A New Criterion for Confounder Selection
Open accessAbstract
We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, "Is the covariate a cause of the treatment?" and "Is the covariate a cause of the outcome?" If the answer to either question is "yes" then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion.
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In Figure 13c, no set of pre-treatment controls is sufficient to identify the causal effect of T on Y, so the VanderWeele and Shpitser rule does not apply.
“In short, there exists no set of pre-treatment controls that is sufficient for identifying the causal effect of T on Y, and hence the VanderWeele & Shpitser (2011) rule does not apply.”
From Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable (2014) · cites this paper as VanderWeele & Shpitser 2011
If the analyst assumes that controlling for some combination of observed pre-treatment variables is sufficient to identify the total causal effect, then it is sufficient to control for all variables that cause treatment or outcome or both.
“If the analyst is willing to assume that controlling for some combination of observed pre-treatment variables is sufficient to identify the total causal effect of treatment, then it is sufficient to control for all variables that (directly or indirectly) cause treatment or outcome or both (VanderWeele & Shpitser 2011).”
From Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable (2014) · cites this paper as VanderWeele & Shpitser 2011
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- Authors
- VanderWeele, T. J., & Shpitser, I.
- Affiliations
- Harvard University (US)
- Corresponding author
- VanderWeele, Tyler J.
- Venue
- Biometrics
- Publisher
- Oxford University Press (OUP)
- Published
- 2011-05-31
- Volume
- 67
- Issue
- 4
- Pages
- 1406-1413
- ISSN
- 0006-341X (ISSN-L)
- PMC
- PMC3166439
- OpenAlex
- W2025309870
- Cited by
- 434
- References
- 36
- Citations by year
- 2026: 25 · 2025: 46 · 2024: 33 · 2023: 47 · 2022: 41 · 2021: 53 · 2020: 59 · 2019: 32 · 2018: 17 · 2017: 25 · 2016: 13 · 2015: 14 · 2014: 10 · 2013: 11 · 2012: 4
- FWCI
- 7.85
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Biometrics (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- ePrints Soton (University of Southampton) (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Institutes of Health
- National Institute of Allergy and Infectious Diseases (R01AI104459)
- National Institute of Environmental Health Sciences (ES017876, R01ES017876, R56ES017876)
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (R03HD060696, HD060696)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Keywords
- confounder selection, confounding adjustment, causal graphs, unconfoundedness, covariate selection, causal structure
- MeSH terms
- Algorithms, Biometry, Computer Simulation, Data Interpretation, Statistical, Epidemiologic Methods, Humans, Numerical Analysis, Computer-Assisted, Risk Factors, Models, Statistical, Confounding Factors, Epidemiologic, Confidence Intervals, Statistical Distributions, Proportional Hazards Models, Outcome Assessment, Health Care, Risk Assessment
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