The Table 2 Fallacy: When Every Adjusted Coefficient Looks Like a Cause
Anas H. Alzahrani, MD PhD MPH
Department of Preventive Medicine and Public Health
Faculty of Medicine, King Abdulaziz University
Open almost any observational clinical paper and you will find Table 2: a tidy column of adjusted odds ratios or hazard ratios, one row per variable in the model. The exposure of interest sits at the top, and beneath it march age, sex, comorbidity, smoking, and a dozen other covariates, each with its own estimate and confidence interval. It reads like a leaderboard of causes.
It is not. The Table 2 fallacy, named by Daniel Westreich and Sander Greenland in 2013, is the habit of interpreting every coefficient in a single adjusted model as if it were that variable’s own causal effect. The model was built to estimate one thing well. The other rows are byproducts of that choice, and treating them as findings quietly manufactures conclusions the data never supported.
The Core Decision Rule
A regression model has exactly one adjustment set that is correct at a time, and it is correct for one exposure. The coefficients on the other variables were estimated under that same adjustment set, which is almost never the right one for them.
Decision rule:
Interpret only the coefficient you designed the adjustment set for. Every other coefficient in the same model is conditional, possibly confounded, possibly stripped of its own mediated effect, and should not be read as a causal estimate without its own separate analysis.
Why One Model Cannot Serve Every Variable
Suppose you want the effect of a medication on stroke, and you correctly adjust for a confounder like baseline hypertension. That adjustment does two jobs at once, and only one of them is what you asked for.
For the medication, conditioning on hypertension blocks a backdoor path and cleans the estimate. For hypertension itself, the picture is different. Its coefficient is now estimated holding the medication fixed — but the medication may be one of the roads through which hypertension affects stroke. Hold that road shut and you have amputated part of hypertension’s real effect. Worse, nothing in the model was chosen to control the confounders of the hypertension–stroke relationship, so its coefficient can be biased by common causes you never touched.
The two failure modes for secondary coefficients
Mediator amputation. If the covariate’s effect partly travels through the exposure, adjusting for the exposure blocks that path, so the coefficient reports only a direct effect it never advertised.
Uncontrolled confounding. The adjustment set was built for the exposure, not for the covariate, so common causes of the covariate and the outcome remain wide open.
See It Move
The simulator below builds a world where the true exposure effect is fixed and known. The model adjusts for a covariate Z that both drives who gets exposed and affects the outcome. Adjusting for Z is exactly correct for the exposure. Move the sliders and watch the exposure coefficient stay honest while the covariate coefficient in the very same table drifts away from its real effect.
Interactive Table 2 explorer
One regression, two coefficients, only one of them trustworthy
The exposure of interest is X. The model adjusts for a covariate Z, which both drives who gets exposed and affects the outcome. Adjusting for Z is exactly right for estimating X. Watch what that same model does to the Z coefficient printed one row below it.
Higher values mean more of Z’s real effect runs through the exposure — a path the model blocks when it adjusts for X.
The part of Z’s effect that does not pass through the exposure. Only this piece survives adjustment.
A common cause of Z and the outcome that no one measured. It leaves the exposure coefficient untouched and distorts only the covariate coefficient.
| Coefficient in Table 2 | Model estimate | True causal effect | Verdict |
|---|---|---|---|
| X — exposure of interest | +0.294 | +0.300 | Interpretable |
| Z — adjustment covariate | +0.521 | +0.460 | Not a causal effect |
What to notice
With little mediation and little unmeasured confounding, the secondary coefficient happens to land near the real effect. This is the trap: it is coincidence, not a guarantee, and it disappears the moment the structure gets more realistic.
The exposure coefficient tracks its truth across every slider because Z blocks its backdoor paths. The covariate coefficient drifts because the same adjustment set that is correct for X is wrong for Z.
Why the Z number breaks
- Adjusting for X blocks the part of Z’s effect that flows through the exposure.
- No one adjusted for the unmeasured common cause of Z and the outcome.
- A single model cannot be the right adjustment set for every variable it contains.
Why Smart Analysts Fall for It
The output looks symmetric
Software prints every coefficient in the same font with the same confidence interval. Nothing on the screen signals that only one row is interpretable.
The covariates are clinically real
Age and smoking obviously matter for the outcome, so a coefficient next to them feels like it must be reporting how much they matter.
Reviewers ask for it
Discussion sections and even peer reviewers routinely narrate secondary rows — “diabetes was independently associated with” — which trains everyone to keep doing it.
A Concrete Clinical Example
Case
A statin–mortality model that also “finds” a diabetes effect
A cohort study estimates the effect of statin therapy on mortality and adjusts for diabetes, LDL, blood pressure, age, and smoking. The statin coefficient is carefully constructed: the authors chose these covariates to close backdoor paths into statin prescribing.
The discussion then reports that diabetes was “independently associated with a 40% higher mortality.” But that number is the diabetes coefficient holding LDL, blood pressure, and statin use fixed — several of which sit on the causal pathway from diabetes to death. It also ignores any confounder of the diabetes–mortality link that was irrelevant to statins and therefore never entered the model. The statin estimate can be trustworthy and the diabetes sentence can be meaningless, in the same paragraph.
Total Effects, Direct Effects, and What the Coefficient Actually Is
| You want… | What that requires | What the Table 2 row gives you |
|---|---|---|
| The exposure effect | The adjustment set the model was designed around. | A valid estimate — this is the one row you may interpret. |
| A covariate’s total effect | Its own adjustment set, with no mediators of that covariate in the model. | A coefficient with mediated paths blocked — not the total effect. |
| A covariate’s direct effect | Correct control of exposure-induced and baseline confounding of the mediator. | A coefficient usually still confounded — direct-effect estimation has its own rules. |
Reviewer Red Flags
What a defensible paper does
- Interprets and defends one coefficient: the exposure the adjustment set was built for.
- Presents covariates as adjustment machinery, not as a list of secondary findings.
- Labels the estimand for each effect it does claim, and runs a separate model when it wants a covariate’s effect.
- Notes that adjusting for a mediator changes what the exposure coefficient means, too.
What should make you nervous
- The discussion narrates several covariate rows as if each were a causal result.
- “Independently associated” is used as a synonym for “causes.”
- The same model is asked to deliver effects for the exposure and for its own confounders.
- A mediator of the exposure is in the model and the exposure effect is still called “total.”
Decision Rules That Travel Well
- Name the one exposure your adjustment set was built for, and interpret only its coefficient.
- Treat every other row as machinery, not as a result, unless you built a model for it.
- Ask whether a covariate’s effect could run through the exposure before quoting its coefficient.
- If you want a covariate’s effect, draw its own diagram and choose its own adjustment set.
- Replace “independently associated” with a precise estimand or drop the sentence.
Where Aqrab Fits
The Table 2 fallacy is easy to miss because it lives in the sentences around a perfectly good primary estimate. Aqrab is built to read a methods section and its results the way a careful reviewer would: separating the one coefficient a model can defend from the secondary rows that were never estimated for interpretation.
If you want a second pass on which claims your model actually supports before submission, start with Aqrab Try and make each estimand explicit before Table 2 turns into a list of findings.
Keep reading
Don't stop at one method.
Good methods judgment comes from contrast. Read the neighboring guides, see where the assumptions diverge, and avoid treating every observational problem like it needs the same hammer.
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