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
Flagged first, then by citations
9 of the 108 references couldn’t be matched to a known paper.
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 201–300 of 933
Smoking and subsequent human papillomavirus infection: a mediation analysis
Eldridge, R. C., Pawlita, M., Wilson, L. E., Castle, P. E., Waterboer, T., Gravitt, P. E., SCHIFFMAN, M. H., & Wentzensen, N. (2017) · Annals of Epidemiology · doi:10.1016/j.annepidem.2017.10.004 · Cited by 48
“Though non-collapsibility of the odds ratio makes comparing the two methods more difficult (40), the difference between the two methods cannot be ignored.”
Bias Due to Confounders for the Exposure–Competing Risk Relationship
Lesko, C. R., & Lau, B. M. (2016) · Epidemiology · doi:10.1097/ede.0000000000000565 · Cited by 46
“35 Furthermore, the cause-specific hazard ratios in our simulation were unbiased because the correct models were fit; in practice, correct model specification will never be assured.”
On the collapsibility of measures of effect in the counterfactual causal framework
Huitfeldt, A., Stensrud, M. J., & Suzuki, E. (2019) · Emerging Themes in Epidemiology · doi:10.1186/s12982-018-0083-9 · Cited by 47
“a weighted average of the stratum-specific measures of association [1]. The relationship between collapsibility and confounding has been subject to an extensive and ongoing discussion in the literature[2]. In this paper, we argue that the concept of collapsibility can be made clearer by framing the discussion in terms…”
BackgroundCausal logistic models for non‐compliance under randomized treatment with univariate binary response
Have, T. R. T., Joffe, M. M., & Cary, M. S. (2003) · Statistics in Medicine · doi:10.1002/sim.1401 · Cited by 47
“We also show with simulations that the marginal and conditional causal methods perform better than intent-to-treat (ITT) analyses and commonly-used regression on observed treatmentreceived (as-treated), which have been shown to be generally biased for estimating causal e ects [5, 6].”
MethodNebel, M. B., Lidstone, D. E., Wang, L., Benkeser, D. C., Mostofsky, S. H., & Risk, B. B. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119296 · Cited by 50
Causal theory and the etiology of periodontal diseases
Heaton, B., & Dietrich, T. (2011) · Periodontology 2000 · doi:10.1111/j.1600-0757.2011.00414.x · Cited by 47
Assessment of Structured Socioeconomic Effects on Health
Kaufman, J. S., & Kaufman, S. (2001) · Epidemiology · doi:10.1097/00001648-200103000-00006 · Cited by 46
On quantifying the magnitude of confounding
Janes, H., Dominici, F., & Zeger, S. L. (2010) · Biostatistics · doi:10.1093/biostatistics/kxq007 · Cited by 45
Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies
Harbord, R. M., Didelez, V., Palmer, T., Meng, S., Sterne, J. A. C., & Sheehan, N. A. (2012) · Statistics in Medicine · doi:10.1002/sim.5659 · Cited by 46
“xC1; x/ because of the non-collapsibility of the odds ratio [24,25] and consequent ‘shrinkage’ of estimates that marginalize over a covariate compared with those that condition on it.”
BackgroundDorie, V., Hill, J., Shalit, U., Scott, M. A., & Cervone, D. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1707.02641 · Cited by 45
Monitoring Network Neutrality: A Survey on Traffic Differentiation Detection
Garrett, T., Setenareski, L. E., Peres, L. M., Bona, L. C. E., & Duarte, E. P. (2018) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2018.2812641 · Cited by 44
“in observable differences for different types of traffic – the so-called confounds [88].”
BackgroundMethodOn the logic of collapsibility for causal effect measures
Didelez, V., & Stensrud, M. J. (2021) · Biometrical Journal · doi:10.1002/bimj.202000305 · Cited by 43
“…study, is sometimesmeasured by comparing an estimate of the simple associational measure 𝜙 with an estimate of the causal marginal effect 𝜇, where 𝜇 is obtained by suitable adjustment such as standardisation or inverse probability of treatment weighting (IPTW) (Greenland et al., 1999).”
BackgroundInfluentialRemiro‐Azócar, A., Heath, A., & Baio, G. (2022) · Research Synthesis Methods · doi:10.1002/jrsm.1565 · Cited by 46
Shen, W., Hu, L.-C., & Hannum, E. C. (2021) · Social Science Research · doi:10.1016/j.ssresearch.2021.102576 · Cited by 43
Matched Versus Unmatched Analysis of Matched Case-Control Studies
Wan, F., Colditz, G. A., & Sutcliffe, S. S. (2021) · American Journal of Epidemiology · doi:10.1093/aje/kwab056 · Cited by 42
Multinomial Extension of Propensity Score Trimming Methods: A Simulation Study
Yoshida, K., Solomon, D. H., Haneuse, S., Kim, S. C., Patorno, E., Tedeschi, S. K., Lyu, H., Franklin, J. M., Stürmer, T., Hernández–Dı́az, S., et al. (2018) · American Journal of Epidemiology · doi:10.1093/aje/kwy263 · Cited by 42
A Structural Approach to the Familial Coaggregation of Disorders
Hudson, J. I., Javaras, K. N., Laird, N. M., VanderWeele, T. J., Pope, H. G., & Hernán, M. A. (2008) · Epidemiology · doi:10.1097/ede.0b013e31816a9de7 · Cited by 42
2, O. B. O. G. W. P., Pate, A., Candlish, J., Sperrin, M., & van Staa, T. P. (2016) · BMC Medical Research Methodology · doi:10.1186/s12874-016-0208-1 · Cited by 41
“If there was a greater variation between clusters, you would expect a lack of collapsibility to cause a difference between the marginal and frailty estimates [36].”
BackgroundStatistical Learning Methods for Neuroimaging Data Analysis with Applications
Hongtu Zhu, B., Li, T., & Zhao, B. (2023) · Annual Review of Biomedical Data Science · doi:10.1146/annurev-biodatasci-020722-100353 · Cited by 46
“Causality research can be roughly divided into causal discovery for determining causal relationships among a set of variables and causal inference for estimating causal effects deriving from a change of a certain variable over an outcome of interest in a large system (Imbens and Rubin, 2015; Pearl, 2009; Greenland et…”
BackgroundCausal inference with a quantitative exposure
Zhang, Z., Zhou, J., Cao, W., & Zhang, J. (2012) · Statistical Methods in Medical Research · doi:10.1177/0962280212452333 · Cited by 43
Carriger, J. F., & Parker, R. A. (2020) · Journal of Environmental Management · doi:10.1016/j.jenvman.2020.111478 · Cited by 41
“Acausal pathways also exist that move against the arrows in the graph when observations are made (Greenland et al., 1999).”
BackgroundStampf, S., Graf, E., Schmoor, C., & Schumacher, M. C. (2010) · Statistics in Medicine · doi:10.1002/sim.3811 · Cited by 40
“To some extent, the bias of the PS stratified MH estimator is due to the problem of non-collapsibility [31].”
BackgroundGeneralizability and effect measure modification in sibling comparison studies
Sjölander, A., Öberg, A. S., & Frisell, T. (2022) · European Journal of Epidemiology · doi:10.1007/s10654-022-00844-x · Cited by 36
“for logistic models) non-collapsibility of the chosen effect measure [27].”
BackgroundAnnequin, M., Weill, A., Thomas, F., & Chaix, B. (2015) · Annals of Epidemiology · doi:10.1016/j.annepidem.2015.02.002 · Cited by 39
“Even if it is not possible to compare the variance of successive logistic models [28, 29], Table 4 suggests that including the density of psychiatrists in the model led to a larger decrease of the betweenneighborhood variance than including neighborhood income.”
On the interpretation of risk and rate advancement periods
Discacciati, A., Bellavia, A., Orsini, N., & Greenland, S. (2015) · International Journal of Epidemiology · doi:10.1093/ije/dyv320 · Cited by 39
Self-citationMsaouel, P., Lee, J., & Thall, P. F. (2021) · Cancers · doi:10.3390/cancers13112741 · Cited by 38
“For risk ratios, the standardized risk ratio is an example of such a collapsible summary, and it can be calculated using the following formula [21], which first weighs each subgroup-specific proportion by multiply-”
BackgroundMethodHistory of the modern epidemiological concept of confounding
Morabia, A. (2010) · Journal of Epidemiology and Community Health · doi:10.1136/jech.2010.112565 · Cited by 35
“It also focuses on the theory of confounding, and does not cover the statistical approaches to confoundingrelated issues, (eg, collapsibility(5)) methods of adjusting for confounding, or the history of causal inference, which, even though closely related and overlapping at times with that of confounding, has a broader…”
BackgroundSources of bias in ecological studiesof non-rare events
Salway, R., & Wakefield, J. C. (2005) · Environmental and Ecological Statistics · doi:10.1007/s10651-005-1516-5 · Cited by 37
Leyrat, C., Caille, A., Donner, A. P., & Giraudeau, B. (2014) · Statistics in Medicine · doi:10.1002/sim.6185 · Cited by 36
“Of note, this means that the treatment effect is assumed to be constant, a necessary condition for collapsibility of the RR [31] (see in the following text).”
BackgroundRubin, D. B. (2007) · Handbook of statistics · doi:10.1016/s0169-7161(07)27002-6 · Cited by 39
Unemployment and subsequent depression: A mediation analysis using the parametric G-formula
Bijlsma, M. J., Tarkiainen, L., Myrskylä, M., & Martikainen, P. (2017) · Social Science & Medicine · doi:10.1016/j.socscimed.2017.10.011 · Cited by 40
Interpreting Randomized Controlled Trials
Msaouel, P., Lee, J., & Thall, P. F. (2023) · Cancers · doi:10.3390/cancers15194674 · Cited by 38
“Accordingly, randomization was further blocked within the M0 subpopulation to balance the ECOG performance status and geographic location of patients randomized to adjuvant pembrolizumab or placebo control [54].”
Analysis of 1 : 1 Matched Cohort Studies and Twin Studies, with Binary Exposures and Binary Outcomes
Sjölander, A., Johansson, A. L. V., Lundholm, C., Altman, D., Almqvist, C., & Yudi Pawitan, Y. (2012) · Statistical Science · doi:10.1214/12-sts390 · Cited by 37
“For a more thorough discussion on (non)collapsibility and the special properties of odds ratios, we refer the reader to Greenland et al. (1999).”
Causal inference for clinicians
Stovitz, S. D., & Shrier, I. (2019) · BMJ Evidence-Based Medicine · doi:10.1136/bmjebm-2018-111069 · Cited by 36
Steiger, E., Mußgnug, T., & Kroll, L. E. (2021) · PLoS ONE · doi:10.1371/journal.pone.0237277 · Cited by 38
Greenland, S. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2021.06.004 · Cited by 36
Self-citationNoncollapsibility, confounding, and sparse-data bias. Part 1: The oddities of odds
Greenland, S. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2021.06.007 · Cited by 36
Self-citationModel Averaged Double Robust Estimation
Cefalu, M. S., Dominici, F., Arvold, N. D., & Parmigiani, G. (2016) · Biometrics · doi:10.1111/biom.12622 · Cited by 32
“One such example may be a model that is sufficient for controlling confounding (Greenland et al., 1999; De Luna et al., 2011; Vansteelandt et al., 2012).”
BackgroundMatching Methods for Causal Inference
King, G. (2011) · Cited by 35
Bawah, A. A., Awoonor‐Williams, J. K., Asuming, P. O., Jackson, E. F., Boyer, C., Kanmiki, E. W., Achana, F. S., Akazili, J., & Phillips, J. F. (2019) · PLoS ONE · doi:10.1371/journal.pone.0218025 · Cited by 37
Ripamonti, E., Azoulay, L., Abrahamowicz, M., Platt, R. W., & Suissa, S. (2018) · Diabetic Medicine · doi:10.1111/dme.13854 · Cited by 36
Deciphering how early life adiposity influences breast cancer risk using Mendelian randomization
Vabistsevits, M., Smith, G. D., Sanderson, E. C. M., Richardson, T. G., Lloyd‐Lewis, B., & Richmond, R. C. (2022) · Communications Biology · doi:10.1038/s42003-022-03272-5 · Cited by 36
Kreif, N., Gruber, S., Radice, R., Grieve, R., & Sekhon, J. S. (2014) · Statistical Methods in Medical Research · doi:10.1177/0962280214521341 · Cited by 39
Causes and consequences of child growth faltering in low- and middle-income countriesPreprint
Mertens, A., Benjamin‐Chung, J., Colford, J. M., Coyle, J., van der Laan, M. J., Hubbard, A., Rosete, S., Malenica, I., Hejazi, N. S., Sofrygin, O., et al. (2020) · medRxiv · doi:10.1101/2020.06.09.20127100 · Cited by 34
Approaches for Quantifying the ICC in Multilevel Logistic Models: A Didactic Demonstration
Devine, S., Uanhoro, J., Otto, A. R., & Flake, J. K. (2024) · Collabra Psychology · doi:10.1525/collabra.94263 · Cited by 38
“…variance is fixed across logistic models, estimated model parameters are automatically scaled across models to reflect changes in residual variance across models (an issue referred to as non-collapsibility or unobserved heterogeneity depending on the literature; Greenland et al., 1999; Mood, 2010).”
BackgroundBoonstra, T. W., Faes, L., Kerkman, J. N., & Marinazzo, D. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.116093 · Cited by 35
Bounding Analysis as an Inadequately Specified Methodology
Greenland, S. (2004) · Risk Analysis · doi:10.1111/j.0272-4332.2004.00509.x · Cited by 33
“Adoption of potential outcomes has statistical implications for confounding identification and control, especially in an application that uses odds ratios or rate ratios as measures of effect for a common disease (Greenland, 1987; Rothman & Greenland, 1998, Ch. 4; Greenland et al., 1999).”
BackgroundInfluentialSelf-citationYears of Life Lost due to exposure: Causal concepts and empirical shortcomings
Morfeld, P. (2004) · Epidemiologic Perspectives & Innovations · doi:10.1186/1742-5573-1-5 · Cited by 32
“1999b [58]) can help to identify and avoid such empirical shortcomings.”
BackgroundWang, T., Li, H.-K., Su, P., Yu, Y.-Y., Sun, X.-R., Liu, Y., Yuan, Z.-S., & Xue, F.-Z. (2017) · BMJ Open · doi:10.1136/bmjopen-2016-015640 · Cited by 31
A non-technical explanation of the counterfactual definition of confounding.
Bours, M. (2020) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2020.01.021 · Cited by 30
Teisen, M. N., Vuholm, S., Niclasen, J., Aristizabal‐Henao, J. J., Stark, K. D., Geertsen, S. S., Damsgaard, C. T., & Lauritzen, L. (2020) · American Journal of Clinical Nutrition · doi:10.1093/ajcn/nqaa050 · Cited by 37
Estimation and modeling of the restricted mean time lost in the presence of competing risks
Conner, S. C., & Trinquart, L. (2021) · Statistics in Medicine · doi:10.1002/sim.8896 · Cited by 32
Unsupervised Visual Attention and Invariance for Reinforcement Learning
Wang, X., Lian, L., & Yu, S. X. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.00661 · Cited by 38
Korsiak, J., Lavigne, É., You, H., Pollitt, K. J. G., Kulka, R., Hatzopoulou, M., Evans, G. J., Burnett, R. T., & Weichenthal, S. (2022) · American Journal of Respiratory and Critical Care Medicine · doi:10.1164/rccm.202205-0896oc · Cited by 34
Decoupling, Sparsity, Randomization, and Objective Bayesian Inference
Stern, J. M. (2008) · PhilPapers (PhilPapers Foundation) · Cited by 32
The conundrum of causality in tumor virology: The cases of KSHV and MCV
Moore, P. S., & Chang, Y. (2013) · Seminars in Cancer Biology · doi:10.1016/j.semcancer.2013.11.001 · Cited by 31
“Hume instead used a counterfactual argument to define causality: we can say object A causes object B when B follows A and when A does not occur, then B does not occur [11, 18, 25].”
BackgroundDeep Learning-based Propensity Scores for Confounding Control in Comparative Effectiveness Research
Weberpals, J. G., Becker, T., Davies, J., Schmich, F., Rüttinger, D., Theis, F. J., & Bauer‐Mehren, A. (2021) · Epidemiology · doi:10.1097/ede.0000000000001338 · Cited by 30
“24 Simulations of treatment effects other than a null treatment effect were not considered to avoid complications with the collapsibility 25 and proportional hazards assumption 26 of HRs.”
Learning Causal Effects From Observational Data in Healthcare: A Review and Summary
Shi, J.-P., & Norgeot, B. (2022) · Frontiers in Medicine · doi:10.3389/fmed.2022.864882 · Cited by 38
“There are two widely accepted frameworks in the literature for causal inference: the structural causal model (SCM) (14– 16) and the potential outcome framework (POF) (12, 17, 18).”
Occupational Exposure to PM2.5 and Incidence of Ischemic Heart Disease
Brown, D., Petersen, M. L., Costello, S., Noth, E. M., Hammond, K., Cullen, M. R., van der Laan, M. J., & Eisen, E. (2015) · Epidemiology · doi:10.1097/ede.0000000000000329 · Cited by 32
Evaluating Methods to Estimate the Effect of State Laws on Firearm Deaths: A Simulation Study
Schell, T. L., Griffin, B. A., & Morral, A. R. (2018) · RAND Corporation eBooks · doi:10.7249/rr2685 · Cited by 31
Causation and Causal Inference
Greenland, S. (2011) · Springer eBooks · doi:10.1007/978-3-642-04898-2_9 · Cited by 31
Self-citationChu, R., Walter, S. D., Guyatt, G. H., Devereaux, P. J., Walsh, M. W., Thorlund, K., & Thabane, L. (2012) · PLoS ONE · doi:10.1371/journal.pone.0036677 · Cited by 30
“This is also referred to as the non-collapsibility problem [16], because the odds ratio as the measure of association between the treatment and the binary outcome within each category of the baseline covariates (i.”
BackgroundCovariate Imbalance and Adjustment for Logistic Regression Analysis of Clinical Trial Data
Ciolino, J. D., Martin, R. H., Zhao, W., Jauch, E. C., Hill, M. D., & Palesch, Y. Y. (2013) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2013.834912 · Cited by 30
“, the overall OR does not necessarily equal the weighted average of the stratum-specific ORs) (Kent et al., 2009; Greenland et al., 1999; Robinson and Jewell, 1991).”
BackgroundAssessing the impact of unmeasured confounding for binary outcomes using confounding functions
Kasza, J., Wolfe, R. S., & Schuster, T. (2017) · International Journal of Epidemiology · doi:10.1093/ije/dyx023 · Cited by 30
Nonlinear mediation analysis with high‐dimensional mediators whose causal structure is unknown
Loh, W. W., Moerkerke, B., Loeys, T., & Vansteelandt, S. (2020) · Biometrics · doi:10.1111/biom.13402 · Cited by 30
“tors, diers from the eect that is unconditional on 4 the other mediators, due to non-collapsibility of certain non-linear eect measures, such as the odds ratio, even in the absence of confounding (Greenland et al., 1999). VanderWeele and Tchetgen Tchetgen (2017) suggested interventional eects using (counterfactual) me…”
BackgroundAustin, P. C., & Stafford, J. E. (2008) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610910801942430 · Cited by 30
“Greenland (1987), Greenland and Robins (1986), and Greenland et al. (1999) referred to this phenomenon as the non collapsibility of the odds ratio.”
BackgroundMethodMethods for Estimating Subgroup Effects in Cost-Effectiveness Analyses That Use Observational Data
Kreif, N., Grieve, R., Radice, R., Sadique, Z., Ramsahai, R. R., & Sekhon, J. S. (2012) · Medical Decision Making · doi:10.1177/0272989x12448929 · Cited by 30
“Instead, regression and matching approaches warrant consideration, provided the crucial assumption that all potential confounders have been observed can be justified.(10) Regression methods, recommended for subgroup analysis in CEA of RCTs,(11,12) are common in CEA that use NRS.”
MethodInfluentialThe logic of Simpson’s paradox
Bandyoapdhyay, P. S., Nelson, D., Greenwood, M., Brittan, G. G., & Berwald, J. (2010) · Synthese · doi:10.1007/s11229-010-9797-0 · Cited by 30
“Our analysis of the paradox, however, differs sharply from the causal account offered by Judea Pearl (Pearl 2000; Greenland et al. 1999).1 In our view, his account is not persuasive.”
ResultForman‐Rabinovici, A., & Sommer, U. (2019) · Democratization · doi:10.1080/13510347.2019.1661993 · Cited by 31
Estimating a Marginal Causal Odds Ratio Subject to Confounding
Zhang, Z. (2008) · Communication in Statistics- Theory and Methods · doi:10.1080/03610920802200076 · Cited by 30
“This phenomenon has been noted by Gail et al. (1984) in the context of generalized linear models and is also known as non-collapsibility in causal inference (Greenland et al., 1999).”
BackgroundEffect of Facility on the Operative Costs of Distal Radius Fractures
Mather, R. C. “., Wysocki, R. W., Aldridge, J. M., Pietrobon, R. S., & Nunley, J. A. (2011) · The Journal Of Hand Surgery · doi:10.1016/j.jhsa.2011.03.042 · Cited by 29
Controlling for continuous confounding factors: non- and semiparametric approaches
Slama, R., & Werwatz, A. (2005) · Revue d Épidémiologie et de Santé Publique · doi:10.1016/s0398-7620(05)84769-8 · Cited by 29
Zhang, B., Thacker, D., Zhou, T., Zhang, D., Lei, Y., Chen, J., Chrischilles, E. A., Christakis, D., Fernández, S., Garg, V., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-56284-0 · Cited by 31
Socioeconomic determinants of disability in Chile
Melo, P. Z., & Cabieses, B., V (2011) · Disability and health journal · doi:10.1016/j.dhjo.2011.06.002 · Cited by 29
“A confounder is a distortion in the estimated exposure effect that results from differences in risk between the exposed and unexposed that are not due to exposure [58, 59].”
BackgroundExact parametric causal mediation analysis for a binary outcome with a binary mediator
Doretti, M., Raggi, M., & Stanghellini, E. (2021) · Statistical Methods & Applications · doi:10.1007/s10260-021-00562-w · Cited by 26
Xiao, M., Chen, Y., Cole, S. R., MacLehose, R. F., Richardson, D. B., & Chu, H. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2021.08.004 · Cited by 27
Xiao, M., Chu, H., Cole, S. R., Chen, Y., MacLehose, R. F., Richardson, D. B., & Greenland, S. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2021.08.002 · Cited by 28
Self-citationRotation‐based multiple testing in the multivariate linear model
Solari, A., Finos, L., & Goeman, J. J. (2014) · Biometrics · doi:10.1111/biom.12238 · Cited by 28
On hazard ratio estimators by proportional hazards models in matched-pair cohort studies
Shinozaki, T., Mansournia, M. A., & Matsuyama, Y. (2017) · Emerging Themes in Epidemiology · doi:10.1186/s12982-017-0060-8 · Cited by 28
“This representation would be useful because HR (like OR) is known to be a noncollapsible measure: even under homogeneity of conditional HR across strata and in the absence of confounding, marginal (unadjusted) HR is not necessarily equal to the conditional one [16, 17].”
BackgroundResultMatsuyama, Y. (2002) · Statistics in Medicine · doi:10.1002/sim.1002 · Cited by 28
“Note that in randomized trials our estimation goal is the comparison of the expected outcome of the entire study group if everyone had been treated and the expected outcome of this group if no one had been treated [6; 14].”
BackgroundZhu, R., Tu, X., & Huang, J. X. (2019) · Studies in big data · doi:10.1007/978-3-030-33966-1_13 · Cited by 29
Causal Support: Modeling Causal Inferences with Visualizations
Kale, A. M., Wu, Y., & Hullman, J. R. (2021) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2021.3114824 · Cited by 28
“Whether or not a factor seems to be collapsible —whether or not patterns the data seem to change depending on whether the data are grouped by that factor—can be a visual signal for reasoning about causal relationships such as confounding [20].”
InfluentialCriteria for Confounders in Epidemiological Studies
Geng, Z., Guo, J., & Fung, W. (2002) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00321 · Cited by 27
“Whittemore (1978), Ducharme and LePage (1986), Geng (1992) and Guo and Geng (1995). The other approach, called `comparability based', considers confounding as arising from the exposed and unexposed populations which are not comparable.”
BackgroundMethodErrors in causal inference: an organizational schema for systematic error and random error.
Suzuki, E., Tsuda, T., Mitsuhashi, T., Mansournia, M., & Yamamoto, E. (2016) · Annals of Epidemiology · doi:10.1016/j.annepidem.2016.09.008 · Cited by 28
Remiro‐Azócar, A., Heath, A., & Baio, G. (2021) · UCL Discovery (University College London) · Cited by 26
Reporting of treatment effects from randomized trials: A plea for multivariable risk ratios
Groenwold, R. H. H., Moons, K. G. M., Peelen, L. M., Knol, M. J., & Hoes, A. W. (2011) · Contemporary Clinical Trials · doi:10.1016/j.cct.2010.12.011 · Cited by 27
“However, when odds ratios (using logistic regression) or hazard ratios are estimated, the marginal and conditional effects do differ, even when confounding is absent, such as in a trial with perfectly balanced covariates [9,11].”
BackgroundOn the Uses and Abuses of Regression Models: A Call for Reform of Statistical Practice and Teaching
Carlin, J. B., & Moreno‐Betancur, M. (2025) · Statistics in Medicine · doi:10.1002/sim.10244 · Cited by 37
“Second,oncethe preferred target effect measure (estimand) has been decided, and identifiability issues considered, what practical problems may arise in its estimation?”
Burgess, S., & Thompson, S. G. (2010) · Statistics in Medicine · doi:10.1002/sim.3843 · Cited by 25
“However, they do not provide unbiased estimators of a non-zero causal parameter [2], due to the non-collapsibility of the log-odds function over the distribution of the unknown confounders [39].”
Causality and Causal Models: A Conceptual Perspective*
Frosini, B. V. (2006) · International Statistical Review · doi:10.1111/j.1751-5823.2006.tb00298.x · Cited by 24
Methodological issues of confounding in analytical epidemiologic studies.
Hajian‐Tilaki, K. (2012) · Europe PMC (PubMed Central) · Cited by 26
Phillippo, D., Dias, S., Ades, A. E., & Welton, N. J. (2021) · Statistics in Medicine · doi:10.1002/sim.8965 · Cited by 23
Interaction Contrasts and Collider Bias
Mansournia, M. A., Nazemipour, M., & Etminan, M. (2022) · American Journal of Epidemiology · doi:10.1093/aje/kwac103 · Cited by 25
Estimating the Per-Exposure Effect of Infectious Disease Interventions
O’Hagan, J. J., Lipsitch, M., & Hernán, M. Á. (2013) · Epidemiology · doi:10.1097/ede.0000000000000003 · Cited by 25
van der Wal, W. M., Noordzij, M., Dekker, F. W., Boeschoten, E. W., Krediet, R. T., Korevaar, J. C., & Geskus, R. B. (2010) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1166 · Cited by 25
Three controversies in health data science
Peek, N. B., & Rodrigues, P. P. (2018) · International Journal of Data Science and Analytics · doi:10.1007/s41060-018-0109-y · Cited by 29
“Over the last twodecades, tremendous improvements have been made in our understanding of the concept of causality, and in methods for causal inference from observational data [20,22,23].”
BackgroundMarginal Time-Dependent Causal Effects in Mediation Analysis With Survival Data
Fasanelli, F., Giraudo, M. T., Ricceri, F., Valeri, L., & Zugna, D. (2019) · American Journal of Epidemiology · doi:10.1093/aje/kwz016 · Cited by 25
Whitcomb, B. W., & Naimi, A. I. (2020) · American Journal of Epidemiology · doi:10.1093/aje/kwaa267 · Cited by 24
Simpson, D. A., Carson, C., Kurinczuk, J. J., & QUIGLEY, M. A. (2021) · European Journal of Clinical Nutrition · doi:10.1038/s41430-021-01031-z · Cited by 23
“Potential biases, residual confounding and the non-collapsibility of the OR mean that differences between ORs between surveys should be interpreted cautiously[44].”
Distributed Cox proportional hazards regression using summary-level information
Li, D., Lu, W., Shu, D., Toh, S., & Wang, R. (2022) · Biostatistics · doi:10.1093/biostatistics/kxac006 · Cited by 24
Tu, W., & Zhou, X. (2002) · Health Services and Outcomes Research Methodology · doi:10.1023/a:1024212107921 · Cited by 24
“Causal inferences on the average treatment effect in observational studies are difficult because the effect could be confounded with the covariates whose distributions differ systematically in the two treatment groups, and a direct estimation of the treatment effect is often biased [9, 17, 18].”
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
