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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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“The mutual adjustment fallacy, often termed the Table 2 fal-lacy (Westreich & Greenland, 2013), is extremely common in ecology, with studies reporting all of the coef fi cients of a regression (or marginal effects) as if they can all be interpreted in the same way (Cole & Hern (cid:2) an, 2002;…”
Renin–angiotensin system blockade in the COVID-19 pandemic
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Kriss, J. L., Albert, A. P., Carter, V. M., Jiles, A. J., Liang, J. L., Mullen, J. N., Rodríguez, L., Howards, P. P., Orenstein, W. A., Omer, S. B., et al. (2018) · Maternal and Child Health Journal · doi:10.1007/s10995-018-2633-8 · Cited by 23
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Hyperthermic intraperitoneal chemotherapy in colorectal cancer
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“Equally, patients who received MMC-HIPEC were less likely to receive adjuvant systemic chemotherapy, which was independently associated with improved OS—albeit this exposure needs to be interpreted with caution due to risk of overadjustment bias and ‘Table 2 fallacy’ 14,27 .”
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“Westreich and Greenland called this problem the table 2 fallacy, 13 because many studies include a table 1 describing the distribution of exposure variables in a study sample and a table 2 showing multi-variable associations between the exposures and an outcome.”
Chandran, A., Knapp, E. A., Liu, T., & Dean, L. T. (2021) · Pediatric Research · doi:10.1038/s41390-021-01386-w · Cited by 23
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MethodFactors affecting mortality after coronary bypass surgery: a scoping review
Hardiman, S., Villán, Y., Conway, J., Sheehan, K. J., & Sobolev, B. (2022) · Journal of Cardiothoracic Surgery · doi:10.1186/s13019-022-01784-z · Cited by 24
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“A standard mistake is to assign causal interpretations to parameters with no identification strategy, sometimes termed the ‘ table 2 fallacy ’ [18].”
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“Giving a causal interpretation to regression estimates for covariates included in the same regression model is known as the mutual adjustment or Table 2 fallacy [16] and is very prevalent in health promotion publications, including papers written by the authors of this commentary.”
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Greenland, S. (2021) · American Journal of Epidemiology · doi:10.1093/aje/kwab069 · Cited by 22
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Prevalence and risk factors of food insecurity among Libyan migrant families in Australia
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“Therefore, they should not be interpreted as causal mechanisms to avoid the so-called “table 2 fallacy” (51).”
BackgroundTo Evaluate the Age–Happiness Relationship, Look Beyond Statistical Significance
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“Our recommendations are in line with Westreich & Greenland (2013) who discuss a similar problem with respect to the interpretation of potentially endogenous controls in epidemiology.”
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Gestational Weight Gain and Long-term Maternal Obesity Risk: A Multiple-Bias Analysis
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“[47], as effect measures for secondary risk factors can be biased if they are interpreted in the same way as the primary risk factor.”
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“Interpreting the effect estimates of confounders that are present in the model as representative of their association with the outcome or ‘mutually adjusted’ is known as the Table 2 Fallacy and should be avoided [22].”
BackgroundBoer, O. D., Marroun, H. E., & Muetzel, R. L. (2024) · Molecular Psychiatry · doi:10.1038/s41380-024-02471-2 · Cited by 24
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“Each of the 3 effect measures (total, direct, and indirect) has a different interpretation and is not directly comparable with the others (11).”
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MethodRana, J., Ahmmad, Z., Sen, K. K., Bista, S., & Islam, R. M. (2020) · PLoS ONE · doi:10.1371/journal.pone.0218767 · Cited by 20
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Bariatric surgery as urate-lowering therapy in severe obesity
Choi, H. K., & Zhang, Y. (2014) · Annals of the Rheumatic Diseases · doi:10.1136/annrheumdis-2013-204861 · Cited by 21
Identifying and Addressing Confounding Bias in Violence Prevention Research
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Parlier‐Ahmad, A. B., Radic, M., Svikis, D. S., & Martin, C. E. (2022) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2022.109337 · Cited by 19
The Impact of Increased Minimum Wage on Child Neglect Varies by Developmental Age of Child
Ash, M. J., Livingston, M. D., Komro, K. A., Spencer, R. A., Walker, A. L., & Woods-Jaeger, B. A. (2023) · Journal of Interpersonal Violence · doi:10.1177/08862605221150458 · Cited by 20
“Associations from other modeled predictors are treated as nuisance variables and not interpreted to avoid the “Table 2” fallacy (Westreich & Greenland, 2013).”
BackgroundZhong, X., Ashiru-Oredope, D. A. I., Pate, A., Martin, G. P., Sharma, A. K., Dark, P. M., Felton, T., Lake, C., MacKenna, B., Mehrkar, A., et al. (2023) · EClinicalMedicine · doi:10.1016/j.eclinm.2023.102321 · Cited by 19
“49 Furthermore, our study only assessed mortality within 30 days of sepsis onset, and deaths could have resulted from other causes, suggesting that they were not solely due to sepsis.”
BackgroundInterdental Cleaning and Oral Health Status in an Adult Cohort, 2015 to 2018
Chaffee, B., Persai, D., & Vora, M. (2020) · Journal of dentistry research · doi:10.1177/0022034520926139 · Cited by 19
“While study objectives related to interdental cleaning, other model covariables associated with oral health offer insight, with the caveat that such associations should be considered direct effects controlled for interdental cleaning (Westreich and Greenland 2013).”
BackgroundPrediction of quality of life in early breast cancer upon completion of adjuvant chemotherapy
Carmona‐Bayonas, A., Calderón, C., Hernández, R., Montés, A. F., Castelo, B., Ciria‐Suarez, L., Antoñanzas, M., Rogado, J., Pacheco-Barcía, V., Asensio, E., et al. (2021) · npj Breast Cancer · doi:10.1038/s41523-021-00296-8 · Cited by 19
Moyo, S., Ismail, F., Mkhondo, N., der Walt, M. L. V., Dlamini, S. S., Mthiyane, T., Naidoo, I., Zuma, K. K., Tadolini, M., Law, I., et al. (2023) · PLoS ONE · doi:10.1371/journal.pone.0282125 · Cited by 19
“Given the potential complex and causal pathways and confounding factors from symptoms to care seeking (that we did not investigate), the adjusted odd ratios cannot necessarily be interpreted in the same manner [42].”
BackgroundRacial Discrimination in International Visa Policies
Rosenberg, A. S. (2023) · International Studies Quarterly · doi:10.1093/isq/sqad032 · Cited by 20
Estimating causal effects from panel data with dynamic multivariate panel models
Helske, J., & Tikka, S. (2024) · Advances in Life Course Research · doi:10.1016/j.alcr.2024.100617 · Cited by 23
Best clinical model predicting extubation failure: a diagnostic accuracy post hoc analysis
Villamizar, P. R., Thille, A. W., Doblas, M. M., Frat, J. P., Sanz, P. L., Alonso, E., País, V., Morales, G., Colinas, L., Propín, A., et al. (2025) · Intensive Care Medicine · doi:10.1007/s00134-024-07758-0 · Cited by 18
Todorova, B., Steyrl, D., Hornsey, M. J., Pearson, S. G., Brick, C., Lange, F., Bavel, J. J. V., Vlasceanu, M., Lamm, C., & Doell, K. C. (2025) · npj Climate Action · doi:10.1038/s44168-025-00251-4 · Cited by 21
“Theselected analysis approach balances predictive performance with interpretability, enabling us to extract meaningful insights from complex relationships within the data and was chosen due to the numerous advantages it has over more traditional regression-based models 26 – 29 .”
Faiman, I., Hodsoll, J. P., Young, A. H., & Shotbolt, P. (2022) · Journal of Neurology Neurosurgery & Psychiatry · doi:10.1136/jnnp-2022-329093 · Cited by 18
Rates of ecological knowledge learning in Pemba, Tanzania: Implications for childhood evolution
Pretelli, I., Mulder, M. B., & McElreath, R. L. (2022) · Evolutionary Human Sciences · doi:10.1017/ehs.2022.31 · Cited by 18
O’Dea, A. L., Feng, R., Glaser, L. J., Kubrak, C., Rubenstein, R. C., Dorgan, D. J., Hadjiliadis, D., Kawut, S. M., & Hong, G. (2023) · Annals of the American Thoracic Society · doi:10.1513/annalsats.202210-852oc · Cited by 17
Crutzen, R., & Peters, G.-J. (2023) · Health Psychology and Behavioral Medicine · doi:10.1080/21642850.2023.2268684 · Cited by 28
“…‘ holding a person ’ s smoking level and HIV status constant as they age, which would be unethical for smokers (among whom reduction should be encouraged) and infeasible even if desirable for those HIV negative (because some will maintain unsafe practices) ’ (Westreich & Greenland, 2013, p. 297).”
BackgroundNelsen, D. R., Corbit, A. G., Chuang, A., Deitsch, J. F., Sitvarin, M. I., & Coyle, D. R. (2023) · Ecology and Evolution · doi:10.1002/ece3.10728 · Cited by 18
Factors influencing canine rabies vaccination among dog-owning households in Nigeria
Mshelbwala, P. P., Rupprecht, C. E., Osinubi, M. O. V., Njoga, E. O., Orum, T. G., Weese, J. S., & Clark, N. J. (2024) · One Health · doi:10.1016/j.onehlt.2024.100751 · Cited by 18
Doing Genders: Partner’s Gender and Labor Market Behavior
Jaspers, E., Mazrekaj, D., & Machado, W. (2024) · American Sociological Review · doi:10.1177/00031224241252079 · Cited by 18
Disparities in Hospice Utilization for Older Cancer Patients Living in the Deep South
Turkman, Y., Williams, C., Jackson, B. E., Dionne-Odom, J. N., Taylor, R. A., Ejem, D., Kvale, E. A., Pisu, M., Bakitas, M. A., & Rocque, G. B. (2019) · Journal of Pain and Symptom Management · doi:10.1016/j.jpainsymman.2019.04.006 · Cited by 18
“We examined unadjusted models only due to the exploratory nature of this analysis.(17) Results The sample consisted of 12,725 UAB CCN Medicare decedents (average age at death = 77 [SD 7.”
MethodPanchal, K., Lawson, C. A., Chandramouli, C., Lam, C. S. P., Khunti, K., & Zaccardi, F. (2023) · Diabetes Research and Clinical Practice · doi:10.1016/j.diabres.2023.111054 · Cited by 18
Scheim, A. I., Restar, A., Zubizarreta, D., Lucas, R., Cole, S. W., Everhart, A. R., Baker, K., & Rodriguez, M. I. (2025) · Social Science & Medicine · doi:10.1016/j.socscimed.2025.118147 · Cited by 28
Criminogenic or criminalized? Testing an assumption for expanding criminogenic risk assessment.
Prins, S. J. (2019) · Law and Human Behavior · doi:10.1037/lhb0000347 · Cited by 17
State earned income tax credits and suicidal behavior: A repeated cross-sectional study
Morgan, E. R., DeCou, C. R., Hill, H. D., Mooney, S. J., Rivara, F. P., & Rowhani‐Rahbar, A. (2020) · Preventive Medicine · doi:10.1016/j.ypmed.2020.106403 · Cited by 18
Laura, T., Melvin, C., & Yoong, D. Y. (2022) · BMC Geriatrics · doi:10.1186/s12877-022-03343-6 · Cited by 13
“This ensures only common causes (confounders) are adjusted for in our multiple logistic regression models, without inappropriate adjustment for mediators that would attenuate or even reverse the true causal effect of exposure [37].”
BackgroundCOVID-19 vaccine uptake among people who inject drugs in Tijuana Mexico
Vera, A., Muñoz, S., Artamónova, I., Abramovitz, D. A., Mittal, M. L., Rosales, C., Strathdee, S. A., & Rangel, M. G. (2022) · Frontiers in Public Health · doi:10.3389/fpubh.2022.931306 · Cited by 17
Primer on Logistic Regression for Emergency Care Researchers
Ehrman, R. R., & Kline, J. A. (2022) · Journal of Emergency Medicine · doi:10.1016/j.jemermed.2022.09.032 · Cited by 17
A model for understanding the causes and consequences of walking impairments
Schwartz, M. H., Steele, K. M., Ries, A. J., Georgiadis, A. G., & MacWilliams, B. A. (2022) · PLoS ONE · doi:10.1371/journal.pone.0270731 · Cited by 17
“This misrepresentation is called the “Table 2 Fallacy” [6].”
BackgroundZhang, X., Liang, Q., & Lee, C. (2022) · The Quarterly Review of Economics and Finance · doi:10.1016/j.qref.2022.12.005 · Cited by 17
Kaufman, J. S. (2024) · Canadian Journal of Cardiology · doi:10.1016/j.cjca.2024.02.005 · Cited by 18
Gezer, F., Howard, K. A., Litwin, A. H., Martin, N. K., & Rennert, L. (2024) · The Lancet Public Health · doi:10.1016/s2468-2667(24)00076-8 · Cited by 17
Maternal obesity and attention-related symptoms in the preterm offspring
van der Burg, J. W., Jensen, E. T., van de Bor, M., Joseph, R. M., O’Shea, T. M., Kuban, K., Allred, E. N., Scott, M., Hunter, S. J., Hooper, S. R., et al. (2017) · Early Human Development · doi:10.1016/j.earlhumdev.2017.08.002 · Cited by 17
“The odds ratios of potential confounders should be as just that, and not as measures of causal effects [30].”
Ponkilainen, V., Uimonen, M., Raittio, L., Kuitunen, I., Eskelinen, A. P., & Reito, A. R. (2021) · Osteoarthritis and Cartilage · doi:10.1016/j.joca.2021.03.020 · Cited by 17
Bartram, D., & Jarochová, E. (2021) · Journal of Ethnic and Migration Studies · doi:10.1080/1369183x.2021.1922273 · Cited by 17
“In general, when variables are selected as controls (W) for the estimation of X→Y, the coefficients for the controls cannot be treated as estimates of effects denoted by W→Y; interpretation along these lines amounts to the ‘Table 2 fallacy’ (Westreich and Greenland 2013).”
BackgroundNazif‐Muñoz, J. I., Laurent, J. G. C., Browning, M. H. E. M., Spengler, J. D., & Alvarez, H. A. O. (2020) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph17218146 · Cited by 16
“This strategy was adopted to avoid the “Table 2 fallacy” [61], which occurs when investigating multiple predictors using a single multivariable model.”
MethodPredictors of plasma polychlorinated biphenyl concentrations among reproductive-aged black women
Wesselink, A. K., Bethea, T. N., McClean, M. D., Weuve, J., Williams, P. L., Hauser, R. B., Sjödin, A., Brasky, T. M., Baird, D. D., & Wise, L. A. (2019) · International Journal of Hygiene and Environmental Health · doi:10.1016/j.ijheh.2019.06.008 · Cited by 16
“Some associations may be adjusted for covariates that plausibly lie on a causal pathway to exposure; others may be affected by residual or unmeasured confounding (Westreich and Greenland, 2013).”
BackgroundLodge, E. K., Engel, L. S., Ferrando‐Martínez, S., Wildman, D. E., Uddin, M., Galea, S., & Aiello, A. E. (2020) · Journal of Exposure Science & Environmental Epidemiology · doi:10.1038/s41370-020-0226-2 · Cited by 16
“interpreted causally, however, due to potential unresolved confounding by other covariates not included in our analysis [40].”
Background
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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