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The Table 2 Fallacy: Presenting and Interpreting Confounder and Modifier Coefficients
Open accessAbstract
It is common to present multiple adjusted effect estimates from a single model in a single table. For example, a table might show odds ratios for one or more exposures and also for several confounders from a single logistic regression. This can lead to mistaken interpretations of these estimates. We use causal diagrams to display the sources of the problems. Presentation of exposure and confounder effect estimates from a single model may lead to several interpretative difficulties, inviting confusion of direct-effect estimates with total-effect estimates for covariates in the model. These effect estimates may also be confounded even though the effect estimate for the main exposure is not confounded. Interpretation of these effect estimates is further complicated by heterogeneity (variation, modification) of the exposure effect measure across covariate levels. We offer suggestions to limit potential misunderstandings when multiple effect estimates are presented, including precise distinction between total and direct effect measures from a single model, and use of multiple models tailored to yield total-effect estimates for covariates.
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“After controlling for gender and age as potential confounding factors, independent associations between the outcome variables of burnout as well as anxiety/depression and the explanatory variables (i.e., ALTs, psychological flexibility) were examined [58].”
From The mediating role of psychological flexibility in the association of autistic-like traits with burnout and depression in medical students during clinical clerkships in Japan: a university-based cross-sectional study (2023) · cites this paper as [58]
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“This may very well be the case when a set of covariates is entered in a multiple regression model, and all regression coefficients for variables in X are evaluated as effects of risk factors, without taking the underlying causal structure into account (known as the Table 2 fallacy) [42].”
Zhu, X., Yang, Y., Wright, H. R., Speyer, L. G., Allitt, M., Obsuth, I., Errington, P. J., & Murray, A. L. (2025) · SSM - Mental Health · doi:10.1016/j.ssmmh.2025.100582 · Cited by 7
Smida, T., Kimbrell, J. M., Kreinbrook, J., Gan, G. H., Odom, W., Bouthillet, T., Walsh, B., Shukis, M., Scheidler, J. F., Martin, P. S., et al. (2025) · Resuscitation · doi:10.1016/j.resuscitation.2025.110934 · Cited by 5
Earle, W., Watson, N. W., Juraschek, S. P., Cluett, J., Krawisz, A. K., & Secemsky, E. A. (2026) · Hypertension · doi:10.1161/hypertensionaha.125.25659 · Cited by 5
Remalante-Rayco, P. P. M., Passalent, L., Chim, T., Vijayan, H., Alnasser, M., Baskurt, Z., Inman, R. D., Haroon, N., & Poddubnyy, D. (2026) · Arthritis & Rheumatology · doi:10.1002/art.70202 · Cited by 5
Seixas, B. V., & Macinko, J. A. (2023) · SSM - Population Health · doi:10.1016/j.ssmph.2023.101416 · Cited by 5
Rotenberg, M., Gozdyra, P., Anderson, K. K., & Kurdyak, P. A. (2023) · PLoS ONE · doi:10.1371/journal.pone.0287334 · Cited by 5
“These secondary effects must be interpreted with caution, as these estimates may be biased due to the models not being constructed to obtain unconfounded estimates of the relationship between the secondary exposures and outcomes for people with a history of substance use [35, 36].”
BackgroundWhat does the general public know about palliative care? A population-based survey
Matthys, M., Chambaere, K., Beernaert, K., Cohen, J., Brussel, L. V., Deforche, B. I., Quintiens, B., Deliëns, L., & Dhollander, N. (2023) · BMJ Supportive & Palliative Care · doi:10.1136/spcare-2023-004384 · Cited by 5
Kurdi, S. M., Alamer, A., Albaggal, A., Alsuwaiket, M., Alotaibi, F. M., Asiri, I. M., Alshayban, D., Alsultan, M. M., Alshehail, B. M., Almalki, B. A., et al. (2024) · Journal of Clinical Medicine · doi:10.3390/jcm13020419 · Cited by 6
“In addition, the current study was not designed to assert the associations reported in Table 3 as this will require making assumptions about the data-generating process via DAGs and collecting more pertinent variables to test each variable of interest with the outcome of interest [16,32].”
BackgroundRural–urban differences in the perceived impact of COVID-19 on mental health by European women
Rodríguez, M., & Ballesta, J. A. C. (2024) · Archives of Women s Mental Health · doi:10.1007/s00737-024-01443-3 · Cited by 5
“It is important to note that odds ratios cannot be interpreted as total-effects (Westreich and Greenland 2013).”
BackgroundMcIntyre, K. J., Tassiopoulos, K. N., Jeffrey, C., Stranges, S., & Martin, J. E. (2024) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2024.111532 · Cited by 5
Experience sampling method studies in physical activity research: the relevance of causal reasoning
Poppe, L., Paepe, A. L. D., Deforche, B. I., Dyck, D. V., Loeys, T., & Cauwenberg, J. V. (2025) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-025-01723-w · Cited by 7
“This mismatch results in ambiguity, bias, and misinterpretation of research results [11, 12], also in ESM studies [9].”
Missed Opportunities for Chlamydia Screening in Title X Family Planning Clinics
Salomon, S., Torrone, E., Nakatsukasa-Ono, W., & Fine, D. (2017) · Sexually Transmitted Diseases · doi:10.1097/olq.0000000000000641 · Cited by 5
“Finally, we caution readers not to interpret our univariate results as total effect estimates for each covariate, because these were exploratory analyses not informed by causal models.(26) Our interest was comparing approximate strengths of associations across covariates, not precisely estimating each association.”
HPV vaccination and sexual behaviour in healthcare seeking young women in Luxembourg
Soudeyns, C., Speybroeck, N., Brisson, M., Mossong, J., & Latsuzbaia, A. (2020) · PeerJ · doi:10.7717/peerj.8516 · Cited by 5
Varnet, L., Léger, A. C., Boucher, S., Bonnet, C., Petit, C., & Lorenzi, C. (2021) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2021.640522 · Cited by 5
An automated line-clearing chest tube system after cardiac surgery
Obafemi, O. O., Wang, H., Bajaj, S. S., O’Donnell, C. T., Elde, S., & Boyd, J. H. (2022) · JTCVS Open · doi:10.1016/j.xjon.2022.02.020 · Cited by 5
Danese, M. D., Schenfeld, J., Shaw, J. L., Gawade, P. L., Balasubramanian, A., Kelsh, M. A., Hernandez, R. K., & Lyman, G. H. (2022) · Advances in Therapy · doi:10.1007/s12325-022-02141-1 · Cited by 5
“The effects of other exposures deserve comment, noting that the causal interpretation of other covariates from a model may be confounded even if the primary exposure of interest is not [40].”
BackgroundCalderwood, C., Tlali, M., Karat, A. S., Hoffmann, C. J., Charalambous, S., Johnson, S., Grant, A. D., & Fielding, K. (2022) · Open Forum Infectious Diseases · doi:10.1093/ofid/ofac265 · Cited by 5
“Model B included all identified risk factors to describe direct effects [30].”
BackgroundLuijken, K., van de Wall, B. V. D., Hooft, L., Leenen, L., Houwert, R., & Groenwold, R. (2022) · European Journal of Trauma and Emergency Surgery · doi:10.1007/s00068-022-02031-9 · Cited by 2
“A final note on confounders is that it is advisable not to interpret coefficients of confounding variables as causal effects or independent prognostic associations [29].”
BackgroundShelton, B. A., Sawinski, D. L., MacLennan, P. A., Lee, W., Wyatt, C. M., Nadkarni, G. N., Fatima, H., Mehta, S. G., Crane, H. M., Porrett, P. M., et al. (2022) · EClinicalMedicine · doi:10.1016/j.eclinm.2022.101653 · Cited by 5
Liu, L., Wang, H., Zhang, Z., Zhang, W., Zhuang, S., Wang, S., Silva, E. A., Lv, T., Chio, C. O., Wang, Y., et al. (2022) · npj Urban Sustainability · doi:10.1038/s42949-022-00074-w · Cited by 5
Roumans, C. A. M., van der Bogt, R. D., Nieboer, D., Steyerberg, E. W., Rizopoulos, D., Lansdorp‐Vogelaar, I., Biermann, K., Bruno, M. J., & Spaander, M. C. W. (2022) · Diseases of the Esophagus · doi:10.1093/dote/doac113 · Cited by 5
Chen, Y., Hu, K., Chan, C., Huang, C., Huang, Y., Wang, Y.-F., Wang, S., Chen, S., & Lee, M. (2023) · Headache The Journal of Head and Face Pain · doi:10.1111/head.14491 · Cited by 5
Nazif‐Muñoz, J. I., Quesnel‐Vallée, A., & van den Berg, A. (2023) · Accident Analysis & Prevention · doi:10.1016/j.aap.2023.107122 · Cited by 5
Fleming, V. H., Xu, J., Chen, X., Hall, D. B., & Southwood, R. L. (2023) · Annals of Pharmacotherapy · doi:10.1177/10600280231210275 · Cited by 5
“This approach follows work of Westreich and Greenland 25 and others 26 who argue that such effects can remain confounded and are not amenable to straightforward interpretation.”
Whibley, D., Shieu, M. M., Dunietz, G. L., & Braley, T. J. (2023) · Sleep Epidemiology · doi:10.1016/j.sleepe.2023.100071 · Cited by 5
“Our decisions regarding adjustment variables were underpinned by the concept of Table 2 Fallacy [40], which also informed our decision not to mutually adjust for all sleep-related variables in a single model.”
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Occupation and COVID-19: Lessons From the Pandemic
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Directed acyclic graphs to foster transparency and scientific dialogue
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Patel, H. V., Li, K. D., Rourke, K. F., Smith, T. G., Voelzke, B. B., Myers, J. B., Broghammer, J. A., Alsikafi, N. F., Buckley, J. C., Zhao, L. C., et al. (2024) · The Journal of Urology · doi:10.1097/ju.0000000000004188 · Cited by 5
“18 Given these considerations, it is essential to interpret this association with caution, and further studies are warranted to validate and understand the underlying mechanisms between smoking and outcomes in reconstructive surgery.”
Zhu, R., Pitchik, H. O., Nduku, T., Engelmann, J. M., Fernald, L. C. H., & Alison Gopnik, C. (2024) · Developmental Science · doi:10.1111/desc.13579 · Cited by 5
Metadata
- Authors
- Westreich, D., & Greenland, S.
- Affiliations
- Duke University (US)
- Corresponding author
- Westreich, D.
- Venue
- American Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2013-01-30
- Volume
- 177
- Issue
- 4
- Pages
- 292-298
- ISSN
- 0002-9262 (ISSN-L)
- 1476-6256
- PMC
- PMC3626058
- OpenAlex
- W2138008655
- Cited by
- 1,276
- References
- 30
- Citations by year
- 2026: 177 · 2025: 213 · 2024: 212 · 2023: 176 · 2022: 192 · 2021: 108 · 2020: 84 · 2019: 39 · 2018: 29 · 2017: 11 · 2016: 3 · 2015: 15 · 2014: 13 · 2013: 4
- FWCI
- 10.27
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- American Journal of Epidemiology (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institutes of Health (AI064518)
- Duke Global Health Institute, Duke University
- University of California, Los Angeles
- National Institute of Allergy and Infectious Diseases (P30AI064518)
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (R00HD063961)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- causal graphs, confounding, odds ratio, logistic regression
- MeSH terms
- HIV Seropositivity, Humans, Mathematical Computing, North Carolina, Regression Analysis, Risk Factors, Smoking, Statistics as Topic, Violence, Work, HIV Infections, Confounding Factors, Epidemiologic, Multivariate Analysis, Logistic Models, Odds Ratio, Epidemiologic Studies, Risk Assessment, Stroke
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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.
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