Statistical association

A statistical association is a systematic dependence between variables. It need not represent a causal effect, because it may arise from confounding, selection, or reverse causation.

An observational study measures exposures and outcomes without assigning the exposure by an intervention. Its causal interpretation therefore requires assumptions that address confounding and selection bias.

A case–control study selects subjects according to an outcome: cases have the outcome and controls represent an appropriate comparison population. It compares their prior exposures or genetic variants to study association. Its retrospective sampling must be accounted for when interpreting risks; selection bias and confounding can distort an unadjusted association. In genetics, matched family pseudo-control genotypes can replace unrelated controls for a conditional transmission disequilibrium test.

A longitudinal study observes the same individuals repeatedly. Within-person changes distinguish temporal development from persistent differences between people, although calendar-period changes, selective dropout and measurement error still require attention. A random-intercept linear mixed model can represent persistent individual differences and correlated repeated measurements.

A cross-sectional study measures different individuals during one observation period. Differences between ages can reflect confounding or birth-cohort differences as well as changes within individuals; a longitudinal study is needed to measure the latter directly.

Reverse causality occurs when an apparent exposure-outcome association is partly or wholly generated by the outcome, or by an early stage of it, affecting the measured exposure.