The DOI matches its Crossref record; 46 of the 46 references it cites were found in a registry or an index.
On the definition of a confounder
Open accessAbstract
The causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence. The literature has not, however, come to any consensus on a formal definition of a confounder, as it has given priority to the concept of confounding over that of a confounder. We consider a number of candidate definitions arising from various more informal statements made in the literature. We consider the properties satisfied by each candidate definition, principally focusing on (i) whether under the candidate definition control for all “confounders” suffices to control for “confounding” and (ii) whether each confounder in some context helps eliminate or reduce confounding bias. Several of the candidate definitions do not have these two properties. Only one candidate definition of those considered satisfies both properties. We propose that a “confounder” be defined as a pre-exposure covariate $C$ for which there exists a set of other covariates $X$ such that effect of the exposure on the outcome is unconfounded conditional on $(X,C)$ but such that for no proper subset of $(X,C)$ is the effect of the exposure on the outcome unconfounded given the subset. We also provide a conditional analogue of the above definition; and we propose a variable that helps reduce bias but not eliminate bias be referred to as a “surrogate confounder.” These definitions are closely related to those given by Robins and Morgenstern [Comput. Math. Appl. 14 (1987) 869–916]. The implications that hold among the various candidate definitions are discussed.
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“A great deal of variability in cellular responses to treatment may be attributable to underlying confounding variation10.”
From Causal identification of single-cell experimental perturbation effects with CINEMA-OT (2023) · cites this paper as [10]
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Cites
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Johnston, R., Jones, K., & Manley, D. (2018) · Quality & Quantity · doi:10.1007/s11135-017-0584-6 · Cited by 1,181
“The result is frequently termed confounding, the situation when the relationship between two variables is distorted because of the strength of the relationships between either one or both of them and a third variable included in the analysis (see, for example, Kish 1959; Morabia 2011; VanderWheele and Shpitser 2013).”
BackgroundTennant, P. W. G., Murray, E. J., Arnold, K. F., Berrie, L., Fox, M. P., Gadd, S. C., Harrison, W. J., Keeble, C. M., Ranker, L. R., Textor, J. C., et al. (2020) · International Journal of Epidemiology · doi:10.1093/ije/dyaa213 · Cited by 1,065
“Competing exposures are not always included in sufficient adjustment sets, unless they are caused by one or more unobserved confounders for which they can serve as a surrogate confounder.(22)”
BackgroundThe contribution of health behaviors to socioeconomic inequalities in health: A systematic review
Petrović, D., de Mestral, C., Bochud, M., Bartley, M., Mika Kivimaki, B., Vineis, P., Mackenbach, J. P., & Stringhini, S. (2018) · Preventive Medicine · doi:10.1016/j.ypmed.2018.05.003 · Cited by 541
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Addressing context dependence in ecology
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“Type: apparent; source: (ii) confounding factors Confounding occurs when two ormore independent variables, X and C, are correlated such that their effects on dependent variable Y cannot be disentangled [40,41].”
Background
Metadata
- Authors
- VanderWeele, T. J., & Shpitser, I.
- Affiliations
- Harvard University (US)
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2013-02-01
- Volume
- 41
- Issue
- 1
- Pages
- 196-220
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- PMC
- PMC4276366
- OpenAlex
- W2067177016
- Cited by
- 268
- References
- 46
- Citations by year
- 2026: 18 · 2025: 23 · 2024: 28 · 2023: 25 · 2022: 23 · 2021: 46 · 2020: 33 · 2019: 20 · 2018: 17 · 2017: 15 · 2016: 11 · 2015: 5 · 2014: 3 · 2013: 1
- FWCI
- 5.87
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- Collection of Biostatistics Research Archive (submittedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- Project Euclid (Cornell University) (submittedVersion)
- ePrints Soton (University of Southampton) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Institutes of Health (ES017876)
- National Institute of Environmental Health Sciences (R01ES017876, R56ES017876)
- 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 and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- confounding, causal inference, unconfoundedness, covariate control
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