Chance, bias, confounding or cause
- Concept
When two things show up together in a study there are four possible explanations. Cause is accepted only after the other three are ruled out.
What it is
Any association seen between an exposure and an outcome may be due to chance, to bias (a systematic error in how participants were chosen or data measured), to confounding (a third factor mixed up with the exposure) or to a real causal relationship. They are checked in that order: chance with the p value and confidence interval, bias by reviewing design and measurement, confounding by adjusting or stratifying, and cause with the criteria for causation.
Worked example
- Cohort of 2 000 adults: 1 000 drink coffee daily (600 smokers) and 1 000 do not (200 smokers). Lung cancer cases are counted.
- Cancer: 34 of 1 000 coffee drinkers (3.4%) and 18 of 1 000 non-drinkers (1.8%).
- Crude RR = 3.4% / 1.8% ≈ 1.9.
- Chance: the 95% CI of the RR is about 1.1 to 3.3; it excludes 1, so chance is unlikely.
- Bias: cancers come from the same registry for both groups; no obvious measurement error.
- Confounding: stratify by smoking. Smokers: 5% with coffee and 5% without. Non-smokers: 1% and 1%.
- RR in each stratum = 1.0: the crude association disappears once smoking is separated out.
- Reading: coffee does not cause the cancer; the association arose because coffee drinkers smoke more (confounding).
The four explanations and how each is checked
| Explanation | What it is | How it is checked |
|---|---|---|
| Chance | Random sampling variation | P value, confidence interval, sample size |
| Bias | Systematic error in selection or measurement | Review design, selection and measurement |
| Confounding | A third factor linked to exposure and outcome | Stratify or adjust and compare with the crude estimate |
| Cause | The exposure produces the outcome | Criteria for causation: temporality, strength, gradient, consistency |
Markers
- p
- 95% CI
- RR
In practice
- When reading a paper, ask the four questions in order before accepting a causal conclusion.
- A narrow CI does not protect against bias or confounding: a huge study can be very precise and wrong.
Common pitfalls
- Believing a small p value proves causation: it only makes chance less likely.
- Thinking a larger sample corrects a bias.
- Jumping straight to cause without looking for confounders.
Test yourself
Think of the answer, then tap the question to see it.
What are the four explanations of an observed association?
Chance, bias, confounding and a real causal relationship.
Why does a bigger study not remove a bias?
Because bias is a systematic error: it repeats in every participant and persists however large the sample.
After stratifying, a crude RR of 1.9 becomes 1.0 in each stratum. What does this mean?
That the crude association was due to confounding by the stratifying variable.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Chapter 25: Assessing risk of bias in a non-randomized study (Cochrane, 2024); Confounding | Catalog of Bias (Catalogue of Bias Collaboration, 2018); Principles of Epidemiology | Lesson 1 - Section 7 (Centers for Disease Control and Prevention, 2012).
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Representative model, for educational purposes only.