Every "independent predictor" in every paper comes from one regression doing one specific job
"After adjusting for age, diabetes, and renal function, the laparoscopic approach remained an independent predictor of complications (adjusted OR 1.6)." You have read some version of this sentence in nearly every clinical paper. But what did the model actually do when it "adjusted"?
The crude (unadjusted) estimate looks at your exposure alone. The adjusted estimate asks: among patients who are alike on age, diabetes, and renal function, does the exposure still matter? When those two numbers disagree, the difference is the whole story.
Adjustment is how multivariable regression separates a real effect from the company it keeps. The crude OR includes everything tangled together; the adjusted OR tries to isolate the exposure. Knowing which variables belong in the model -- and which must stay out -- is the core skill of reading observational research.
Confounding, and the worked example where adjustment flips the answer.
A confounder is a variable that is (1) associated with the exposure, (2) associated with the outcome, and (3) not on the causal pathway between exposure and outcome. A confounder creates a spurious association -- or hides a real one -- by riding along with the exposure.
Classic surgical example: sicker patients are steered toward one approach. Severity drives both the choice of approach (exposure) and the complication rate (outcome). That is confounding by indication, the dominant bias in surgical comparisons.
A registry compares open and laparoscopic colorectal resection for 30-day major morbidity. Surgeons reserve the open approach for higher-risk, more complex cases (locally advanced tumors, frailer patients). Look at what happens to the open-approach effect before and after adjusting for case severity.
| Model | Exposure: Open (vs lap) | OR | 95% CI | p-value |
|---|---|---|---|---|
| Crude (unadjusted) | Open approach | 2.10 | 1.62 -- 2.72 | <0.001 |
| Adjusted | Open approach | 1.08 | 0.80 -- 1.46 | 0.61 |
The adjusted OR for the open approach is the effect estimated at fixed values of every other covariate. In a logistic model, the coefficient for "open" is the change in log-odds of the outcome for open vs. laparoscopic among patients with the same ASA class, the same stage, the same frailty score.
It is a within-stratum comparison made simultaneously across all covariate strata. You are comparing like with like. That is why adjusted and crude estimates differ: the crude estimate compares groups that differ on the covariates; the adjusted estimate removes that difference mathematically -- as far as the measured covariates allow.
Three roles a variable can play. Adjusting blindly for all of them is a mistake.
Sits upstream of both exposure and outcome (a common cause). Example: case severity affects both surgical approach and complications. Leaving it out biases the exposure effect. Including it removes the spurious association.
Rule: If a variable is a common cause of exposure and outcome and is not on the causal path, adjust for it.
Sits on the causal pathway between exposure and outcome -- the exposure causes it, and it causes the outcome. Example: surgical approach affects operative blood loss, which affects complications. Blood loss is a mediator, a mechanism by which the approach works.
Rule: Adjusting for a mediator removes part of the very effect you are trying to measure. If you want the total effect of the exposure, leave mediators out. Only adjust for them deliberately in a mediation analysis aimed at the direct effect.
Sits downstream of both exposure and outcome (a common effect, an arrow pointing into it from both). Conditioning on a collider -- adjusting for it, or restricting/selecting on it -- opens a spurious association between exposure and outcome that did not exist before.
Rule: Never adjust for a variable that is a common consequence of the exposure and the outcome. Selection bias is collider bias in disguise (e.g., analyzing only admitted patients).
A multivariable model reports a coefficient for every variable in Table 2: the exposure, plus age, diabetes, renal function, and so on. The tempting error is to read each adjusted OR as a clean causal effect of that variable.
It is not. The model was built to estimate the effect of one exposure of interest, with the other variables chosen to confound-control that exposure. The coefficient for "diabetes" in the same table is not properly adjusted for its own confounders -- and it may even be distorted by adjusting for a mediator or collider of the diabetes-outcome relationship.
So: interpret the exposure coefficient causally (if the design supports it). Treat the covariate coefficients as nuisance adjustments, not as standalone causal findings.
Four ways "we adjusted for it" produces a confidently wrong conclusion.
"After adjusting for postoperative blood loss, surgical approach was no longer associated with complications -- so the approach has no effect."
Blood loss is a mediator, not a confounder. The approach causes blood loss, which causes complications. Adjusting for it removes part of the approach's own effect, so the exposure coefficient shrinks toward null by construction. The right conclusion is the opposite: the disappearance of the effect after adjusting for blood loss is evidence that blood loss is the mechanism, not evidence of no effect. For the total effect, leave the mediator out.
"In our model of stroke risk, the adjusted OR for atrial fibrillation was 1.9, so AF independently increases stroke risk by 90% -- and the OR for statin use was 0.7, so statins are protective."
This is the Table 2 fallacy. The model was designed to estimate one exposure's effect; the AF and statin coefficients are nuisance adjustments, not properly confounder-controlled estimates of those variables. The statin coefficient in particular is wide open to confounding by indication and healthy-user bias. You cannot lift each row of a multivariable table out and read it as a causal effect.
"To be thorough, we adjusted for every variable available in the registry -- 30 covariates including postoperative ICU admission and discharge destination."
Overadjustment and collider bias. Throwing everything in is not conservative -- it is dangerous. ICU admission and discharge destination are downstream of the outcome (they are consequences of complications). Adjusting for these mediators and colliders can attenuate the real effect or induce a spurious one. Covariate selection must be guided by a causal structure (a DAG), not by "everything we had."
"After multivariable adjustment, smoking remained an independent risk factor for the outcome (adjusted OR 1.5), confirming a causal effect."
"Independent" means independent of the measured covariates only. The label cannot rule out residual confounding (smoking measured as a yes/no instead of pack-years) or unmeasured confounding (socioeconomic status, diet, occupational exposures never recorded). An adjusted OR away from 1.0 is consistent with a causal effect but does not confirm one. Sensitivity analyses (E-value) tell you how strong an unmeasured confounder would need to be to explain it away.
Before trusting an adjusted estimate, ask three questions: Is every covariate a true confounder (upstream common cause), or did a mediator/collider sneak in? Is the exposure of interest the only coefficient being interpreted causally? And how much residual or unmeasured confounding could remain? If the authors cannot answer these, "adjusted" is just a word.
Classify the variable, interpret the shift, and spot the adjustment error.
Module 5 - Lesson 3 complete
Next lesson: Ordinal, Counts, and the Right Model -- when the outcome is a grade, a stage, or a count, and ordinary logistic or linear regression is the wrong tool.