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Confounding and Collapsibility in Causal Inference
Open accessAbstract
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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“A regression model is said to be collapsible for a parameter (in this case, the hazard ratio) if the covariate-adjusted parameter is the same as the unadjusted parameter.(24) Second, the IP weighting approach yields standardized survival curve estimates.”
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Noncollapsibility and its role in quantifying confounding bias in logistic regression
Schuster, N. A., Twisk, J. W. R., ter Riet, G., Heymans, M. W., & Rijnhart, J. J. M. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01316-8 · Cited by 61
“confounder‐adjusted exposure effect estimates Multivariable regression adjustment and IPW provide identical exposure effect estimates when based on linear regression, but not when based on logistic regression [15, 27].”
BackgroundMethodInfluentialDrug Shortages Prior to and During the COVID-19 Pandemic
Kim, K. C., Rothenberger, S. D., Tadrous, M., Hernandez, I., Gellad, W. F., Devine, J. W., Hershey, T. B., Maillart, L. M., & Suda, K. J. (2024) · JAMA Network Open · doi:10.1001/jamanetworkopen.2024.4246 · Cited by 60
Best (but oft-forgotten) practices: propensity score methods in clinical nutrition research
Ali, M. S., Groenwold, R. H. H., & Klungel, O. H. (2016) · American Journal of Clinical Nutrition · doi:10.3945/ajcn.115.125914 · Cited by 60
“However, adjustment for other types of variables (intermediates, colliders, and instrumental variables) is unnecessary and may even induce bias (17, 20, 23–26).”
Health Recommendations and Selection in Health Behaviors
Oster, E. F. (2020) · American Economic Review Insights · doi:10.1257/aeri.20190355 · Cited by 58
Rijnhart, J. J. M., Valente, M. J., MacKinnon, D. P., Twisk, J. W. R., & Heymans, M. W. (2020) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2020.1811709 · Cited by 59
“The scale of a logistic path coefficient is dependent on the variables in the model (Greenland et al., 1999; Mood, 2010).”
MethodGarcia Santa Cruz, B., Bossa, M. N., Sölter, J., & Husch, A. D. (2021) · Medical Image Analysis · doi:10.1016/j.media.2021.102225 · Cited by 89
Use of statins is associated with an increased risk of rheumatoid arthritis
de Jong, H. J. I., Klungel, O. H., van Dijk, L., Vandebriel, R. J., Leufkens, H. G. M., van der Laan, J., Tervaert, J. W. C., & Loveren, H. V. (2011) · Annals of the Rheumatic Diseases · doi:10.1136/ard.2011.155622 · Cited by 57
Causal Analysis in the Health Sciences
Greenland, S. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10473924 · Cited by 61
Self-citationSimpkin, A. J., Sayers, A., Gilthorpe, M. S., Heron, J., & Tilling, K. (2017) · Annals of Human Biology · doi:10.1080/03014460.2017.1391877 · Cited by 56
“Therefore, the use of age at PHV estimated by any method in stratum-specific control of confounding should be effective (Greenland et al., 1999).”
MethodGreen, M. J., & Popham, F. (2019) · BMC Public Health · doi:10.1186/s12889-018-6364-y · Cited by 56
“Such a situation might be investigated using a mutually-adjusted regression model of health on education, occupation and income, but the coefficients or odds ratios (ORs) associated with these three SEP measures represent different causal effects [36].”
BackgroundInfluentialInstrumental Variable Estimation with the R Package ivtools
Sjölander, A., & Martinussen, T. (2019) · Epidemiologic Methods · doi:10.1515/em-2018-0024 · Cited by 56
“This bias essentially arises from the non-collapsibility of non-linear effect measures, such as the odds ratio and the hazard ratio (Greenland et al. 1999).”
BackgroundRandomization Does Not Help Much, Comparability Does
Saint‐Mont, U. (2015) · PLoS ONE · doi:10.1371/journal.pone.0132102 · Cited by 55
“es between the groups in one or more of the prognostic factors can occur by chance. [...] At this point the primary objective of randomisation — exclusion of confounding factors — has failed.” 9 (iv) Greenland et al. (1999: 35): [...] random imbalances may be severe, especially if the study size is small [...] (v) Ros…”
BackgroundVermeulen, K., Thas, O., & Vansteelandt, S. (2014) · Statistics in Medicine · doi:10.1002/sim.6386 · Cited by 60
“Even when the model (3) is correctly specified (and thus no treatment-covariate interactions are present), a marginal and conditional log odds ratio β and βA are generally not identical due to non-collapsibility [14].”
BackgroundInfluentialDoi, S. A. R., Furuya‐Kanamori, L., Xu, C., Chivese, T., Lin, L., Musa, O. A. H., Hindy, G., Thalib, L., & Harrell, F. E. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2021.08.003 · Cited by 55
Monte Carlo Simulation Approaches for Quantitative Bias Analysis: A Tutorial
Banack, H. R., Hayes‐Larson, E., & Mayeda, E. R. (2021) · Epidemiologic Reviews · doi:10.1093/epirev/mxab012 · Cited by 54
Learning consistent representations with temporal and causal enhancement for knowledge tracing
Huang, C., Wei, H.-W., Huang, Q., Jiang, F., Han, Z., & Huang, X. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.123128 · Cited by 58
Too many covariates and too few cases? – a comparative study
Chen, Q., Nian, H., Zhu, Y., Talbot, H. K., Griffin, M. R., & Harrell, F. E. (2016) · Statistics in Medicine · doi:10.1002/sim.7021 · Cited by 54
“However, due to non-collapsibility of the odds ratio [25], the PS-based approaches can provide unbiased estimation of the risk difference, but not the adjusted odds ratios [13, 14, 26].”
BackgroundBounding Causal Effects Under Uncontrolled Confounding Using Counterfactuals
MacLehose, R. F., Kaufman, S., Kaufman, J. S., & Poole, C. (2005) · Epidemiology · doi:10.1097/01.ede.0000166500.23446.53 · Cited by 53
An Investigation of the Significance of Residual Confounding Effect
Liang, W., Zhao, Y., & Lee, A. H. (2014) · BioMed Research International · doi:10.1155/2014/658056 · Cited by 53
“According to the epidemiological literature, a confounder must meet the following conditions: (i) being a cause of the disease, or a proxy of cause(s), in unexposed people; (ii) being correlated with exposure in the study population; (iii) not being an intermediate step in the causal pathway between the exposure and t…”
BackgroundKreif, N., Grieve, R., & Sadique, Z. (2012) · Health Economics · doi:10.1002/hec.2806 · Cited by 54
“Under this assumption, the allocation of two individuals, who have similar observed characteristics but are in different treatment arms, can be thought of as effectively at random (Greenland et al., 1999).”
BackgroundCausal Interpretation of Between-Within Models for Twin Research
Sjölander, A., Frisell, T., & Öberg, A. S. (2012) · Epidemiologic Methods · doi:10.1515/2161-962x.1015 · Cited by 51
“Thus, for these links the population effect equals the common subpopulation effect; we say that the mean difference and the log risk ratio are are ‘collapsible’ (Greenland et al, 1999, 1).”
BackgroundA Note on the Noncollapsibility of Rate Differences and Rate Ratios
Sjölander, A., Dahlqwist, E., & Zetterqvist, J. (2015) · Epidemiology · doi:10.1097/ede.0000000000000433 · Cited by 51
On the collapsibility of measures of effect in the counterfactual causal framework
Huitfeldt, A., Stensrud, M. J., & Suzuki, E. (2019) · NORA - Norwegian Open Research Archives · Cited by 51
The formal approach to quantitative causal inference in epidemiology: misguided or misrepresented?
Daniel, R., Stavola, B. L. D., & Vansteelandt, S. (2016) · International Journal of Epidemiology · doi:10.1093/ije/dyw227 · Cited by 62
“Other examples where this approach has led to new insights and/or methods include the low birth weight and obesity “paradoxes” [24–27] (see further discussion in section 3), the comparison of dynamic regimes [28], the impact of measurement error [29, 30], noncompliance in clinical trials [31], distinguishing confoundi…”
On the 12th Day of Christmas, a Statistician Sent to Me . . .
Riley, R. D., Cole, T. J., Deeks, J. J., Kirkham, J. J., Morris, J., Perera, R., Wade, A. M., & Collins, P. G. S. (2022) · BMJ · doi:10.1136/bmj-2022-072883 · Cited by 50
Contribution of physician assistants/associates to secondary care: a systematic review
Halter, M., Wheeler, C., Pelone, F., Gage, H., de Lusignan, S., Parle, J., Grant, R., Gabe, J., Nice, L., & Drennan, V. M. (2018) · BMJ Open · doi:10.1136/bmjopen-2017-019573 · Cited by 51
Mao, H., Li, L., Yang, W. P., & Shen, Y. (2018) · Statistics in Medicine · doi:10.1002/sim.7839 · Cited by 51
Wang, C., Dominici, F., Parmigiani, G., & Zigler, C. M. (2015) · Biometrics · doi:10.1111/biom.12315 · Cited by 46
“In contrast to the special case of linear regression, where the exposure coefficient in the outcome model corresponds to the ACE in certain circumstances (Schafer and Kang, 2008), estimation of ACEs in GLMs differs from estimation of a single model coefficient because of non-collapsibility, that is the fact that the m…”
BackgroundMethodBandoli, G., Palmsten, K. K., Flores, K. F., & Chambers, C. (2016) · Paediatric and Perinatal Epidemiology · doi:10.1111/ppe.12302 · Cited by 48
Marginal or conditional regression models for correlated non‐normal data?
Muff, S., Held, L., & Keller, L. F. (2016) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12623 · Cited by 48
“, 1984; Lee & Nelder, 2004), a phenomenon that is also known as non-collapsibility (Greenland et al., 1999).”
Background
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
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