Cited by 933Advanced Causal Inference TechniquesStatistical Methods in EpidemiologyPhilosophy of Biology and Scientific Explanation

The DOI matches its Crossref record; 99 of the 108 references it cites were found in a registry or an index.

Confounding and Collapsibility in Causal Inference

Open access

Greenland, Sander, Pearl, Judea, Robins, James M.·1999·Statistical Science

DOI 10.1214/ss/1009211805

Open this paper in CoChat — free account Open PDF

Abstract

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.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1214/ss/1009211805

Cites

99 of 99 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

The central role of the propensity score in observational studies for causal effects
ROSENBAUM, P. R., & RUBIN, D. B. (1983) · Biometrika · doi:10.1093/biomet/70.1.41 · Cited by 31,241
Specification Tests in Econometrics
Hausman, J. A. (1978) · Econometrica · doi:10.2307/1913827 · Cited by 18,820
A Treatise of Human Nature
Hume, D. A. (1739) · Cambridge University Press eBooks · doi:10.1017/cbo9780511620409.040 · Cited by 9,910
The Statistical Analysis of Failure Time Data.
Aitkin, M. A., Kalbfleisch, J. D., & Prentice, R. L. (1981) · Biometrics · doi:10.2307/2530581 · Cited by 9,875
Estimating causal effects of treatments in randomized and nonrandomized studies
Rubin, D. B. (1974) · Journal of Educational Psychology · doi:10.1037/h0037350 · Cited by 9,436
Statistics and Causal Inference
Holland, P. W. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478354 · Cited by 5,293
Discrete Multivariate Analysis: Theory and Practice.
Beniger, J. R., Bishop, Y. M. M., Feinberg, S. E., Holland, P. W., Light, R. J., & Mosteller, F. C. (1975) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2063625 · Cited by 5,119
Design of Experiments
Fisher, R. A. (1936) · BMJ · doi:10.1136/bmj.1.3923.554-a · Cited by 4,980
Causal Diagrams for Epidemiologic Research
Greenland, S., Pearl, J., & Robins, J. M. (1999) · Epidemiology · doi:10.1097/00001648-199901000-00008 · Cited by 3,728
Self-citation
Air Pollution and Hospital Admissions for Heart Disease in Eight U.S. Counties
Schwartz, J. D. (1999) · Epidemiology · doi:10.1097/00001648-199901000-00005 · Cited by 3,045

Show all 108 references

Research works printed but not linked: 9

Clayton, D. and Hills, M. (1993). Statistical Models in Epidemiology. Oxford Univ. Press.
Feynman, R. P. (1963). Lectures on Physics. Addison-Wesley, Reading, MA.
Gail, M. H. (1986). Adjusting for covariates that have the same distribution in exposed and unexposed cohorts. In Modern Statistical Methods in Chronic Disease Epidemiology (S. H. Moolgavkar, and R. L. Prentice, eds.) 3-18. Wiley, New York.
MacMahon, B. and Pugh, T. F. (1967). Causes and entities of disease. In Preventive Medicine (D. W. Clark and B. MacMahon, eds.) 11-18. Little Brown, Boston.
McKechnie, J. L. (ed.) (1979). Webster's New Twentieth Century Dictionary. Simon and Schuster, New York.
Neyman, J. (1935). Statistical problems in agricultural experimentation (with discussion). J. Roy. Statist. Soc. Suppl. 2 107-180. · DOI
Pearl, J. and Robins, J. M. (1995). Probabilitic evaluation of sequential plans from causal model with hidden variables. In Uncertainty in Artificial Intelligence (P. Besnard and S. Hanks, eds.) 11 444-453. Morgan-Kaufman, San Francisco.
Robins, J. M. (1998). Correction for non-compliance in equivalence trials. Statistics in Medicine 17 269-302. · DOI
Rothman, K. J. and Greenland, S. (1998). Modern Epidemiology, 2nd ed. Lippincott-Raven, Philadelphia.

Sorted by citations

Items 601–700 of 933

Satisfaction Among LGBTQIA+ Individuals with Gender, Sex, and Sexuality Survey Questions
Mesalles, V., Lepore, N., Morelli, A., Magee, L., Siswandjo, J., & Harel, D. (2025) · Journal of Homosexuality · doi:10.1080/00918369.2025.2507884 · Cited by 3
“…effect and reduces residual variance in the regression model, if an ordinal logistic regression model were to be used, we would encounter issues of non-collapsibility of the odds ratios and complicate the interpretations of the model coefficients (Greenland & Pearl, 2011; Greenland et al., 1999).”
Accounting for Misclassification of Binary Outcomes in External Control Arm Studies for Unanchored Indirect Comparisons: Simulations and Applied Example
Nourredine, M., Gavoille, A., Lepage, C., Kassaï, B., Cucherat, M., & Subtil, F. (2025) · Statistics in Medicine · doi:10.1002/sim.70236 · Cited by 3
COADVISE: covariate adjustment with variable selection in randomized controlled trials
Liu, Y., Zhu, K., Han, L., & Yang, S. (2025) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1093/jrsssa/qnaf171 · Cited by 4
“In contrast, the “finite-population” framework (Bloniarz et al., 2016; Greenland et al., 1999; Schochet, 2010; Stuart et al., 2011) is applicable when focusing on the ATE for a policy applied to a fixed number of units, such as the states in the U.S., where the number of units is finite and fixed.”
Illustration of the Impact of Unmeasured Confounding Within an Economic Evaluation Based on Nonrandomized Data
Guertin, J. R., Bowen, J. M., Rose, G. D., O’Reilly, D. J., & Tarride, J. (2017) · MDM Policy & Practice · doi:10.1177/2381468317697711 · Cited by 3
Controlling for confounding via propensity score methods can result in biased estimation of the conditional AUC: A simulation study
Galadima, H. I., & McClish, D. K. (2019) · Pharmaceutical Statistics · doi:10.1002/pst.1948 · Cited by 3
“This result is consistent with results regarding other nonlinear models such as logistic and proportional hazards regression, particularly when not all covariates associated with Y (outcome) are included.(9,14,24,25) Brumback et al developed an approach to control for covariates when the covariate of interest, X, is d…”
Result
Investigating the Performance of Propensity Score Approaches for Differential Item Functioning Analysis
Liu, Y., Kim, C., Wu, A. D., Gustafson, P., Kroc, E., & Zumbo, B. D. (2020) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1556669280 · Cited by 3
“(e.g., Yule, 1903; Cohen & Nagel, 1934; Greenland et al., 1999; Greenland & Pearl, 2011).”
Shoulder Range of Motion Measurements and Baseball Elbow Injuries: Ambiguity in Scientific Models, Approach, and Execution is Hurting Overhead Athlete Health
Bullock, G. S., Thigpen, C. A., Martin, C. L., Losciale, J. M., Michener, L. A., Whiteley, R. J., Waterman, B. R., Tokish, J. M., Camp, C. L., & Shanley, E. (2022) · Arthroscopy Sports Medicine and Rehabilitation · doi:10.1016/j.asmr.2022.11.001 · Cited by 3
“, confounders) and other research biases (Table 1).(30) Causal factors can be used to identify potential interventions.”
Background
Detecting multiple confounders
Wang, X., Geng, Z., Chen, H., & Xie, X. (2008) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2008.06.013 · Cited by 3
Relationships between Linear Statistical Models
Panov, V. G., & Вараксин, А. Н. (2015) · British Journal of Mathematics & Computer Science · doi:10.9734/bjmcs/2015/20493 · Cited by 3
Adjusting for abstinence time in semen analyses: some considerations
Michels, K. A., Kim, K., Yeung, E. H., Plowden, T. C., Chaljub, E. N., Lu, Y., & Mumford, S. L. (2016) · Andrology · doi:10.1111/andr.12285 · Cited by 3
“Causal diagrams are also a great tool to visualize the relationships between abstinence time, an exposure, and an outcome (Greenland et al., 1999a).”
Background
Safety profiles of non-small cell lung cancer patients treated with pemetrexed plus carboplatin: a real-world retrospective, observational, cohort study
Chen, L., Antonio, B. S., Yan, Y., Chen, J., Goodloe, R., & John, W. J. (2017) · Current Medical Research and Opinion · doi:10.1080/03007995.2017.1297700 · Cited by 3
Unopposed estrogen and endometrial cancer: association or causation?
LaCroix, A. Z., Šimunić, V., & Vukičević, S. (2019) · Croatian Medical Journal · doi:10.3325/cmj.2019.60.389 · Cited by 3
Inferential Pluralism in Causal Reasoning from Randomized Experiments
Baetu, T. M. (2022) · Acta Biotheoretica · doi:10.1007/s10441-022-09446-2 · Cited by 3
Validity and bias in epidemiological research
Greenland, S., & VanderWeele, T. J. (2015) · doi:10.1093/med/9780199661756.003.0116 · Cited by 3
Self-citation
Response to Comment on: “Black Box Prediction Methods in Sports Medicine Deserve a Red Card for Reckless Practice: A Change of Tactics is Needed to Advance Athlete Care”
Bullock, G. S., Hughes, T., Arundale, A. J. H., Ward, P., Collins, P. G. S., & Kluzek, S. (2022) · Sports Medicine · doi:10.1007/s40279-022-01771-3 · Cited by 3
“Identifying the most influential predictors in a model is not how causal inference is performed, as this approach may be biased by open backdoor paths, collider bias, or blocking the actual causal pathway [3, 6].”
Improving Propensity Score Methods in Pharmacoepidemiology
Ali, M. S. (2014) · Utrecht University Repository (Utrecht University) · Cited by 3
Comments on ‘A cautionary note concerning the use of stabilized weights in marginal structural models’ by D. Talbot, J. Atherton, A. M. Rossi, S. L. Bacon, and G. Lefebvre
Taguri, M. (2015) · Statistics in Medicine · doi:10.1002/sim.6422 · Cited by 3
“Under the logistic or Cox MSMs, even if in the absence of interactions, δ1 is not equal to γ1 in general because of the non-collapsibility of the odds and hazard ratios [6].”
Background
A simple example as a pedagogical device?
Suzuki, E., Mitsuhashi, T., Tsuda, T., & Yamamoto, E. (2014) · Annals of Epidemiology · doi:10.1016/j.annepidem.2014.04.003 · Cited by 3
Design and evaluation of digital learning material for academic education in human nutrition
Busstra, M. C. (2008) · doi:10.18174/121952 · Cited by 3
LETTER TO THE EDITOR Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: A Monte Carlo study (p n/a)
Austin, P. C., Grootendorst, P. V., Normand, S. T., Anderson, G. M., Martens, E. P., Pestman, W. R., & Klungel, O. H. (2007) · Cited by 3
Sensitivity Analysis for Unmeasured Confounding via Effect ExtrapolationPreprint
Loh, W. W., & Vansteelandt, S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.01935 · Cited by 3
Discussion of Kallus and Mo, Qi, and Liu: New Objectives for Policy Learning
Vansteelandt, S., & Dukes, O. (2021) · Journal of the American Statistical Association · doi:10.1080/01621459.2020.1844718 · Cited by 3
“…indeed difficult to interpret and therefore difficult to connect to the scientific question at hand: they can be too mathematically complex (cf. odds ratios), suffer non-collapsibility (Greenland, Robins, and Pearl 1999), or even be affected by a built-in selection bias (Hernan and Robins 2010).”
Background
Validity and Interpretation of Two-Sample Mendelian Randomization with Binary TraitsPreprint
Wu, Z., & Wang, J. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.06.09.598150 · Cited by 3
Introduction and Approach to Causal Inference
Office on Smoking (2004) · Cited by 3
Confounding Equivalence in Causal Inference
Pearl, J., & Paz, A. (2014) · Journal of Causal Inference · doi:10.1515/jci-2013-0020 · Cited by 35
“Theorem 3 generalizes closely related theorems by Stone (1993) and Robins (1997), in which T ∪ S is assumed to be admissible (see also Greenland et al. (1999)).”
Self-citation
Keep asking: What do I want? What do I have? What do I do?
Ung, L., & Dahabreh, I. J. (2025) · European Journal of Epidemiology · doi:10.1007/s10654-025-01222-z · Cited by 2
Tree canopy cover and injurious pedestrian falls: a location-based case-control study
Burford, K., Lo, A. X., Quinn, J. W., Crowe, R. P., Just, A. C., Kondo, M. C., Beard, J., & Rundle, A. (2025) · American Journal of Epidemiology · doi:10.1093/aje/kwaf231 · Cited by 2
The cerebral palsy directed acyclic graph: A structural causal model of aetiology
Goldsmith, S. C., McIntyre, S. J., Badawi, N. A., Dan, B., Day, S. M., Himmelmann, K., Hollung, S. J., Jacobsson, B., Rackauskaite, G., & Reynolds, R. J. (2026) · Developmental Medicine & Child Neurology · doi:10.1111/dmcn.70267 · Cited by 2
“9–11 DAGs have also supported the development of robust methods for causal inference.”
Point and interval estimation of baseline risk and treatment effect based on logistic model for observational studies
Wang, X., & Yin, L. (2015) · Biometrical Journal · doi:10.1002/bimj.201400019 · Cited by 2
“Because it is only possible to observe potential outcome of a patient under either z = 1 or z = 0, certain assumption is needed to allow for estimation of R0 and RD (Rosenbaum and Rubin, 1983; Greenland and Robins, 1986; Rosenbaum, 1995; Greenland et al., 1999).”
BackgroundMethod
Item response theory network analysis of European universities
Sagan, A., Brzezińska, J., Rybicka, A., Sztemberg-Lewandowska, M., & Pełka, M. (2021) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2021.1941109 · Cited by 2
Different effects for different questions: An illustration using short cervix and the risk of preterm birth
Ross, R. K., Cole, S. R., Westreich, D. J., Edwards, J. K., Musonda, P., Vwalika, B., Kasaro, M. P., Price, J. T., & Stringer, J. S. A. (2022) · International Journal of Gynecology & Obstetrics · doi:10.1002/ijgo.14372 · Cited by 2
MR‐BOIL: Causal inference in one‐sample Mendelian randomization for binary outcome with integrated likelihood method
Shi, D., Wang, Y., Zhang, Z., Cao, Y., & Hu, Y. (2023) · Genetic Epidemiology · doi:10.1002/gepi.22520 · Cited by 2
“When confounders are taken into account, the existing methods tend to fail due to the so‐called noncollapsibility of the logistic model (Burgess & CRP CHDGenetics Collaboration, 2013; Greenland et al., 1999; Pang et al., 2016).”
Method
Using Directed Acyclic Graphs to Inform Statistical Analysis Plans in Pediatric Research
Smith, M. J. (2023) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2023.113821 · Cited by 2
A cautionary note on the recently proposed ICE Falcon method
Sjölander, A., & Frisell, T. (2024) · International Journal of Epidemiology · doi:10.1093/ije/dyae131 · Cited by 2
“In particular, due to the non-collapsibility of odds ratios and hazard ratios, 5 we conjecture that it is very hard to derive universal patterns of the regression coefficients of logistic regression models and Cox regression models under the mechanisms in Figure 1, even in the absence of unmeasured…”
Method
Definition and identification of causal ratio effects.
Kiefer, C., Lugauer, B., & Mayer, A. (2024) · Psychological Methods · doi:10.1037/met0000711 · Cited by 2
A risk score model for predicting intraprocedural cardiac injury during implantable cardioverter defibrillator implantation: Insights from the National Cardiovascular Data Registry
Padala, S. K., Gunda, S., Li, S., Sharma, P. S., Koneru, J. N., Varosy, P. D., & Ellenbogen, K. A. (2018) · Journal of Cardiovascular Electrophysiology · doi:10.1111/jce.13823 · Cited by 2
Assessment of Glucose Lowering Medications’ Effectiveness for Cardiovascular Clinical Risk Management of Real-World Patients with Type 2 Diabetes: Targeted Maximum Likelihood Estimation under Model Misspecification and Missing Outcomes
Sciannameo, V., Fadini, G. P., Bottigliengo, D., Avogaro, A., Baldi, I., Gregori, D., & Berchialla, P. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph192214825 · Cited by 2
“cOR is more reliable in a randomized controlled setting, where, generally, problems related to unmeasured confounding are controlled by the randomization itself [35].”
Background
Introduction and Motivating Examples
Wakefield, J. (2012) · Springer series in statistics · doi:10.1007/978-1-4419-0925-1_1 · Cited by 2
Inferência causal em epidemiologia: o modelo de respostas potenciais
Luiz, R. R., & Struchiner, C. J. (2002) · Editora FIOCRUZ eBooks · doi:10.7476/9788575412688 · Cited by 2
Aggregation of comparisons data and reversal phenomena of metrological interest
D’Errico, G. E. (2014) · Measurement · doi:10.1016/j.measurement.2014.01.014 · Cited by 2
Comparative syllogism and counterfactual knowledge
Wang, L., & Ma, W. (2013) · Synthese · doi:10.1007/s11229-013-0330-0 · Cited by 2
“The guarantee of even distribution is only 17 In the literature, there are two ways to de-confound (control confounding): one is to de-confound by experimental designs, and the other uses data analysis (cf. Greenland et al. 1999).”
Method
Confounding in (non-) randomized comparison studies
Tan, F. E. S. (2013) · OA Epidemiology · doi:10.13172/2053-079x-1-3-1089 · Cited by 2
RESEARCH METHODS & REPORTING
Grant, R. (2014) · Cited by 2
High Decision Latitude at Work Combined with Traumatic Life Events in Private Life is Associated with Reduced Sleep Quality: Results from the GAZEL Study
Dich, N., Lange, T., Goldberg, M., Zins, M., & Rod, N. H. (2018) · Scandinavian Journal of Work and Organizational Psychology · doi:10.16993/sjwop.39 · Cited by 2
“Potential confounders were identified based on existing knowledge about risk factors for the relation of interest (Greenland, Robins, and Pearl, 1999).”
Background
A work-relatedness assessment in epidemiological case investigation of occupational cancers: I. Principles
Kim, K., & Kim, J. (2020) · Annals of Occupational and Environmental Medicine · doi:10.35371/aoem.2020.32.e30 · Cited by 2
Confident identification of subgroups from SNP testing in RCTs with binary outcomes
Wei, Y., Wang, X., Chew, E. Y., & Ding, Y. (2021) · Biometrical Journal · doi:10.1002/bimj.202000170 · Cited by 2
“This logic-respecting property is related to “collapsibility,” which is defined for measures of association in the literature (Pearl, 2000) as well as for measures of causal effect (Greenland et al., 1999; Hernan and Robins, 2020; Huitfeldt et al., 2019).”
Background
Exchangeability of Measures of Association Before and After Exposure Status Is Flipped: Its Relationship With Confounding in the Counterfactual Model
Suzuki, E., Yamamoto, M., & Yamamoto, E. (2022) · Journal of Epidemiology · doi:10.2188/jea.je20210352 · Cited by 2
Statistical methods of indirect comparison with real-world data for survival endpoint under non-proportional hazards
Lin, Z., Zhao, D., Lin, J., Ni, A., & Lin, J. (2022) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2022.2080696 · Cited by 2
“Several previous papers (Greenland et al. 1999; Hernán, Hernández-Diaz; Hernán et al. 2004; Hernán 2010) have discussed the inappropriateness of using hazard ratio as a causal treatment effect measure since it generally does not provide a valid causal interpretation.”
Background
Inclusion of binary proxy variables in logistic regression improves treatment effect estimation in observational studies in the presence of binary unmeasured confounding variables
Rosenbaum, C. L., Yu, Q., Buzhardt, S., Sutton, E. F., & Chapple, A. G. (2023) · Pharmaceutical Statistics · doi:10.1002/pst.2323 · Cited by 2
Regression Methods for Epidemiological Analysis
Greenland, S. (2024) · Springer eBooks · doi:10.1007/978-1-4614-6625-3_17-1 · Cited by 2
Self-citation
Causal Inference in Pharmacoepidemiology
Buchanan, A. L., Sun, T., & Katenka, N. (2020) · Springer eBooks · doi:10.1007/978-3-030-48555-9_5 · Cited by 2
Noncollapsibility of the odds ratio unraveled
Abdulmajeed, J., Kostoulas, P., Shi, Z., & Doi, S. A. R. (2023) · Current Opinion in Epidemiology and Public Health · doi:10.1097/pxh.0000000000000022 · Cited by 2
Confounds and Objectives in Economic ExperimentsPreprint
Zizzo, D. J. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1909739 · Cited by 2
“1 See Davidson and MacKinnon (1993) for a standard econometric analysis and Greenland et al. (1999) for an example of analysis from a statistician’s perspective on confounding.”
RE: An alternate characterization of hazard in occupational epidemiology: Years of life lost per years worked. Am J Ind Med 42:1–10, 2002
Morfeld, P. (2003) · American Journal of Industrial Medicine · doi:10.1002/ajim.10205 · Cited by 2
Capture-recapture Estimation for Conflict Data and Hierarchical Models for Program Impact Evaluation
Mitchell, S. (2014) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 2
On Statistical Analysis of Brain VariabilityPreprint
Chén, O. Y., Phan, H., Nagels, G., & Vos, M. D. (2020) · Preprints.org · doi:10.20944/preprints202008.0428.v1 · Cited by 2
“, the arrow in ‘A à B’) to represent causal relationship between each pair of vertices, and edge width (which can be quantified using the probability of A causes B) to indicate the strength of causation (Pearl, 1993)(Pearl et al., 1999)(Hinton, 2005).”
Background
Protocol: the International Milk Composition (IMiC) Consortium - a Harmonized Secondary Analysis of Human Milk from 4 StudiesPreprint
Fehr, K. B., Mertens, A., Shu, C.-H., Dailey-Chwalibóg, T., Shenhav, L., Allen, L. H., Beggs, M. R., Bode, L., Chooniedass, R., DeBoer, M. D., et al. (2025) · doi:10.12688/verixiv.402.1 · Cited by 2
Causal Inference Methods in Pharmacoepidemiology
Pazzagli, L., & Li, X. (2021) · Springer eBooks · doi:10.1007/978-3-319-56015-1_14-1 · Cited by 1
Marginal versus conditional rate estimation for count and recurrent event data with an estimand framework
Conner, S. C., Zhou, Y., & Xu, T. (2023) · Contemporary Clinical Trials · doi:10.1016/j.cct.2023.107414 · Cited by 1
A pseudo-response approach to constructing confidence intervals for the subset of patients expected to benefit from a new treatment
Liu, W., Zhang, Z., Hu, Z., Xu, P., & Cohen, C. J. (2024) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1093/jrsssc/qlad108 · Cited by 1
Basic Concepts
Rothman, K. J., & Greenland, S. (2023) · Springer eBooks · doi:10.1007/978-1-4614-6625-3_44-1 · Cited by 1
Self-citation
Covariate Adjustment in Analyzing Randomized Clinical Trials: Approaches, Software, and Application
Liu, J., Wang, X., & Pang, H. (2024) · Springer eBooks · doi:10.1007/978-3-031-65937-9_14 · Cited by 1
Causal Reasoning and Inference in Epidemiology
Didelez, V. (2024) · Springer eBooks · doi:10.1007/978-1-4614-6625-3_74-1 · Cited by 1
The AMP Reflects Gradual Differences in Attitude Extremity, Not Intensity
Roscher, O. M., & Neumann, R. (2025) · Social Psychology · doi:10.1027/1864-9335/a000576 · Cited by 1
What to do with a mediating and confounding variable that is partly a mediator and partly a confounder in causal inference
Takahashi, M. (2025) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2025.2571971 · Cited by 1
Time to live birth and associated factors following fertility treatments: a retrospective record review among couples attending fertility centres in Addis Ababa, Ethiopia
Kasahun, S., Bizuneh, A., Ansa, M., Wondimagegnehu, A., & Asfaw, Z. G. (2025) · BMJ Open · doi:10.1136/bmjopen-2024-093455 · Cited by 1
Participant and musical characteristics influence singers’ physiological stress during opera performances
Cui, A., Hu, G., Yeganeh, N. M., VanHandel, L., Hermiston, N., Werker, J. F., Boyd, L. A., & Ciocca, V. (2025) · Musicae Scientiae · doi:10.1177/10298649251385724 · Cited by 1
“In contrast, a direct causal effect isolates the effect of a predictor on an outcome (Greenland et al., 1999; Tennant et al., 2021).”
Improving causal inference from unreplicated on‐farm strip trials with propensity score matching: Application to plant growth regulator effects in wheat
Niemeyer, C., & Sulik, J. J. (2025) · Agronomy Journal · doi:10.1002/agj2.70260 · Cited by 1
Estimating the impact of out-of-home placement on health risk behavior in adolescents exposed to maltreatment: An advanced causal inference approach
Blake, A. F., Moeyaert, M., Thoemmes, F. J., MacKinnon, D. P., & Chassin, L. (2026) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2026.107882 · Cited by 1
Transfer learning-based two-sample Mendelian randomization method for heterogeneous population
Wei, Y., Chen, H., Liu, X., Sun, X., Yu, Y., Hou, L., Xue, F., & Li, H. (2026) · Briefings in Bioinformatics · doi:10.1093/bib/bbag019 · Cited by 1
“As an alternative, we adopt a log-linear model for the outcome [12, 25].”
Association of insomnia, insulin resistance traits, and cardiovascular disease risk: A two‐step Mendelian randomization study
Yu, B., Xu, Y., Wang, X., Ye, S., Cui, R., Sun, Y., Li, M., Li, Y., Yuan, W., Guo, S., et al. (2026) · Sleep research. · doi:10.1002/slp2.70030 · Cited by 1
Causal Inference in Medicine Part I-Counterfactual Models-An Approach to Clarifying Discussions in Research and Applied Public Health-
Suzuki, E., Komatsu, H., Yorifuji, T., Yamamoto, E., Doi, H., & Tsuda, T. (2009) · Nippon Eiseigaku Zasshi (Japanese Journal of Hygiene) · doi:10.1265/jjh.64.786 · Cited by 1
Spurious effects in variational corpus linguistics
Tummers, J., Speelman, D., & Geeraerts, D. (2014) · International Journal of Corpus Linguistics · doi:10.1075/ijcl.19.4.02tum · Cited by 1
Model Misspecification When Excluding Instrumental Variables from PS Models in Settings Where Instruments Modify the Effects of Covariates on Treatment
Wyss, R., Ellis, A. R., Lunt, M., Brookhart, M. A., Glynn, R. J., & Stürmer‎, T. (2014) · Epidemiologic Methods · doi:10.1515/em-2013-0012 · Cited by 1
“We simulated a normally distributed outcome for simplicity and to avoid issues with the non-collapsibility of the odds ratio (Greenland et al., 1999; Whittemore, 1978).”
Method
COMPARISON BETWEEN ESTIMATES OF THE POTENTIAL PROPORTION WITH AND WITHOUT STANDARDIZATION FOR A NON-CONFOUNDER
Wang, X., Geng, Z., Zhao, Q., & Qi, Q. (2007) · Cited by 1
Collection of Biostatistics Research Archive
VanderWeele, T. J., & Shpitser, I. (2011) · Cited by 1
False Appearance of Gene–Environment Interactions in Genetic Association Studies
Su, Y.-S., & Lee, W. (2016) · Medicine · doi:10.1097/md.0000000000002743 · Cited by 1
Noncollapsibility and Censoring
Goossens, L. M. A., Redekop, K., & van Gils, C. (2014) · Epidemiology · doi:10.1097/ede.0000000000000197 · Cited by 1
Evaluación de la presencia de confusión en algunos miembros de la familia exponencial. (Evaluating the Presence of Confounding in Some Members of the Exponential Family)
Avena, L. M. A., & Salazar-Uribe, J. C. (2015) · CIENCIA EN DESARROLLO · doi:10.19053/01217488.3654 · Cited by 1
Maximum-likelihood estimation and presentation for the interaction between treatments in observational studies with a dichotomous outcome
Yin, L., Wang, X., & Ye, W. (2016) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2016.1230213 · Cited by 1
“Because we can only observe the potential outcome of a patient under one of the four treatments (z1, z2) = (0, 0), (0, 1), (1, 0), (1, 1), we need a certain assumption to allow for estimation of TE1(z2),TE2(z1), and INT (Greenland et al., 1999; Greenland and Robins, 1986; Rosenbaum and Rubin, 1983; Rosenbaum, 1995; Ru…”
BackgroundMethodInfluential
The Case-Control Approach Can be More Powerful for Matched Pair Observational Studies When the Outcome is Rare
Wang, W., Small, D. S., Cafri, G., & Paxton, E. W. (2021) · The American Statistician · doi:10.1080/00031305.2021.1972835 · Cited by 1
“One can then recover a marginal interpretation of the odds ratio, even though in general the odds ratio is not collapsible (Greenland, Pearl, and Robins 1999).”
Background
Frequentist Inference
Wakefield, J. (2012) · Springer series in statistics · doi:10.1007/978-1-4419-0925-1_2 · Cited by 1
Doubly weighted estimating equations and weighted multiple imputation for causal inference with an incomplete subgroup variable
Cuerden, M. S., Diao, L., Cotton, C. A., & Cook, R. J. (2022) · Biostatistics & Epidemiology · doi:10.1080/24709360.2022.2069457 · Cited by 1
“treatment selection is independent of (Si,Xi)), and (ii) the model is collapsible [16].”
Background
Targeted Policy Recommendations using Outcome-aware Clustering
Balashankar, A., Fraiberger, S. P., Deregt, E., Görgens, M., & Subramanian, L. (2022) · ACM SIGCAS/SIGCHI Conference on Computing and Sustainable Societies (COMPASS) · doi:10.1145/3530190.3534797 · Cited by 1
Kausalität
Kühnel, S., & Dingelstedt, A. (2022) · Springer eBooks · doi:10.1007/978-3-658-37985-8_46 · Cited by 1
Bias attenuation results for dichotomization of a continuous confounder
Gabriel, E. E., Peña, J. M., & Sjölander, A. (2022) · Journal of Causal Inference · doi:10.1515/jci-2022-0047 · Cited by 1
Simple design and analysis strategies for solving problems in observational orthopaedic clinical research
Brown, K., Flores, M. J., Slobogean, G. P., Shearer, D., Gitajn, I. L., & Morshed, S. (2023) · OTA International The Open Access Journal of Orthopaedic Trauma · doi:10.1097/oi9.0000000000000239 · Cited by 1
Evaluación de la política tecnológica. Propensity Score Matching
(2022) · doi:10.22201/iiec.9786073056687e.2022 · Cited by 1
Deconfounded Opponent Intention Inference for Football Multi-Player Policy Learning
Wang, S., Pan, Y. F., Pu, Z., Liu, B., & Yi, J. (2023) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros55552.2023.10341469 · Cited by 1
Deep doubly robust outcome weighted learning
Jiang, X., Zhou, X., & Kosorok, M. R. (2023) · Machine Learning · doi:10.1007/s10994-023-06484-w · Cited by 1
“DDROWL utilizes the augmented inverse probability weighting estimator (AIPWE), which is semiparametric efficient and also has the desirable property of double robustness (Robins et al., 1994; Greenland et al., 1999; Scharfstein et al., 1999; Kang & Schafer, 2007).”
Empowering Predictive Modeling by GAN-based Causal Information Learning
Zeng, J., Zhang, G., Yuan, J., Li, Y., & Jin, D. (2024) · ACM Transactions on Intelligent Systems and Technology · doi:10.1145/3652610 · Cited by 1
“Furthermore, even if the causal relationships can be determined, we cannot accurately calculate the causal effects due to the general existence of confounding biases [10].”
Background
A simple Cox approach to estimating risk ratios without sharing individual-level data in multisite studies
Shu, D., Zou, G., Hou, L., Petrone, A. B., Maro, J. C., FIREMAN, B. H., Toh, S., & Connolly, J. G. (2024) · American Journal of Epidemiology · doi:10.1093/aje/kwae188 · Cited by 1
Regression Methods for Epidemiological Analysis
Greenland, S. (2024) · Springer eBooks · doi:10.1007/978-1-4614-6625-3_17-2 · Cited by 2
Self-citation
Some approximations to the path formula for some nonlinear models
Kartsonaki, C. (2024) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12753 · Cited by 1
“These differences are induced by the nonlinearity of the model and in the case of the Cox proportional hazards model because hazards are based on conditional probabilities (Daniel et al., 2021; Greenland et al., 1999).”
Unravelling the effects of knowledge-sharing dynamics on crowdsourcing contest participation
Khasraghi, H. J., Wang, X., Li, Y., & Mao, X. (2024) · Behaviour and Information Technology · doi:10.1080/0144929x.2024.2446400 · Cited by 1
“Conversely, inverse probability weighting addresses and mitigates biases in different scenarios (Greenland, Robins, and Pearl 1999) and reduces selection bias from various sources (Hernán and Robins 2010), aiming to equilibrate the treatment and control groups.”
Predictive Factors of Initial Pain and Disability in Patients Presenting With Neck Pain for Rehabilitation
Kapernaros, E., Moutzouri, M., Krekoukias, G., Chrysagis, N., & Koumantakis, G. Α. (2025) · Cureus · doi:10.7759/cureus.87361 · Cited by 1
Linking agricultural conservation to water quality outcomes in the United States at multiple scales: Do we have the information we need?
Naslund, L. C., Kirk, L., Compton, J. E., & Neale, A. (2025) · Journal of Environmental Quality · doi:10.1002/jeq2.70086 · Cited by 1
Nonparametric Regression with Multiple Predictors
Wakefield, J. (2012) · Springer series in statistics · doi:10.1007/978-1-4419-0925-1_12 · Cited by 1
Hypothesis Testing and Variable Selection
Wakefield, J. (2012) · Springer series in statistics · doi:10.1007/978-1-4419-0925-1_4 · Cited by 1
The Safety of Anesthetics: The National Halothane Study
Mosteller, F. C. (2009) · Springer eBooks · doi:10.1007/978-0-387-77956-0_5 · Cited by 1

Authors: Greenland, S., Pearl, J., & Robins, J. M.
ORCID: Greenland, Sander
Robins, James 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
DOI: 10.1214/ss/1009211805
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 ›

Are you an author, or do you see a problem with this page? Request a review

Confounding and Collapsibility in Causal Inference

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Self-check

Citations

Cites

Cited by

Related

Metadata

Record

About these checks