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 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.
Overview
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
Cites
Statistics
Verification
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?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“The causal interpretation of the estimated treatment effects relies on the standard identification assumptions used in the program-evaluation literature [16, 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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
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
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
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-citationAir 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
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.
Cited by
Sorted by citations
Items 501–600 of 933
Extracting Best-Practice Using Mixed-Methods
Poppe, E., Pika, A., Wynn, M. T., Eden, R., Andrews, R., & ter Hofstede, A. H. M. (2021) · Business & Information Systems Engineering · doi:10.1007/s12599-021-00698-9 · Cited by 7
Multiplicative effect modelling: the general case
Yin, J., Markes, S., Richardson, T. S., & Wang, L. (2021) · Biometrika · doi:10.1093/biomet/asab064 · Cited by 7
Sensitivity analysis for causal effects with generalized linear models
Sjölander, A., Gabriel, E. E., & Ciocănea‐Teodorescu, I. (2022) · Journal of Causal Inference · doi:10.1515/jci-2022-0040 · Cited by 7
Temporally Causal Discovery Tests for Discrete Time Series and Neural Spike Trains
Theocharous, A., Gregoriou, G. G., Sapountzis, P., & Kontoyiannis, I. (2024) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2024.3371899 · Cited by 7
“Indeed, in observational studies such as in the present context of time series analysis, allowing for potential confounders is extremely important, as it often facilitates the distinction between simple correlation and actual causality [24].”
BackgroundAarsman, S. R., Greenwood, C. J., Linardon, J., Rodgers, R. F., Messer, M., Jarman, H. K., & Fuller‐Tyszkiewicz, M. (2024) · Body Image · doi:10.1016/j.bodyim.2024.101704 · Cited by 7
Measles Immunization and Vitamin A for Prevention of Pneumonia in Indonesia
Widoyo, R. (2016) · Kesmas National Public Health Journal · doi:10.21109/kesmas.v11i1.841 · Cited by 7
Zhu, Y., Lawless, J. F., & Cotton, C. A. (2017) · Statistics in Medicine · doi:10.1002/sim.7234 · Cited by 7
“[50] defined the difference between the population-averaged causal effect and the raw marginal association between treatment and outcome as the amount of confounding bias.”
BackgroundOn Mendelian randomization analysis of case‐control study
Zhang, H., Qin, J., Berndt, S. I., Albanes, D., Deng, L., Gail, M. H., & Yu, K. F. (2019) · Biometrics · doi:10.1111/biom.13166 · Cited by 7
“First, because of noncollapsibility, the marginal relationship between the outcome and instruments after integrating out the confounder and the exposure does not follow a logistic regression model (Greenland et al., 1999).”
BackgroundJi, J., Wang, C., He, Z., Hay, K. E., Barnes, T. S., & O'Connor, A. M. C. (2020) · PLoS ONE · doi:10.1371/journal.pone.0233960 · Cited by 7
“The causal inference approaches enable estimation of the marginal causal effects, which correspond with the traditional parameters of interest in randomized trials [10–12].”
Schwartz, M. H., & Ries, A. J. (2020) · Developmental Medicine & Child Neurology · doi:10.1111/dmcn.14709 · Cited by 8
“This random assignment eliminates confounding factors and hence produces an unbiased estimate of the true causal effect size.(20) In routine clinical practice, we tend to observe a sizeable degree of ‘apparent randomness’ in treatment assignment.”
BackgroundCONSERVATIVE TENDENCY OF THE CRUDE ODDS RATIO
Doi, M., Nakamura, T., & Yamamoto, E. (2001) · JOURNAL OF THE JAPAN STATISTICAL SOCIETY · doi:10.14490/jjss1995.31.53 · Cited by 7
“Miettinen and Cook introduced this as an example of noncollapsibility of the odds ratio in the no confounding case, as mentioned in Section 1. Our mathematical analysis ensures their assertion. The example (ii) is cited from Whittemore (1978). This example shows that the crude odds ratio lies between two stratum-speci…”
BackgroundInfluentialHernán, M. Á. (2008) · Encyclopedia of Quantitative Risk Analysis and Assessment · doi:10.1002/9780470061596.risk0642 · Cited by 7
Zhang, B., Wu, Q., Jhaveri, R. R., Zhou, T., Becich, M. J., Bisyuk, Y., Blanceró, F., Chrischilles, E. A., Chuang, C. H., Cowell, L., et al. (2025) · medRxiv · doi:10.1101/2025.03.28.25324858 · Cited by 7
“37,38 Lastly, we conducted an extensive sensitivity analysis including: 1) negative control experiments 39,40 to address systematic bias and control unmeasured confounders, 2) analyses across different selected populations, and 3) a series of subgroup analyses to examine the robustness of our…”
Prospective and retrospective causal inferences based on the potential outcome framework
Geng, Z., Zhang, C., Wang, X., Liu, C., & Wei, S. (2024) · Journal of Causal Inference · doi:10.1515/jci-2023-0063 · Cited by 6
Liu, Y., Yang, M., Kil, S., Li, J., Mondal, S., Shentu, Y., Tian, H., Wang, L., & Yung, G. (2023) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2023.2186945 · Cited by 6
“This summary is then said to be collapsible” according to Greenland, Pearl, and Robins (1999) which is consistent with the definition in Huitfeldt et al. (2019).”
BackgroundResultCase–control matching on confounders revisited
Mansournia, M. A., & Poole, C. (2023) · European Journal of Epidemiology · doi:10.1007/s10654-023-01046-9 · Cited by 6
McJames, N., Parnell, A. C., & O’Shea, A. (2024) · Learning and Instruction · doi:10.1016/j.learninstruc.2024.101968 · Cited by 6
Model-Based Causal Feature Selection for General Response Types
Kook, L., Saengkyongam, S., Lundborg, A. R., Hothorn, T., & Peters, J. (2024) · Journal of the American Statistical Association · doi:10.1080/01621459.2024.2395588 · Cited by 13
“Many commonly applied regression models are not closed under marginalization or the inclusion or exclusion of covariates that are associated with the response (collapsibility, Greenland 1996; Greenland, Pearl, and Robins 1999; Didelez and Stensrud 2022, see also Appendix A2).”
Expérimentation, inférence statistique et analyse causale
Lecoutre, B. (2004) · Intellectica Revue de l Association pour la Recherche Cognitive · doi:10.3406/intel.2004.1713 · Cited by 6
“Des références qui se situent dans cette même ligne d’analyse contrefactuelle sont notamment Rosenbaum et Rubin, 1983 [ordre des auteurs inverse dans la biblio] ; Holland, 1986; Robins, 1986 ; Manski, 1995 ; Greenland et al., 1999.”
BackgroundValidity and bias in epidemiological research
Greenland, S. (2009) · Oxford University Press eBooks · doi:10.1093/med/9780199218707.003.0037 · Cited by 6
Self-citationBirth cohort appeared to confound effect estimates of guideline changes on statin utilization
Bijlsma, M. J., Janssen, F., Lub, R., Bos, J., de Vries, F. M., Vansteelandt, S., & Hak, E. (2014) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2014.10.010 · Cited by 6
“In general, non-collapsibility can occur in the absence of confounding and vice versa [25], but noncollapsibility does not play a role in our study because of the use of a log link in our models [26].”
MethodYu, Y., Li, H., Sun, X., Su, P., Wang, T., Liu, Y., Yuan, Z., Liu, Y., & Xue, F. (2017) · BMC Medical Research Methodology · doi:10.1186/s12874-017-0449-7 · Cited by 6
“, the effect of the exposure, the prevalence and effect of the covariate [4, 33].”
BackgroundWeinstein, S. M., Davatzikos, C. A., Doshi, J. J., Linn, K. A., Shinohara, R. T., & Initiative, A. D. N. (2022) · Biostatistics · doi:10.1093/biostatistics/kxac031 · Cited by 6
Causal inference for oncology: past developments and current challenges
Moodie, E. E. M. (2022) · The International Journal of Biostatistics · doi:10.1515/ijb-2022-0056 · Cited by 6
Determinants of online professor reviews: an elaboration likelihood model perspective
Li, Y., Wang, X., & Slyke, C. V. (2022) · Internet Research · doi:10.1108/intr-11-2020-0627 · Cited by 9
Model Averaging for Improving Inference from Causal Diagrams
Hamra, G., Kaufman, J., & Vahratian, A. (2015) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph120809391 · Cited by 7
“In addition, investigators should be wary of averaging non-collapsible causal estimates such as odds ratios and hazard ratios, which will, in general, differ across alternative confounder adjustment sets [32].”
Causal reasoning in epidemiology: Philosophy and logic
Maldonado, G., & Cox, L. A. (2020) · Global Epidemiology · doi:10.1016/j.gloepi.2020.100020 · Cited by 4
The Role of Exchangeability in Causal Inference
Saarela, O., Stephens, D. A., & Moodie, E. E. M. (2023) · Statistical Science · doi:10.1214/22-sts879 · Cited by 9
Dimension reduction summaries for balanced contrasts
Nelson, D. B., & Noorbaloochi, S. (2008) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2008.04.031 · Cited by 6
“, pr(Z = k − 1 |X)) discussed by Imbens (2000), Lechner (1999) and others.”
BackgroundA Survey of Controlled Experiments in Software Engineering
Prasad, D. (2022) · Journal of Science and Technology · doi:10.46243/jst.2022.v7.i02.pp395-422 · Cited by 6
Cullings, H. M., & COLOGNE, J. B. (2008) · Encyclopedia of Quantitative Risk Analysis and Assessment · doi:10.1002/9780470061596.risk0314 · Cited by 6
RE: “INVITED COMMENTARY: BEWARE THE TEST-NEGATIVE DESIGN”
Ferdinands, J. M., Foppa, I., Fry, A. M., Flannery, B. L., Belongia, E. A., & Jackson, M. L. (2016) · American Journal of Epidemiology · doi:10.1093/aje/kww227 · Cited by 6
Chambers, C., Johnson, D. L., Luo, Y. J., Xu, R., Adam, M. P., Braddock, S. R., & Jones, K. L. (2025) · The American Journal of Gastroenterology · doi:10.14309/ajg.0000000000003593 · Cited by 5
“Three criteria were applied to de fi ne confounders (17,18): (i) by assessing each considered variable in a logistic regression model The American Journal of GASTROENTEROLOGY”
Bian, H., Pang, M., Wang, G., & Lu, Z. (2024) · BMC Medical Research Methodology · doi:10.1186/s12874-024-02402-3 · Cited by 5
“When focusing on the coefficient of the treatment and collapsing over covariate(s), the conditional effect does not equal the marginal effect even in the absence of confounding and effect modification 4-6 .”
IDEAL: Interpretable-by-Design ALgorithms for learning from foundation feature spaces
Angelov, P. P., Kangin, D., & Zhang, Z. (2025) · Neurocomputing · doi:10.1016/j.neucom.2025.129464 · Cited by 8
“The phenomenon of confounding takes its origin in causal modelling and is informally described, as per Greenland et al. (1999), as ’a mixing of effects of extraneous factors (called confounders) with the effects of interest’ .”
Mediation Analysis with Attributable Fractions
Sjölander, A. (2018) · Epidemiologic Methods · doi:10.1515/em-2017-0010 · Cited by 5
“Indirectly, the validity of the OR-based estimators is thus related to the concept of non-collapsibility, which is a wellknown feature of the odds ratio (Greenland, Robins, and Pearl 1999).”
BackgroundIdentification of key somatic oncogenic mutation based on a confounder-free causal inference model
Liu, Y., Sun, J., Sun, H., & Chang, Y. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010529 · Cited by 5
“One crucial step in inferring the causal relationship (M!Y) is to eliminate the misleading effect caused by confounders which affect both treatment (M, via Z!M) and outcome (Y, via Z!Y) and lead to the spurious statistical correlation between M and Y [31].”
BackgroundCox regression can be collapsible and Aalen regression can be non-collapsible
Samuelsen, S. O. (2022) · Lifetime Data Analysis · doi:10.1007/s10985-022-09578-0 · Cited by 5
“Collapsibility is of relevance for causalmodeling (Greenland et al. 1999).”
McGuire, F. H., Goldbach, J. T., Senese, J., Cabrera, J. R., Schrager, S. M., & Duncan, A. E. (2023) · Body Image · doi:10.1016/j.bodyim.2023.02.007 · Cited by 5
Heineck, P., & Deutsch, R. (2023) · Journal of Experimental Social Psychology · doi:10.1016/j.jesp.2023.104548 · Cited by 5
Unbiased Pseudo-Labeling for Learning with Noisy Labels
Higashimoto, R., Yoshida, S., Horihata, T., & Muneyasu, M. (2023) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.2023mul0002 · Cited by 5
Model-based standardization using multiple imputation
Remiro‐Azócar, A., Heath, A., & Baio, G. (2024) · BMC Medical Research Methodology · doi:10.1186/s12874-024-02157-x · Cited by 5
“In the estimation of marginal treatment effects, covariate adjustment is desirable across a range of settings: (1) it is applied in the analysis of randomized controlled trials (RCTs) to correct for “chance” covariate imbalances and increase power, precision and efficiency [13]; (2) it allows for…”
PCSK9 Inhibitors and the Risk of Vitiligo: A Mendelian Randomization Study
Kang, T.-J., Lee, S. Y., Yoon, S., Kim, E. G., Kim, J. O., Kim, J. S., Park, J., & Nam, K. (2024) · Journal of Investigative Dermatology · doi:10.1016/j.jid.2024.07.021 · Cited by 5
A nonparametric framework for treatment effect modifier discovery in high dimensions
Boileau, P., Leng, N., Hejazi, N. S., van der Laan, M. J., & Dudoit, S. (2024) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1093/jrsssb/qkae084 · Cited by 5
“These conditional parameters are said to be noncollapsible [for a discussion and worked example, see Greenland et al., 1999], in the sense that marginalizing over the other covariates in the model may produce a marginal parameter whose value differs from the marginal parameter directly obtained by…”
BackgroundEvaluating risk factor assumptions: a simulation-based approach
Rutter, C. M., Miglioretti, D. L., & Savarino, J. E. (2011) · BMC Medical Informatics and Decision Making · doi:10.1186/1472-6947-11-55 · Cited by 5
“Collapsing across age groups results in greater estimated risk reduction (across the 45-79 year age range) than age-specific RRs, demonstrating Simpson’s paradox [32,33].”
BackgroundCausality Modeling and Statistical Generative Mechanisms
Mandel, I. (2018) · Lecture notes in computer science · doi:10.1007/978-3-319-99492-5_7 · Cited by 5
Suzuki, E., Komatsu, H., Yorifuji, T., Yamamoto, E., Doi, H., & Tsuda, T. (2009) · Nippon Eiseigaku Zasshi (Japanese Journal of Hygiene) · doi:10.1265/jjh.64.796 · Cited by 5
Xu, R., Chen, G., Connor, M. J., Jr., & Murphy, J. D. (2022) · Journal of Clinical Oncology · doi:10.1200/jco.21.01957 · Cited by 5
Pearce, N. E., & Greenland, S. (2022) · European Journal of Epidemiology · doi:10.1007/s10654-022-00931-z · Cited by 5
“This definition is in line with Hume’s definition of causation (often regarded as the founding concept for counterfactuals or potential outcomes)[15, 16] where a factor can be considered a cause when “if the first object had not been, the second never had existed.”
ResultSelf-citationLikelihood Based Estimation of Logistic Structural Nested Mean Models with an Instrumental Variable
Matsouaka, R., & Tchetgen, E. J. T. (2014) · Collection of Biostatistics Research Archive · Cited by 5
A Cox Model for Biostatistics of the Future
Zeger, S. L., Diggle, P. J., & Liang, K. (2004) · Collection of Biostatistics Research Archive · Cited by 5
Vuistiner, P., Bochud, M., & Rousson, V. (2012) · PLoS ONE · doi:10.1371/journal.pone.0035951 · Cited by 5
“Greenland, Robins and Pearl [24]), it does not even imply that the causal odds-ratio is the same for compliers and for alwaystakers.”
BackgroundTummers, J., Speelman, D., & Geeraerts, D. (2012) · Lirias · Cited by 5
Confounding of Incidence Density Ratio in Case-Control Studies
Greenland, S. (2013) · Epidemiology · doi:10.1097/ede.0b013e3182953c23 · Cited by 5
Self-citationConfounded: Causal Inference and the Requirement of Independence
Lupyan, G. (2005) · eScholarship (California Digital Library) · Cited by 5
Causal diagrams for research about childhood‐onset disabilities
Reynolds, R. J., Goldsmith, S. C., McIntyre, S. J., & Day, S. M. (2025) · Developmental Medicine & Child Neurology · doi:10.1111/dmcn.70064 · Cited by 4
Mponela, P., Le, Q. B., Snapp, S. S., Villamor, G. B., Tamene, L. D., & Borgemeister, C. (2023) · MethodsX · doi:10.1016/j.mex.2023.102467 · Cited by 4
Average treatment effects on binary outcomes with stochastic covariates
Kiefer, C., Woud, M. L., Blackwell, S. E., & Mayer, A. (2024) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12355 · Cited by 3
Advancing Interpretable Regression Analysis for Binary Data: A Novel Distributed Algorithm Approach
Tong, J., Li, L., Reps, J., Lorman, V., Jing, N., Edmondson, M. J., Lou, X., Jhaveri, R. R., Kelleher, K. J., Pajor, N. M., et al. (2024) · Statistics in Medicine · doi:10.1002/sim.10250 · Cited by 4
Donovan, J., Wolbers, M., Thương, N. T. T., Trinh, D. H. K., Nhat, L. T. H., Thwaites, G. E., & Geskus, R. B. (2024) · Wellcome Open Research · doi:10.12688/wellcomeopenres.22498.1 · Cited by 4
“Due to the issue of non-collapsibility, correction for strong predictors of the outcome is not guaranteed to increase power in a non-inferiority design 12 .”
John, E. R., Crowther, M. J., Didelez, V., & Sheehan, N. A. (2024) · Statistical Methods in Medical Research · doi:10.1177/09622802241293765 · Cited by 4
Zhang, D., Zhang, B., Wang, H., Lu, Y., Wolock, C. J., Hu, W., Wang, L., Hripcsak, G. M., & Chen, Y. (2025) · npj Digital Medicine · doi:10.1038/s41746-025-01821-w · Cited by 4
Measuring and estimating treatment effect on dichotomous outcome of a population
Wang, X., Yin, J., & Yin, L. (2013) · Statistical Methods in Medical Research · doi:10.1177/0962280213502146 · Cited by 4
“The ML estimate b pr y 1⁄4 1jz, x ð Þ of pr(y1⁄4 1jz, x) is obtained by replacing by ̂ in model (1) and is presented in Table 1.”
BackgroundMethodInfluentialPoint and Interval Estimations of Marginal Risk Difference by Logistic Model
Wang, X., Yin, J., & Yin, L. (2015) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2013.851229 · Cited by 4
“Because there is no confounding covariate in randomized trial, the stratum z = 0 is exchangeable to the stratum z = 1 (Greenland and Robins, 1986; Greenland et al., 1999); also see the argument in terms of the potential outcome (Rosenbaum and Rubin, 1983; Rosenbaum, 1995; Rubin, 2005).”
BackgroundConsideration of stratification in confirmatory trials with time-to-event endpoint
Wang, Y., Zhou, X., Guo, Z., Fang, X., Liu, F., & Shen, L. (2024) · Contemporary Clinical Trials · doi:10.1016/j.cct.2024.107434 · Cited by 4
Model‐Twin Randomization (MoTR) for Estimating the Recurring Individual Treatment Effect
Daza, E. J., Matias, I., & Schneider, L. D. (2025) · Statistics in Medicine · doi:10.1002/sim.70290 · Cited by 4
The Logic and Philosophy of Causal Inference
Greenland, S. (2011) · Elsevier eBooks · doi:10.1016/b978-0-444-51862-0.50026-5 · Cited by 4
Self-citationNoncollapsibility in studies based on nonrepresentative samples
Pizzi, C., Pearce, N. E., & Richiardi, L. (2015) · Annals of Epidemiology · doi:10.1016/j.annepidem.2015.09.007 · Cited by 4
“[8] discussed issues of noncollapsibility in epidemiologic studies and described the difference between lack of collapsibility and confounding, providing numerical examples.”
BackgroundMethodInfluentialReflection on modern methods: causal inference considerations for heterogeneous disease etiology
Nevo, D., Ogino, S., & Wang, M. (2020) · International Journal of Epidemiology · doi:10.1093/ije/dyaa278 · Cited by 4
Adjustment for biased sampling using NHANES derived propensity weights
Bernstein, O. M., Vegetabile, B., Salazar, C. R., Grill, J. D., & Gillen, D. L. (2022) · Health Services and Outcomes Research Methodology · doi:10.1007/s10742-022-00283-x · Cited by 4
“There are three assumptions needed for estimating propensity scores and making causal conclusions: (1) unconfoundedness, (2) positivity, and (3) the stable unit treatment value assumption (SUTVA) (See Chapter 1 and 12 of Imbens and Rubin (2015) or Appendix 1 of Greenland et al. (1999) for an overview).”
BackgroundDecreased Susceptibility of Marginal Odds Ratios to Finite-sample Bias
Ross, R. K., Cole, S. R., & Richardson, D. B. (2021) · Epidemiology · doi:10.1097/ede.0000000000001370 · Cited by 4
Wei, Y., Hsu, J. C., Chen, W., Chew, E. Y., & Ding, Y. (2021) · Statistics in Medicine · doi:10.1002/sim.9196 · Cited by 7
Hossain, M. B., Mosquera, L., & Karim, M. E. (2022) · BMC Medical Research Methodology · doi:10.1186/s12874-022-01518-8 · Cited by 4
“However, since the odds ratio is a non-collapsible measure, we chose not to use this measure [38].”
MethodKaizar, E. E., Lin, C., Faries, D. E., & Johnston, J. A. (2023) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2022.2162067 · Cited by 5
“Omitting prognostic variables is not an option for non-collapsible effect measures such as odds ratios (Greenland et al. 1999; Huitfeldt et al. 2019; Tang et al. 2013).”
BackgroundPerneger, T., Combescure, C., & Poncet, A. (2023) · Trials · doi:10.1186/s13063-022-07053-7 · Cited by 4
Mitigating Confounding Bias for Recommendation via Counterfactual Inference
He, M., Hu, X., Li, C., Chen, X., & Wang, J. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-26387-3_32 · Cited by 4
“In this work, we treat the exposure data as the evidence of confounders exists in the data (refer [9, 26] for details and proof which we omit for brevity).”
MethodA unified analysis of regression adjustment in randomized experiments
Reluga, K., Ye, T., & Zhao, Q. (2024) · Electronic Journal of Statistics · doi:10.1214/24-ejs2233 · Cited by 4
“…carry over to a wider class of generalized linear model, even if the link function we use is collapsible (a link function is collapsible if including independent regressors does not change the population regression coefficients, see Greenland et al., 1999; Daniel et al., 2021, for more detials).”
BackgroundMatthews, J. N. S., & Badi, N. H. (2015) · Statistics in Medicine · doi:10.1002/sim.6508 · Cited by 4
Bagged one‐to‐one matching for efficient and robust treatment effect estimation
Samuels, L. R., & Greevy, R. A. (2018) · Statistics in Medicine · doi:10.1002/sim.7926 · Cited by 4
Xi, D., & Bretz, F. (2021) · Biometrical Journal · doi:10.1002/bimj.202100060 · Cited by 4
“Note that the collapsibility definition used by Pearl (2009) and Greenland et al. (1999) chooses the prevalence of X as weights, so that their definition is stronger than (1) and the logic-respecting definition in Liu et al. (2021). The subgroup mixable estimation (SME) principle used by Liu et al. (2021) was original…”
MethodInfluentialRubin, D. B. (2006) · Handbook of statistics · doi:10.1016/s0169-7161(06)26024-3 · Cited by 5
Relationship of causal effects in a causal chain and related inference
Geng, Z. (2004) · Science in China Series A Mathematics · doi:10.1360/02ys0374 · Cited by 4
“According to the counterfactual model and the causal diagram, confounding bias may be eliminated by controlling confounders that are not affected by treatment or exposure, called the back door criterion in the causal diagram [3] and standardization in the counterfactual model [5, 6 ] .F urther”
BackgroundSensitivity Analysis in Non-Inferiority Trials with Residual Inconstancy After Covariate Adjustment
Zhang, Z., Nie, L., Soon, G. G., & Zhang, B. (2014) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12050 · Cited by 4
“It will be of interest to extend the proposed approach to those effect measures with appropriate adjustment for possible non-collapsibility (Gail et al., 1984; Greenland et al., 1999).”
BackgroundModèles structuraux et inférence causale
Juhel, J. (2015) · Presses universitaires de Rennes eBooks · doi:10.4000/books.pur.61649 · Cited by 4
Rothman, K. J., & Greenland, S. (2005) · Springer eBooks · doi:10.1007/978-3-540-26577-1_2 · Cited by 4
Self-citationRothman, K. J., & Greenland, S. (2013) · Springer eBooks · doi:10.1007/978-0-387-09834-0_44 · Cited by 4
Self-citationParametric Potential-Outcome Survival Models for Causal Inference
Gong, Z. (2008) · UC Research Repository (University of Canterbury) · doi:10.26021/1683 · Cited by 4
“The observational study counterpart to noncompliance in randomised studies is the problem of confounding by unobserved covariates, and because the observed study data are uninformative about unobserved covariates, causal inference in the observational study setting can be highly sensitive to prior assumptions about th…”
BackgroundBehavioral Feedback: Do Individual Choices Influence Scientific Results?
Oster, E. F. (2018) · National Bureau of Economic Research · doi:10.3386/w25225 · Cited by 4
“This issue is well-known (e.g. Greenland et al, 1999; Vandenbroucke et al, 2007).”
BackgroundEffect Modification and Collapsibility in Evaluations of Public Health Interventions
Luque-Fernández, M. Á., Redondo‐Sánchez, D., & Schomaker, M. (2019) · American Journal of Public Health · doi:10.2105/ajph.2018.304916 · Cited by 4
Hernán, M. Á. (2019) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat03729.pub2 · Cited by 4
Current intelligence bulletin 69: NIOSH practices in occupational risk assessment.
Daniels, R., Gilbert, S., Kuppusamy, S., Kuempel, E., Park, R., Pandalai, S. P., Smith, R. J., Wheeler, M., Whittaker, C., & Schulte, P. (2020) · doi:10.26616/nioshpub2020106 · Cited by 5
“Although Appendix B provides some discussion on specific types of biases that may be encountered, for additional information risk assessors may consult several highly cited articles [Arrighi and Hertz-Picciotto 1994; Delgado-Rodríguez and Llorca 2004; Greenland et al. 1999; Grimes and Schulz 2002; Sackett 1979] and ep…”
BackgroundMatched design for marginal causal effect on restricted mean survival time in observational studies
Lin, Z., Ni, A., & Lü, B. (2023) · Journal of Causal Inference · doi:10.1515/jci-2022-0035 · Cited by 3
“However, the hazard ratio is generally not an appropriate marginal causal effect measure due to its noncollapsibility property [Greenland et al., 1999, Martinussen and Vansteelandt, 2013, Sjölander et al., 2016]. Other effect measures need to be considered to warrant valid marginal causal interpretation for survival d…”
BackgroundInfluentialHade, E. M. (2012) · OhioLink ETD Center (Ohio Library and Information Network) · Cited by 3
Amplification of Bias Due to Exposure Measurement Error
Richardson, D. B., Keil, A. P., & Cole, S. R. (2021) · American Journal of Epidemiology · doi:10.1093/aje/kwab228 · Cited by 3
Hill’s Criterion ‘Experiment’: The Counterfactual Approach in Non-Radiation and Radiation Sciences
Koterov, A. N., Ushenkova, L. N., & Biryukov, A. P. (2021) · Biology Bulletin · doi:10.1134/s1062359021120062 · Cited by 3
“In review publications on the topic and in other documents, it is noted [15, 17, 18, 59, 62, 63] that, for the first time, a counterfactual approach for determining the cause (for various definitions of the cause, see [2]) was proposed by the philosopher D.”
BackgroundRedefining effect modification
Doi, S. A. R., Abdulmajeed, J., & Xu, C. (2022) · Journal of Evidence-Based Medicine · doi:10.1111/jebm.12495 · Cited by 3
Simple Ways to Interpret Effects in Modeling Binary Data
Agresti, A., Tarantola, C., & Varriale, R. (2023) · Statistics for social and behavioral sciences · doi:10.1007/978-3-031-31186-4_5 · Cited by 3
Årnes, A. P., Fjeld, M. K., Stigum, H., Nielsen, C. S., Stubhaug, A., Johansen, A., Hopstock, L. A., Morseth, B., Wilsgaard, T., & Steingrímsdóttir, Ó. A. (2024) · Pain · doi:10.1097/j.pain.0000000000003209 · Cited by 3
Pearce, N. E., & Greenland, S. (2024) · Springer eBooks · doi:10.1007/978-1-4614-6625-3_10-1 · Cited by 3
Self-citationSensitivity Analysis and Bias Analysis
Greenland, S. (2024) · Springer eBooks · doi:10.1007/978-1-4614-6625-3_60-1 · Cited by 3
Self-citation
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 ›
Are you an author, or do you see a problem with this page? Request a review
