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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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“Some of the risk factors can be assumed to be located at a different “distance” from the outcomes, and controlling for more proximal risk factors may reduce the strength of the association between the former and the substance use outcomes (cf. Westreich & Greenland, 2013).”
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“This phenomenon is also referred to as “Table 2 fallacy ” (Westreich and Greenland 2013), or confounding bias.”
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“ICE indicators with large magnitudes of association in unadjusted models were considered in separate adjusted models to estimate the total effect of each indicator on CRI [38].”
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The validity of the selection methods for recruitment to UK core psychiatry training: cohort study
Tiffin, P. A., Morley, E., Paton, L. W., Chakraborty, N., & Patterson, F. (2024) · BJPsych Bulletin · doi:10.1192/bjb.2024.9 · Cited by 8
Insurance-Related Disparities in Withdrawal of Life Support and Mortality After Spinal Cord Injury
Shakil, H., Essa, A. S., Malhotra, A. K., Jaffe, R. H., Smith, C. W., Yuan, E. Y., He, Y., Badhiwala, J. H., Mathieu, F., Sklar, M. C., et al. (2024) · JAMA Surgery · doi:10.1001/jamasurg.2024.2967 · Cited by 9
Sherry, A. D., Msaouel, P., & Ludmir, E. B. (2024) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2024.111540 · Cited by 8
Marzecki, F., Ahmadzadeh, Y. I., Oginni, O. A., Pingault, J., McAdams, T. A., & Zavos, H. M. S. (2024) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.14096 · Cited by 8
“Unadjusted models are given the main interpretative weight Predictors of initiation and stability of self-harm to avoid the ‘table 2’ fallacy (Westreich & Greenland, 2013).”
Taylor, S. A., Kumar, S., Parry, T., Mallett, S., Travis, S. P. L., Raine, T., Clarke, C. S., Weng, J. Y., Bhatnagar, G., Bloom, S. L., et al. (2025) · European Radiology · doi:10.1007/s00330-025-11636-8 · Cited by 8
Statistical modelling in archaeology: some recent trends and future perspectives
Crema, E. R. (2025) · Journal of Archaeological Science · doi:10.1016/j.jas.2025.106295 · Cited by 11
Waldorf, I., Loder, A., Wurster, S., & Bogenberger, K. (2025) · Transportation · doi:10.1007/s11116-025-10640-7 · Cited by 12
Sacha, G. L., Duggal, A., Reddy, A. J., Wang, L., & Bauer, S. R. (2025) · Critical Care Explorations · doi:10.1097/cce.0000000000001284 · Cited by 9
Determinants of Bacille Calmette-Guérin scarification in Danish children
Jensen, T. M., Jensen, S. K., Birk, N. M., Rieckmann, A., Hoffmann, T. U., Benn, C. S., Jeppesen, D. L., Pryds, O. A., & Nissen, T. N. (2021) · Heliyon · doi:10.1016/j.heliyon.2020.e05757 · Cited by 8
“The causal structure of the determinants may be discussed and thus we acknowledge the difficulties in a causal interpretation of some of the mutually adjusted estimates [38].”
BackgroundUrada, L. A., Gaeta-Rivera, A., Kim, J., González‐Zúñiga, P., & Brouwer, K. C. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18083884 · Cited by 8
“Data were analyzed using bivariate and multiple logistic regression methods guided by Westreich and Greenland (2013) [59] to display the exposures significantly associated with CM. Univariate models were constructed with each exposure, with relevant demographic, health, risk history, and risk…”
MethodThanhaeuser, M., Steyrl, D., Fuiko, R., Brandstaetter, S., Binder, C., Thajer, A., Huber-Dangl, M., Haiden, N., Berger, A., & Repa, A. (2022) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2022.10.014 · Cited by 8
Risk factors for mechanical complications of peripherally inserted central catheters in children
Greencorn, D. J., Kuhle, S., Ye, L., Moore, K., Kulkarni, K. P., & Langley, J. M. (2022) · Infection Control and Hospital Epidemiology · doi:10.1017/ice.2022.193 · Cited by 8
“Separate models were developed for each potential risk factor 16 with covariate adjustment sets for each model identified from a directed acyclic graph (DAG) (Fig.”
Leonard, A., Broussard, J., Jain, J. P., Kumar, S., Santos, G., & Dawson-Rose, C. S. (2022) · Journal of Nursing Scholarship · doi:10.1111/jnu.12856 · Cited by 8
“…of each primary effect measure that was significant ( 0.05) at the bivariate level while controlling for age, race/ethnicity, gender identity, and sexual orientation, we built individual models estimating the impact of each exposure on methamphetamine use separately (Westreich & Greenland, 2013).”
MethodInfluentialLichtwarck, H. O., Kazaura, M. R., Moen, K., & Mmbaga, E. J. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph20010698 · Cited by 8
“This analytic strategy avoids “the table 2 fallacy” [48] where two or more coefficients in one single multivariable model are interpreted as estimates for meaningful effects.”
BackgroundMotivation in the dynamics of European youth migration
Tufiş, P. A., & Sandu, D. (2023) · European Societies · doi:10.1080/14616696.2023.2183231 · Cited by 8
“We follow the recommendation in the literature discussing causal inference with observational data, according to which the e ff ects of primary interest explanatory variables and e ff ects of confounders in regression models have di ff erent interpretations (Westreich and Greenland 2013).”
Thakrar, A. P., Faude, S., Perrone, J., Milone, M. C., Lowenstein, M., Snider, C. K., Spadaro, A., Delgado, M. K., Nelson, L. S., & Kilaru, A. S. (2023) · Journal of Addiction Medicine · doi:10.1097/adm.0000000000001155 · Cited by 8
Johnston, A., Smith, G. N., Tanuseputro, P., Coutinho, T. A., & Edwards, J. D. (2024) · Paediatric and Perinatal Epidemiology · doi:10.1111/ppe.13043 · Cited by 8
Liew, J. W., Treu, T. M., Park, Y., Ferguson, J. M., Rosser, M. A., Ho, Y.-L. A., GAGNON, D. R., Stovall, R., Monach, P. A., Heckbert, S. R., et al. (2024) · Seminars in Arthritis and Rheumatism · doi:10.1016/j.semarthrit.2024.152482 · Cited by 8
Laxmeshwar, C., Hegde, A., Dange, A., Mariyappan, K., Soosai, M., Mane, S. G., Sivasubramanian, M., Doddamane, M., Mukherjee, M., Shreenivas, G. S., et al. (2024) · Journal of the International AIDS Society · doi:10.1002/jia2.26348 · Cited by 8
Recent HIV Infection among men who have sex with men and transgender women in Tijuana
Skaathun, B., Pines, H. A., Patterson, T. L., Semple, S. J., Pekar, J. E., Vera, A., Rangel, G., & Mehta, S. R. (2020) · Revista de Saúde Pública · doi:10.11606/s1518-8787.2020054002179 · Cited by 8
“52 Ever experienced physical abuse 6 (33) 78 (49) 0.”
BackgroundLos imperativos éticos de la pandemia de COVID-19: Un análisis desde la ética de los datos
Arriagada-Bruneau, G., Gilthorpe, M. S., & Müller, V. C. (2020) · Veritas · doi:10.4067/s0718-92732020000200013 · Cited by 13
Geyti, C., Christensen, K. S., Dalsgaard, E., Bech, B. H., Gunn, J. M., Maindal, H. T., & Sandbæk, A. (2020) · BMJ Open · doi:10.1136/bmjopen-2020-037731 · Cited by 9
The association between continuity of care and surgery in lumbar disc herniation patients
Kim, E., & Kim, C. (2021) · Scientific Reports · doi:10.1038/s41598-021-85064-1 · Cited by 8
The gist of surgical margins in GIST: a narrative review
Cananzi, F., Ruspi, L., Samà, L., Renne, S. L., Sicoli, F., & Quagliuolo, V. (2021) · Laparoscopic Surgery · doi:10.21037/ls-20-139 · Cited by 8
“A general framework to interpret the heterogeneity of the results can be explained invoking the practice of including in multivariate analysis the parameters that showed significant values on univariable analysis, also known as the “Table 2 fallacy” (18).”
MethodChoice of Outcome in COVID-19 Studies and Implications for Policy: Mortality and Fatality
Westreich, D. J., Edwards, J. K., Tennant, P. W. G., Murray, E. J., & van Smeden, M. (2021) · American Journal of Epidemiology · doi:10.1093/aje/kwab244 · Cited by 8
“We term the general case of the issue identified here the “Missing Link Fallacy”; because Pr ( A & B ) = Pr ( B | A ) × Pr ( A ) , the assertion that Pr ( A & B ) = Pr ( B | A ) is incorrect in that it is missing the “link” of Pr ( A ) .”
BackgroundSelf-citationEquitable access to cancer patient pathways in Norway – a national registry-based study
Olsen, F., Jacobsen, B. K., Heuch, I., Tveit, K. M., & Balteskard, L. (2021) · BMC Health Services Research · doi:10.1186/s12913-021-07250-1 · Cited by 8
“, adjusting for potential confounders and avoiding the Table II fallacy [20], was assessed in separate analyses by causal diagrams or the directed acyclic graph (DAG) methodology [21].”
MethodHumphreys, J. M., Srygley, R. B., Lawton, D., Hudson, A. R., & Branson, D. H. (2022) · Ecological Modelling · doi:10.1016/j.ecolmodel.2022.110043 · Cited by 8
Thoen, P. S., Lygre, S. H. L., Nordsletten, L., Furnes, O. N., Stigum, H., Hallan, G., & Röhrl, S. M. (2022) · Acta Orthopaedica · doi:10.2340/17453674.2022.3474 · Cited by 8
“It is valuable to complete a thorough a priori evaluation of possible causal pathways in a dataset to determine which factors to adjust for in a model, and thereby limit bias and avoid Table II fallacy—adjusting for all known factors without causal pathway consideration (28).”
BackgroundTillett, W. L., Ogdie, A., Passey, A., & Gorecki, P. C. (2023) · RMD Open · doi:10.1136/rmdopen-2022-002533 · Cited by 8
Risk factors for dementia and self‐harm: A linkage study
Walker, A. R., Srasuebkul, P., Trollor, J. N., Wand, A. P. F., Draper, B., Cvejic, R. C., Moxey, A. J., & Reppermund, S. (2023) · Alzheimer s & Dementia · doi:10.1002/alz.13080 · Cited by 8
“27 Italsoallowsustomakeexplicitourassumedcausative relationship between variables.”
Barry, C. M., Livingston, M. D., Livingston, B. J., Kominsky, T. K., & Komro, K. A. (2023) · Journal of Adolescent Health · doi:10.1016/j.jadohealth.2023.07.014 · Cited by 8
Mohsenpour, A., Biddle, L., & Bozorgmehr, K. (2023) · PLOS Global Public Health · doi:10.1371/journal.pgph.0001755 · Cited by 7
“We refrained from reporting effect estimates for covariates conceived as potential confounders in our reporting to prevent ‘Table 2 fallacy’ [34, 35].”
MethodOkawa, Y., & Mitsuhashi, T. (2024) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2024.05.005 · Cited by 8
Usui, G., Shinozaki, T., Jinno, T., Fujibayashi, K., Morikawa, T., Gunji, T., & Matsuhashi, N. (2020) · BMC Gastroenterology · doi:10.1186/s12876-020-01418-5 · Cited by 8
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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