Table 2 Fallacy

The Table 2 fallacy is a pervasive causal inference and reporting error in epidemiology, biostatistics, and clinical medical research in which investigators fit a single multivariable regression model designed to estimate the causal effect of one primary exposure (X) on an outcome (Y) while adjusting for a set of confounders (Z₁, Z₂, …), present the mutually adjusted effect estimates (odds ratios, hazard ratios, or risk ratios) for both the primary exposure X and all secondary covariates Z₁, Z₂ side-by-side in a single summary results table (conventionally "Table 2" of a biomedical paper, following descriptive baseline characteristics in "Table 1"), and then interpret the regression coefficients of the secondary covariates Z as if they represented total causal effects on Y. Named and formalized in 2013 by Daniel Westreich and Sander Greenland in the American Journal of Epidemiology, the Table 2 fallacy arises because a covariate adjustment set that validly closes backdoor confounding paths for a downstream primary exposure X routinely contains causal intermediates (mediators) and colliders relative to upstream secondary covariates Z. Consequently, in that single regression model:

1. The coefficient for the primary exposure β_X estimates the total causal effect of X on Y (because Z precedes X).
2. The coefficient for a secondary confounder β_Z does not estimate the total causal effect of Z on Y; instead, because the model simultaneously conditions on X (which is a downstream mediator on the causal pathway Z → X → Y), β_Z estimates only the controlled direct effect of Z on Y not mediated through X—and if unmeasured common causes (U) affect both X and Y, conditioning on the mediator X induces collider-stratification bias, corrupting even the direct effect of Z!

Mechanism 1: The Primary Exposure (X) Is a Downstream Mediator for the Confounder (Z)

Consider the classic clinical scenario analyzed by Westreich and Greenland (2013). Suppose an investigator wants to estimate the total causal effect of HIV seropositivity (Primary Exposure X) on 10-year incident ischemic stroke (Outcome Y), adjusting for baseline Age (Z₁), Smoking (Z₂), and CD4⁺ T-cell count (M) depending on the causal structure.

To make the geometry crystal clear, consider a three-variable causal directed acyclic graph (DAG) where Hypertension (X, Primary Exposure) is evaluated for its causal effect on Myocardial Infarction (Y, Outcome), adjusting for Obesity (Z, Confounder of X → Y):

Causal Pathways:

1. Obesity (Z) → Hypertension (X) → Myocardial Infarction (Y) (Indirect causal path of Obesity mediated through blood pressure)
2. Obesity (Z) → Myocardial Infarction (Y) (Direct causal path of Obesity via dyslipidemia/insulin resistance independent of blood pressure)

Now suppose the investigator fits a single multivariable logistic or Cox regression model:

logit P(Y = 1 | X, Z) = β₀ + β_X · X (Hypertension) + β_Z · Z (Obesity)

and prints both OR_X = exp(β_X) and OR_Z = exp(β_Z) in "Table 2" under the column heading "Adjusted Odds Ratio (95% CI)":

Numerical Demonstration: How Table 2 Erases a True Causal Risk Factor (RR_total = 2.50 → RR_{Table 2} = 1.00)

Suppose Apolipoprotein B Genetic Variant (Z) raises LDL Cholesterol (X), and elevated LDL Cholesterol (X) causes Coronary Heart Disease (Y), with 100% of the effect of the APOB variant (Z) on heart disease operating through LDL Cholesterol (X):

APOB Variant (Z) → Elevated LDL Cholesterol (X) → Coronary Heart Disease (Y)

In the population:

• Carrying the APOB variant (Z = 1) increases the probability of High LDL (X = 1) from 20% to 80%.
• Having High LDL (X = 1) increases 10-year CHD risk (Y = 1) from 5.0% to 20.0% (True Causal RR_X = 4.00), regardless of how LDL became elevated.
• Therefore, the true Total Causal Risk Ratio of the APOB variant (Z) on CHD is:

P(Y = 1 | Z = 1) = (0.80 × 20.0%) + (0.20 × 5.0%) = 17.0% P(Y = 1 | Z = 0) = (0.20 × 20.0%) + (0.80 × 5.0%) = 8.0% True Total Causal RR_Z = 17.0% / 8.0% = 2.13 (more than doubles heart disease risk!).

Now, an investigator puts both X (High LDL) and Z (APOB variant) into a single multivariable regression model predicting CHD (Y) and publishes Table 2:

• High LDL (X) Adjusted RR = 4.00 (95% CI: 3.40–4.70, p < 0.001)
• APOB Variant (Z) Adjusted RR = 1.00 (95% CI: 0.85–1.18, p = 0.99)

A reader committing the Table 2 fallacy looks at the second row of Table 2 (RR = 1.00, p = 0.99) and writes: "In multivariable analysis, the APOB variant was not independently associated with coronary heart disease (RR = 1.00)"—falsely dismissing a potent 2.13-fold genetic cause of heart disease solely because its downstream mediator (X, LDL cholesterol) was included in the same regression equation!

Even if an author attempts to defend Table 2 by saying, "I know β_Z is not the total effect of Z; I am interpreting β_Z as the direct effect of Z on Y not mediated by X," Westreich and Greenland (2013) proved that this interpretation also fails whenever there is any unmeasured common cause (U) of the primary exposure X and the outcome Y that was not needed to identify X → Y (or a confounder of the mediator–outcome relationship, as established by Judea Pearl and Tyler J. VanderWeele):

Consider the DAG:

• Secondary Covariate Z (e.g., Age) → Primary Exposure X (e.g., Antiretroviral Therapy / Statin Initiation) → Outcome Y (Stroke)
• Suppose Unmeasured Genetic or Lifestyle Frailty (U) also causes both Primary Exposure X and Outcome Y: X ← U → Y.

In this graph, Primary Exposure X is a collider on the pathway Z → X ← U → Y! Because the multivariable regression model conditions on X (by including X and Z together in the linear predictor), conditioning on X opens the collider path Z → [X] ← U → Y (the exact mechanism of Berkson's bias and depletion of susceptibles). Consequently, the Table 2 regression coefficient β_Z is biased for BOTH the total causal effect of Z AND the direct causal effect of Z!

Even when Z is not a direct causal ancestor of X, each exposure variable in an epidemiological dataset has its own unique set of backdoor confounders on a causal DAG:

• To estimate the total causal effect of Exposure X on Y, the minimally sufficient adjustment set might be {Z₁, Z₂, Z₃}.
• To estimate the total causal effect of Covariate Z₁ on Y, the minimally sufficient adjustment set might be {W₁, W₂}—variables that were not even included in the regression model for X!

Presenting a single column of "mutually adjusted odds ratios" in Table 2 encourages the false belief that throwing 15 variables into a kitchen-sink stepwise or multivariable regression simultaneously yields 15 unbiased causal effect estimates ("mutual adjustment for everything"). In reality, almost every secondary row of Table 2 is either overadjusted (conditioned on mediators), underadjusted (missing its own upstream confounders), or collider-biased.

To eliminate the Table 2 fallacy from biomedical publishing, epidemiology journals (American Journal of Epidemiology, Epidemiology, International Journal of Epidemiology, and NEJM/JAMA causal reporting guidelines along with STROBE extensions) recommend four concrete practices:

1. Report Only the Primary Exposure Estimate (X) in the Main Results Table: In Table 2, display the unadjusted and confounder-adjusted effect estimates only for the focal exposure(s) of interest (X), and list the adjustment covariates (Z₁, Z₂, …) in a table footnote (e.g., "Model 2 adjusted for age, sex, socioeconomic status, and baseline smoking; full regression coefficients for adjustment covariates are provided in Supplementary Table S1 for model transparency only and should not be interpreted as causal effect estimates").
2. Construct Separate Causal DAGs and Separate Regression Models for Each Exposure of Interest: If a study genuinely aims to estimate the total causal effects of three different exposures—say, Socioeconomic Status (W), Obesity (Z), and Hypertension (X)—on Myocardial Infarction (Y), fit three separate regression models, each adjusting only for the upstream confounders of that specific exposure (and excluding its downstream mediators!):
   • Model A (Total Effect of Socioeconomic Status W): Adjust for age, sex, and parental factors (do NOT adjust for Obesity Z or Hypertension X).
   • Model B (Total Effect of Obesity Z): Adjust for age, sex, and Socioeconomic Status W (do NOT adjust for Hypertension X).
   • Model C (Total Effect of Hypertension X): Adjust for age, sex, Socioeconomic Status W, and Obesity Z.
3. Use Formal Causal Mediation Analysis (G-Computation / Marginal Structural Models) When Direct vs. Indirect Effects Are Desired: When decomposing a total causal effect into a natural direct effect (NDE) and natural indirect effect (NIE), use Robins' g-formula, inverse probability of treatment and mediator weighting (IPW), or VanderWeele's mediation formulas that explicitly account for exposure–mediator interactions and mediator–outcome confounding.

Why did Daniel Westreich and Sander Greenland name this error the "Table 2 fallacy"?

In the standard structure of a clinical or epidemiological journal article, Table 1 presents the baseline descriptive characteristics of the study cohort stratified by exposure status, and Table 2 presents the results of the primary multivariable regression model (e.g., logistic regression odds ratios or Cox proportional hazards ratios). Historically, statistical software packages (SAS, Stata, R) output a single table of coefficients for every predictor entered into the regression equation, and authors routinely copied that entire software output—the primary exposure plus all 10 to 20 adjustment confounders—directly into Table 2, then discussed the coefficients of the confounders in the Results and Discussion sections as if they were independent total causal effects.

What is wrong with saying a variable is an "independent risk factor" because its p-value is < 0.05 in a multivariable regression table?

When a risk factor Z (such as obesity or physical inactivity) causes an outcome Y (such as stroke) primarily by causing an intermediate physiological state X (such as hypertension or type 2 diabetes), putting both Z and X into the same regression model holds the mediator X constant. Claiming that only variables that remain statistically significant after adjusting for their own downstream biological mechanisms are "independent risk factors" systematically penalizes upstream root causes (like genetics, diet, pollution, and socioeconomic deprivation) in favor of proximate downstream biomarkers measured five minutes before the event!

If reporting confounder coefficients in Table 2 is misleading, should authors hide them completely?

No. For reproducibility, predictive risk-score calibration, and model diagnostics, readers and peer reviewers may wish to inspect the fitted nuisance parameters of the regression model. The correct practice is to place the full list of regression coefficients in an online Supplementary Appendix table clearly labeled as nuisance adjustment parameters, while reserving Table 2 in the main manuscript strictly for the causal exposure(s) for which the adjustment set was designed.

1. Westreich, D., & Greenland, S. (2013). "The Table 2 fallacy: presenting and interpreting confounder and modifier coefficients." American Journal of Epidemiology, 177(4), 292–298. https://doi.org/10.1093/aje/kws412
2. Hernán, M. A., Hernández-Díaz, S., Werler, M. M., & Mitchell, A. A. (2002). "Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology." American Journal of Epidemiology, 155(2), 176–184. https://doi.org/10.1093/aje/155.2.176
3. Cole, S. R., & Hernán, M. A. (2002). "Fallibility in estimating direct effects." International Journal of Epidemiology, 31(1), 163–165. https://doi.org/10.1093/ije/31.1.163
4. Tennant, P. W. G., Murray, E. J., Arnold, K. F., Berrie, L., Fox, M. P., Gadd, S. C., Harrison, W. J., Keeble, C., Ranker, L. R., Textor, J., Tomova, G. D., Gilthorpe, M. S., & Ellison, G. T. H. (2021). "Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations." International Journal of Epidemiology, 50(2), 620–632. https://doi.org/10.1093/ije/dyaa213