An association seen in a study may be real, or it may be due to chance, bias, confounding or reverse causation
Random error (chance) affects precision. It is reduced by a larger sample and is quantified by p-values and confidence intervals (see Hypothesis Testing)
Systematic error (bias) affects accuracy. It is not reduced by a larger sample and must be prevented by good design
Internal validity: are the results correct for the people studied? External validity (generalisability): do they apply to other populations?

## Bias

Bias is any systematic error in the design, conduct or analysis of a study that gives a result different from the truth

Type	Description	Prevention
Selection bias: who gets into or stays in the study
Sampling bias	The sample does not represent the target population (e.g. a clinic sample has more severe disease than the community)	Random population sampling
Volunteer (healthy participant) bias	People who volunteer are healthier and more health-conscious	Random sampling; high response rates
Berkson's bias	Hospital-based cases and controls have different chances of admission, creating false associations	Population-based controls
Attrition bias	Loss to follow-up that differs between groups	Maximise follow-up; intention-to-treat analysis
Allocation bias	The investigator chooses who receives which treatment	Randomisation with allocation concealment
Information (measurement) bias: how data are collected
Recall bias	Cases remember past exposures better than controls (case-control studies)	Records made before the outcome; blinded questioning
Observer (detection) bias	The assessor's knowledge of the group affects the measurement	Blind the outcome assessor; objective measures
Performance bias	Groups receive different care apart from the intervention	Blind participants and clinicians; standard protocols
Hawthorne effect	People change their behaviour because they know they are being studied	A control group under the same observation
Misclassification	Exposure or disease recorded wrongly. Non-differential (equal in both groups) biases towards no effect; differential can bias either way	Validated, standardised measurement
Other
Lead-time and length-time bias	Screening seems to improve survival when it only finds disease earlier, or finds slower disease (see Diagnostic Tests and Screening)	Compare mortality in randomised screened and unscreened groups
Publication bias	Positive studies are more likely to be published	Trial registration; funnel plots

## Confounding

A confounder is a third factor that distorts the association between an exposure and an outcome. It must:

be associated with the exposure
be an independent risk factor for the outcome
not lie on the causal pathway between them

Example: carrying a lighter appears to cause lung cancer, but both are linked to smoking. In ophthalmology, age confounds almost every association between cataract, AMD and other age-related diseases
Confounding by indication: in observational studies, sicker patients are more likely to receive a treatment, so the treatment appears harmful

Stage	Method of controlling confounding
Design	Randomisation (the only method that controls unknown confounders), restriction (e.g. only non-smokers), matching (e.g. age- and sex-matched controls)
Analysis	Stratification (analyse within each stratum, then combine, e.g. Mantel–Haenszel), multivariable regression (adjusted odds ratios), standardisation (e.g. age-standardised rates)

Effect modification (interaction) is different: the effect of an exposure genuinely differs between subgroups (e.g. a treatment that works in one genotype but not another). It is a real finding to report, not a bias to remove
Reverse causation: the outcome causes the exposure (e.g. people with poor vision stop driving, rather than not driving causing poor vision). A cohort design shows which came first

## Causation: the Bradford Hill criteria

Proposed by Austin Bradford Hill (1965) to judge whether an observed association is likely to be causal. Only temporality is essential

Criterion	Meaning
Strength	A large relative risk is less likely to be explained by bias or confounding
Consistency	Repeated in different populations, places and study designs
Specificity	One exposure leads to one disease (the weakest criterion)
Temporality	The exposure comes before the outcome: the only essential criterion
Biological gradient	A dose–response relationship: more exposure, more disease
Plausibility	A believable biological mechanism
Coherence	Fits with what is known about the disease's natural history and biology
Experiment	Removing or reducing the exposure reduces the disease
Analogy	Similar exposures are known to cause similar effects

Smoking and AMD fulfils most of the criteria: a strong, consistent association in many populations, a dose–response effect, a lower risk after stopping, and plausible oxidative mechanisms
Observational studies suggested benefits from many supplements and drugs that RCTs later failed to confirm, usually because of confounding by healthier lifestyles

Study designs are described in Study Design; how to measure the strength of an association in Measures of Disease Frequency and Effect