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Confounding and Collapsibility in Causal Inference
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Consideration of confounding is fundamental to the design and analysis of studies of causal effects. Yet, apart from confounding in experimental designs, the topic is given little or no discussion in most statistics texts. We here provide an overview of confounding and related concepts based on a counterfactual model for causation. Special attention is given to definitions of confounding, problems in control of confounding, the relation of confounding to exchangeability and collapsibility, and the importance of distinguishing confounding from noncollapsibility.
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“Both models account for potential biases and confounding factors [20, 21].”
From Health and Socio-Economic Impacts of Climate-Related Displacement in Bangladesh’s Chars: Causal Evidence From a Household Survey (2026) · cites this paper as [20]
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“The causal interpretation of the estimated treatment effects relies on the standard identification assumptions used in the program-evaluation literature [16, 20, 21].”
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Lui, K., & Chang, K. (2011) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2010.508139 · Cited by 1
“( 1999 ), who employed counterfactual or potential-outcomes concept to define “confounders.”
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Brumback, B., & He, Z. (2012) · Cited by 1
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Introduction, Objectives, and an Alternative
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Lee, K., & Dominici, F. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.10537 · Cited by 1
“Proposition 1 shows the condition for conditional CORs ψ(x) ≤ ψ∗(x), but this condition cannot be generalized to the marginal COR case due to non-collapsibility (Greenland et al., 1999).”
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Markham, A., Das, R., & Grosse-Wentrup, M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.03480 · Cited by 1
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“The causal interpretation of the estimated treatment effects relies on the standard identification assumptions used in the program-evaluation literature [16, 20, 21].”
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“…(3.4.7) ( ) ( ) 0 1 2 | , log 1 | , i i i i i i i i E Y T U T U E Y T U β β β= + ⋅ + ⋅ − (3.4.8) Both equations (3.4.7) and (3.4.8) are non-collapsible for 1α or 1β over U (Greenland, Robins, and Pearl, 1999), that is, if the unobserved confounder U is omitted in the models, *1 1α α≠ , and * 1 1β…”
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“We have RCOR ≠ RMOR and RCRR ≠ RMRR because the odds ratio and the risk ratio are not collapsible [5, 10, 12, 14].”
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“As clearly proven in many papers (Greenland et al., 1999; Miettinen and Cook, 1981) collapsability is a necessary condition for confounding but not sufficient.”
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Confounding of Three Binary-Variable Counterfactual Model with DAG
Liu, J., & Hu, S. (2013) · Applied Mathematics · doi:10.4236/am.2013.410189
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“…confounding is one of many problems that plague studies of cause and effect, special attention need to be given to definitions of confounding and non confounding, and the relationship between confounding and collapsibility (Greenland et al., 1999; Robins and Morgenstern, 1987; Wang and Gao, 2010).”
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Mascie‐Taylor, C. G. N., & Moji, K. (2001) · Japanese Journal of Health and Human Ecology · doi:10.3861/jshhe.67.248
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Metadata
- Authors
- Greenland, S., Pearl, J., & Robins, J. M.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 1999-02-01
- Volume
- 14
- Issue
- 1
- Pages
- 29-46
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W1996016456
- Cited by
- 933
- References
- 108
- Citations by year
- 2026: 43 · 2025: 47 · 2024: 61 · 2023: 53 · 2022: 65 · 2021: 75 · 2020: 48 · 2019: 40 · 2018: 40 · 2017: 36 · 2016: 35 · 2015: 44 · 2014: 52 · 2013: 47 · 2012: 47
- FWCI
- 13.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Science (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Keywords
- confounding, collapsibility, counterfactual modeling, causal inference, exchangeability, causal effects, observational studies
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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