Cited by 1,276Advanced Causal Inference TechniquesStatistical Methods in EpidemiologyMeta-analysis and systematic reviews

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The Table 2 Fallacy: Presenting and Interpreting Confounder and Modifier Coefficients

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Westreich, D., Greenland, S.·2013·American Journal of Epidemiology

DOI 10.1093/aje/kws412PMC PMC3626058

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Abstract

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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Factors associated with time to independent walking recovery post-stroke
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Democratic values, education, and political trust
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“Before moving forward, I will briefly discuss results for the remaining variables, noting that coefficients for adjustment variables should be interpreted with caution (Keele et al., 2020; Westreich and Greenland, 2013).”
Background
‘Going the distance’: an independent cohort study of engagement and dropout among the first 100 000 referrals into a large-scale diabetes prevention program
Howarth, E., Bower, P., Kontopantelis, E., Soiland‐Reyes, C., Meacock, R., William, W., & Cotterill, S. (2020) · BMJ Open Diabetes Research & Care · doi:10.1136/bmjdrc-2020-001835 · Cited by 61
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Variation in Peritoneal Dialysis Time on Therapy by Country
Lambie, M., Zhao, J., McCullough, K. P., Davies, S., Kawanishi, H., Johnson, D. W., Sloand, J. A., Sanabria, M., Kanjanabuch, T., Kim, Y.-L., et al. (2022) · Clinical Journal of the American Society of Nephrology · doi:10.2215/cjn.16341221 · Cited by 60
“8) Body mass index, kg/m(2), n (%) ,20 16 (3) 48 (6) 139 (19) 197 (26) 16 (6) 107 (4) 20–29 339 (68) 516 (65) 573 (77) 508 (68) 198 (69) 1519 (56) 301 141 (28) 231 (29) 33 (4) 40 (5) 74 (26) 1084 (40) Race, n (%) Asian 95 (17) 122 (13) 792 (100) 821 (99) 29 (8) 149 (4) Black 0 (0) 41 (5) 0 (0) 0 (0) 14 (4) 896 (26) Wh…”
Method
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“While the full regression models are reported as supplementary information, the coefficients for the other variables are not interpreted [29].”
Background
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“Similarly, the mutually adjusted OR for education represents a direct effect, not mediated via occupation or income [36].”
BackgroundMethodInfluential
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“20 Census blocks were then ranked as a percentile (1-100) of deprivation relative to the national level; higher ADI scores indicated higher deprivation.”
Background
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“22 Our study is strengthened by use of a rich dataset, allowing detailed analysis of 1031 subcity areas in 314 cities across five countries that have had some of the most severe COVID-19 outbreaks globally.”
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“We identified 11 studies for which SMI was not the main focus, and while inclusion of these studies provides further evidence, caution is needed as they may be subject to confounding and issues of power [90].”
Background
Sedentary Time in Late Childhood and Cardiometabolic Risk in Adolescence
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“The estimates provided for the sociodemographic characteristics in Tables 2 and 3 are direct effects rather than total effects.(52)”
Background
Predictors of pain severity trajectory in older adults: a 10.7-year follow-up study
Pan, F., Tian, J., Aitken, D. A., Cicuttini, F., & Jones, G. (2018) · Osteoarthritis and Cartilage · doi:10.1016/j.joca.2018.08.002 · Cited by 51
Factors associated with dietary diversity and length‐for‐age z ‐score in rural Ethiopian children aged 6–23 months: A novel approach to the analysis of baseline data from the Sustainable Undernutrition Reduction in Ethiopia evaluation
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“…modelling which displays—as a result of modelling a single primary association—figures representing a mixture of different types of causal effect estimates for covariates (secondary, direct and indirect) without explicit distinction or comparability between them (Westreich & Greenland, 2013).”
Background
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“In addition, the interpretation of estimates from multivariable regression is complex due to interrelationships among predictor variables (Westreich and Greenland 2013).”
An Introduction to Causal Diagrams for Anesthesiology Research
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Inferential challenges when assessing racial/ethnic health disparities in environmental research
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“Such practices, also known as the “Table 2 fallacy,” [33] have been identified as a source of confusion in other areas of refugee research.”
Background
Sub-national patterns and correlates of depression among adults aged 45 years and older: findings from wave 1 of the Longitudinal Ageing Study in India
Perianayagam, A., Prina, M. A., Selvamani, Y., Gudekar, D., Salvi, S., Varghese, M., & Dandona, R. (2022) · The Lancet Psychiatry · doi:10.1016/s2215-0366(22)00186-9 · Cited by 48
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Sheppard, N., Carroll, M. T. C., Gao, C. X., & Lane, T. J. (2023) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2023.163272 · Cited by 49
“…2013) to Agency for Health Research Quality (AHRQ) standards using the rubric in Shamsrizi et al. (2020). these are not designed to account for how independent variables may interact (e.g., as mediators or colliders), the statistical associations are less reliable (Westreich and Greenland, 2013).”
Influential
Revisiting the Table 2 fallacy: A motivating example examining preeclampsia and preterm birth
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Flook, M., Jackson, C., Vasileiou, E., Simpson, C. R., Muckian, M. D., Agrawal, U., McCowan, C., Jia, Y., Murray, J., Ritchie, L. D., et al. (2021) · BMC Infectious Diseases · doi:10.1186/s12879-021-05992-1 · Cited by 47
“Where studies focussed on a single risk factor of interest with adjustment for confounding, we extracted all data on potential risks in order to maximise the value of our dataset (whilst accepting that such mutually adjusted estimates for covariates may remain confounded even if that for the primary exposure does not)…”
Method
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“After ssessing for multi-collinearity, relevant covariates were identified s confounders by comparing the −2 log-likelihood ratio values f the models with and without the potential confounder(s) as er the conceptual framework based on directed acyclic graphs Westreich and Greenland, 2013 ).”
Time to onset of cardiovascular and cerebrovascular outcomes after hypertensive disorders of pregnancy: a nationwide, population-based retrospective cohort study
Simon, E. G., Bechraoui‐Quantin, S., Tapia, S., Cottenet, J., Mariet, A., Cottin, Y., Giroud, M., Eicher, J., Thilaganathan, B., & Quantin, C. (2023) · American Journal of Obstetrics and Gynecology · doi:10.1016/j.ajog.2023.03.021 · Cited by 45
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“Effect estimates of our primary covariate of interest, GWG pattern, and effect estimates of secondary covariates (prepregnancy BMI, initial body composition) are reported; other effect estimates are not included in the tables to limit potential misunderstanding of associations [26].”
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“Direct interpretation of the effect estimates for secondary risk factors, therefore, do not necessarily represent total effect estimates, and may be confounded even when the effect estimate for the main exposure is not (Westreich and Greenland, 2013).”
Background
Methodologic limitations of prescription opioid safety research and recommendations for improving the evidence base
Ranapurwala, S. I., Naumann, R. B., Austin, A. E., Dasgupta, N., & Marshall, S. W. (2018) · Pharmacoepidemiology and Drug Safety · doi:10.1002/pds.4564 · Cited by 44
“This results in so called “table 2 fallacy,” a term that refers to improper interpretations of effect estimates and potential selection bias.(47) Fourth, most studies failed to account for time‐varying opioid exposure and confounding by indication (eg, patient selection for abuse‐deterrent formulations).”
Background
Development and validation of prediction models to estimate risk of primary total hip and knee replacements using data from the UK: two prospective open cohorts using the UK Clinical Practice Research Datalink
Yu, D., Jordan, K. P., Snell, K. I. E., Riley, R. D., Bedson, J., Edwards, J., Mallen, C. D., Tan, V., Ukachukwu, V., Prieto‐Alhambra, D., et al. (2018) · Annals of the Rheumatic Diseases · doi:10.1136/annrheumdis-2018-213894 · Cited by 45

Authors: Westreich, D., & Greenland, S.
Affiliations: Duke University (US)
Corresponding author: Westreich, D.
ORCID: Westreich, D.
Greenland, S.
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
DOI: 10.1093/aje/kws412
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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The Table 2 Fallacy: Presenting and Interpreting Confounder and Modifier Coefficients

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