled direct effects to unmeasured sources of confounding bias of the mediatoroutcome relationship, such methods are not applicable in the settings explored here, inwhich the exposure determines common causes of the mediator and outcome (28…”
MethodWang, T., Li, H.-K., Su, P., Yu, Y.-Y., Sun, X.-R., Liu, Y., Yuan, Z.-S., & Xue, F.-Z. (2017) · BMJ Open · doi:10.1136/bmjopen-2016-015640 · Cited by 31
“Furthermore, the effect of adjusting for M was equal to the controlled direct effect.(19) Therefore, the bias of adjusting for the mediator using the logistic regression model could be obtained that is”
MethodDearing, E., & Zachrisson, H. D. (2019) · Child Development Perspectives · doi:10.1111/cdep.12343 · Cited by 32
Latent Class Mediation: A Comparison of Six Approaches
Hsiao, Y., Kruger, E. S., Horn, M. L. V., Tofighi, D., MacKinnon, D. P., & Witkiewitz, K. A. (2020) · Multivariate Behavioral Research · doi:10.1080/00273171.2020.1771674 · Cited by 32
“There are, however, more accurate methods to test mediation using a variety of different approaches, such as the difference in coefficients, product of coefficients (MacKinnon et al., 2002) and methods from the causal inference literature (Imai et al., 2010; VanderWeele, 2010).”
MethodCausal Mediation Analysis in the Multilevel Intervention and Multicomponent Mediator Case
Zheng, C., & Zhou, X. (2014) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12082 · Cited by 32
“One possible way to deal with the sequential ignorability assumption is to perform sensitivity analysis to evaluate how sensitive the result is to the violation of this assumption (VanderWeele, 2010; Imai et al., 2010; Tchetgen and Shpitser, 2012).”
BackgroundLindmark, A., de Luna, X., & Eriksson, M. (2018) · Statistics in Medicine · doi:10.1002/sim.7620 · Cited by 33
Chioléro, A., Paradis, G., & Kaufman, J. S. (2013) · American Journal of Epidemiology · doi:10.1093/aje/kwt228 · Cited by 31
“We used the method recently developed by VanderWeele (12, 16).”
InfluentialLemon, L. S., Naimi, A. I., Caritis, S. N., Platt, R. W., Venkataramanan, R., & Bodnar, L. M. (2018) · Paediatric and Perinatal Epidemiology · doi:10.1111/ppe.12443 · Cited by 31
Neurodevelopmental outcomes in children in relation to placental abruption
Ananth, C., Friedman, A., Lavery, J., VanderWeele, T., Keim, S., & Williams, M. (2017) · BJOG: An International Journal of Obstetrics & Gynaecology · doi:10.1111/1471-0528.14049 · Cited by 30
Self-citationGoldsmith, K., Chalder, T., White, P. D., Sharpe, M., & Pickles, A. R. (2016) · Statistical Methods in Medical Research · doi:10.1177/0962280216666111 · Cited by 31
Sensitivity Analysis of Linear Structural Causal Models
Cinelli, C., Kumor, D. R., Chen, B., Pearl, J., & Bareinboim, E. (2019) · International Conference on Machine Learning · Cited by 30
Deconstructing the smoking-preeclampsia paradox through a counterfactual framework
Luque-Fernández, M. Á., Zoëga, H., Valdimarsdóttir, U. A., & Williams, M. A. (2016) · European Journal of Epidemiology · doi:10.1007/s10654-016-0139-5 · Cited by 30
“Finally, to address this bias, we developed a sensitivity analysis to assess how such an unmeasured common cause (U) of the intermediate (M) and the outcome (Y) might affect the total effect estimated [26, 27, 36].”
Obesity and Periodontal Outcomes: A Population‐Based Cohort Study in Brazil
Nascimento, G. G., Peres, K. G., Mittinty, M., Mejía, G. C., Silva, D. A. S., González‐Chica, D. A., & Peres, M. A. (2016) · Journal of Periodontology · doi:10.1902/jop.2016.160361 · Cited by 29
Bayesian sensitivity analysis for unmeasured confounding in causal mediation analysis
McCandless, L. C., & Somers, J. M. (2017) · Statistical Methods in Medical Research · doi:10.1177/0962280217729844 · Cited by 30
“The approach is a natural Bayesian extension of the methodology of VanderWeele.(9,10) It has the unique advantage that it is able to simultaneously assess unmeasured mediator–outcome, exposure–outcome and exposure–mediator confounding.”
Johannessen, A., Lønnebotn, M., Calciano, L., Benediktsdóttir, B., Bertelsen, R. J., Bråbäck, L., Dharmage, S. C., Franklin, K. A., Gíslason, Þ., Holm, M., et al. (2019) · Journal of Allergy and Clinical Immunology · doi:10.1016/j.jaci.2019.08.030 · Cited by 30
Estimation of Direct and Indirect Effects
Vansteelandt, S. (2012) · Wiley series in probability and statistics · doi:10.1002/9781119945710.ch11 · Cited by 31
Weighting Methods for Assessing Policy Effects Mediated by Peer Change
Hong, G., & Nomi, T. (2012) · Journal of Research on Educational Effectiveness · doi:10.1080/15348431.2012.688421 · Cited by 31
“If the relationship between class peer ability and math achievement could have been confounded by an omitted covariate, sensitivity analysis may be employed to assess the consequence of such an omission (Imai, Keele, & Tingley, 2010; Imai, Keele, & Yamamoto, 2010; VanderWeele, 2010).”
MethodTrani, J., Ballard, E., & Peña, J. B. (2016) · Social Science & Medicine · doi:10.1016/j.socscimed.2016.02.024 · Cited by 29
Yang, L., Lu, X., Deng, J., Zhou, Y., Huang, D., Qiu, F., Yang, X., Yang, R., Fang, W., Ran, P., et al. (2014) · Cancer Causes & Control · doi:10.1007/s10552-014-0475-2 · Cited by 29
“Thus, some omitted possible confounders might lead to biased estimates and incorrect results on the mediation effect of COPD [49].”
Sensitivity Analysis of the No-Omitted Confounder Assumption in Latent Growth Curve Mediation Models
Tofighi, D., Hsiao, Y., Kruger, E. S., MacKinnon, D. P., Horn, M. L. V., & Witkiewitz, K. A. (2018) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2018.1506925 · Cited by 28
“…analysis for (a) single mediator model, an example of which is depicted in Figure 2 (Cox et al., 2013; Imai et al., 2010; Valente et al., 2017; VanderWeele, 2010); (b) multiple mediator model with two mediators that were assumed to be independent, which makes a strong causal assumption about…”
BackgroundMethodInfluentialBécares, L. (2014) · Health & Place · doi:10.1016/j.healthplace.2014.09.010 · Cited by 28
Auger, N., Gilbert, N. L., Naimi, A. I., & Kaufman, J. S. (2014) · International Journal of Epidemiology · doi:10.1093/ije/dyu011 · Cited by 26
Lindmark, A., Norrving, B. G., & Eriksson, M. (2020) · BMC Public Health · doi:10.1186/s12889-020-08629-1 · Cited by 26
Causal inference challenges in social epidemiology: Bias, specificity, and imagination
Glymour, M. M., & Rudolph, K. E. (2016) · Social Science & Medicine · doi:10.1016/j.socscimed.2016.07.045 · Cited by 25
Yuan, M., Qin, F., Zhou, Z., & Fang, Y. (2021) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2021.105079 · Cited by 25
Assessing Omitted Confounder Bias in Multilevel Mediation Models
Tofighi, D., & Kelley, K. (2016) · Multivariate Behavioral Research · doi:10.1080/00273171.2015.1105736 · Cited by 25
“…Preacher, 2011; Tofighi & Thoemmes, 2014), (c) can test whether the Level 2 indirect effect differs from the Level 1 indirect effect (Marsh, 1987; Marsh, Kuyper, Morin, Parker, & Seaton, 2014; Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005; Pituch & Stapleton, 2012), and (d) can test whether…”
BackgroundInfluentialSales, A. (2016) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998616670371 · Cited by 24
“The focus of mediation ’s sensitivity analysis on mediator-outcome confounding, such as U 2 , follows most of the causal mediation literature—though an appendix of VanderWeele (2010) provides a method for treatment-mediator confounding.”
MethodEstimation of a semiparametric natural direct effect model incorporating baseline covariates
Tchetgen, E. J. T., & Shpitser, I. (2014) · Biometrika · doi:10.1093/biomet/asu044 · Cited by 25
“VanderWeele (2010) postulates the existence of an unmeasured confounder U, possibly vector valued, which when included in X recovers the sequential ignorability assumption.”
InfluentialHsiao, Y.-Y., Tofighi, D., Kruger, E. S., Lee Van Horn, M., MacKinnon, D. P., & Witkiewitz, K. (2019) · Mindfulness · doi:10.1007/s12671-018-1023-z · Cited by 23
“There is a large statistical literature on the importance of examining potential confounding and whether there is evidence that assumption of no omitted variables for mediation models is supported (Judd & Kenny, 1981; MacKinnon, 2008; Valeri & Vanderweele, 2013; VanderWeele, 2010).”
BackgroundThe role of frailty in the association between depression and fall risk among older adults
Lohman, M. C., Mezuk, B. R., Fairchild, A. J., Resciniti, N. V., & Merchant, A. T. (2021) · Aging & Mental Health · doi:10.1080/13607863.2021.1950616 · Cited by 27
“We recalculated parameter estimates assuming either no unmeasured confounders, a moderate unmeasured confounder (ORfalls = 1.5) or a strong unmeasured confounder (ORfalls = 5.0) and then compared these estimates qualitatively (Ding & Vanderweele, 2016; VanderWeele, 2010).”
BackgroundResultInfluentialHarris, H. R., Guertin, K. A., Camacho, T. F., Johnson, C. E., Wu, A. H., Moorman, P. G., Myers, E. R., Bethea, T. N., Bandera, E. V., Joslin, C. E., et al. (2022) · International Journal of Cancer · doi:10.1002/ijc.34141 · Cited by 23
Mediators of First- Versus Second-generation Antipsychotic-related Mortality in Older Adults
Jackson, J. W., VanderWeele, T. J., Blacker, D., & Schneeweiß, S. (2015) · Epidemiology · doi:10.1097/ede.0000000000000321 · Cited by 23
Self-citationValdes, A. M., Louca, P., Visconti, A., Asnicar, F., Bermingham, K. M., Nogal, A., Wong, K. E., Michelotti, G. A., Wolf, J., Segata, N., et al. (2024) · BMC Medicine · doi:10.1186/s12916-024-03543-4 · Cited by 22
“We used Vanderweele’s sensitivity analysis [37, 38] to evaluate the robustness of the estimated mediation effects to unmeasured confounding.”
MethodAttendance, Completion, and Heterogeneous Returns to College: A Causal Mediation Approach
Zhou, X. (2022) · Sociological Methods & Research · doi:10.1177/00491241221113876 · Cited by 24
“For a generic causal mediation analysis, VanderWeele and Arah (2011) and VanderWeele (2010) introduced a bias factor approach for assessing the sensitivity of estimated total, direct, and indirect effects to unobserved confounding.”
Lohman, M. C., Fairchild, A. J., & Merchant, A. T. (2020) · The Journals of Gerontology Series A · doi:10.1093/gerona/glaa253 · Cited by 22
“First, to gauge the potential effects of unmeasured confounding, we estimated causal mediation models under different unobserved confounding scenarios—none, moderate, and strong— corresponding to the degree of association between a hypothetical unmeasured confounder and the outcome (43,44).”
BackgroundShih, S., Huang, Y., & Yang, H. (2018) · Genetic Epidemiology · doi:10.1002/gepi.22120 · Cited by 21
“Because only the effect through alcohol consumption was significant in model 1, we used the sensitivity method to understand the biased effects through one mediator (VanderWeele, 2010).”
MethodPeres, M. A., Nascimento, G. G., Peres, K. G., Demarco, F. F., & Menezes, A. M. B. (2017) · Community Dentistry And Oral Epidemiology · doi:10.1111/cdoe.12350 · Cited by 23
Lutz, S. M., Thwing, A., Schmiege, S. J., Kroehl, M., Baker, C. D., Starling, A. P., Hokanson, J. E., & Ghosh, D. (2017) · BMC Bioinformatics · doi:10.1186/s12859-017-1749-y · Cited by 20
Challenges in Systematic Reviews and Meta-Analyses of Mediation Analyses
Vo, T., & Vansteelandt, S. (2022) · American Journal of Epidemiology · doi:10.1093/aje/kwac028 · Cited by 20
CoCoA-diff: counterfactual inference for single-cell gene expression analysis
Park, Y., & Kellis, M. (2021) · Genome biology · doi:10.1186/s13059-021-02438-4 · Cited by 18
A Bayesian semiparametric latent variable approach to causal mediation
Kim, C., Daniels, M. J., Li, Y., Milbury, K., & Cohen, L. G. (2017) · Statistics in Medicine · doi:10.1002/sim.7572 · Cited by 20
Huber, M. (2020) · Springer eBooks · doi:10.1007/978-3-319-57365-6_162-1 · Cited by 23
Ogburn, E. L. (2012) · PubMed · Cited by 20
Chen, S., Wang, X., Lee, B. K., & Gardner, R. M. (2023) · BMC Medicine · doi:10.1186/s12916-023-03116-x · Cited by 19
“First, though we have considered several potential confounders, results of direct and indirect effects could still be biased due to unmeasured confounders [47, 49, 61], such as genetic factors.”
BackgroundChanges in Memory before and after Stroke Differ by Age and Sex, but Not by Race
Wang, Q., Mejía‐Guevara, I., Rist, P. M., Walter, S., Capistrant, B. D., & Glymour, M. M. (2014) · Cerebrovascular Diseases · doi:10.1159/000357557 · Cited by 19
A Weighting Method for Assessing Between-Site Heterogeneity in Causal Mediation Mechanism
Qin, X., & Hong, G. (2017) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998617694879 · Cited by 19
“This assumption also requires that there is no posttreatment covariate that confounds the mediator–outcome relationship (Avin, Shpitser, & Pearl, 2005; VanderWeele, 2010b; Vanderweele et al., 2013).”
BackgroundMethodInfluentialCausal Mediation Analysis with Multiple Time-varying Mediators
Tai, A., Lin, S., Chu, Y.-C., Yu, T., Puhan, M. A., & VanderWeele, T. J. (2022) · Epidemiology · doi:10.1097/ede.0000000000001555 · Cited by 18
Self-citation
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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