Confounding

A confounder meets three conditions: it is associated with the exposure, it independently causes the outcome, and it does not sit on the causal pathway between them. A variable on the pathway is a mediator, and adjusting for it removes part of the effect being estimated; a variable caused by both exposure and outcome is a collider, and adjusting for that manufactures an association where none existed. Randomisation works by making assignment independent of everything preceding it, measured or not, in expectation rather than reliably in any one trial.

Postmenopausal hormone therapy is the canonical case. Observational cohorts through the 1990s reported substantially lower coronary heart disease among users; the Women's Health Initiative randomised trial, whose combined arm was stopped early in 2002, found no such protection and excess harm. Users had been healthier, wealthier and more engaged with medical care to begin with. Confounding by indication runs the other way in drug safety, where the sickest patients get the newest agent.

Adjustment handles confounders that were measured, and measured well; regression, propensity scores and matching share that limit, and residual confounding survives both mismeasurement and anything nobody recorded. The designs that genuinely constrain it are active-comparator new-user cohorts, negative control outcomes, and sensitivity analyses stating how strong an unmeasured confounder would have to be to explain the finding away.

The phrase adjusted for confounders gets read as neutralisation. More adjustment is not automatically safer, since pushing every available covariate into a model invites conditioning on mediators and colliders, which adds bias rather than removing it. The related trap is size: two million records buy precision, not freedom from bias, and deliver a very tight interval around a confounded estimate.