What Is a Confounder? The Third Thing Explaining an Apparent Link

A confounder is a factor associated with the supposed cause and independently affecting the outcome, without lying on the causal path between them. The classic illustration is the association between carrying matches and lung cancer, where smoking causes both and accounts for the link entirely. The three requirements matter individually, since a factor associated with the exposure but not affecting the outcome does no damage, one affecting the outcome but unrelated to the exposure adds noise rather than bias, and one lying on the causal path between exposure and outcome is a mediator, and adjusting for it removes part of the real effect rather than a spurious one. That last distinction is the source of a great many analytical errors, since the statistical appearance is identical and only knowledge of the subject can tell them apart.

Several methods address the problem and each has requirements:

• •Randomisation, which distributes all factors evenly whether known or not and is the only method addressing unmeasured ones
• •Restriction, studying only people who share the confounding characteristic, which removes its influence and narrows the applicable population
• •Matching, pairing participants with similar values of the confounder
• •Stratification, analysing within levels of the confounder separately
• •Statistical adjustment in a model, which is the commonest approach and works only for factors that were measured and measured well
• •Instrumental variables and natural experiments, which exploit a source of variation unrelated to the confounders

The fundamental limitation of observational research is that adjustment only works for confounders that were identified and measured, and there is no way to adjust for a factor nobody thought of. That is why an association in observational data supports a causal conclusion far more weakly than the same association in a randomised trial, and the history of medicine contains several cases where large well-conducted observational studies reported benefits that randomised trials subsequently contradicted, with hormone therapy the most cited example. The usual explanation in such cases is that people receiving the treatment differed systematically from those not receiving it in ways connected to health, which is healthy user bias and is difficult to measure. Sensitivity analysis can estimate how strong an unmeasured confounder would have to be to explain an observed association, which is a useful partial answer.

Several widely reported associations turned out to be explained by a third factor, and the examples are worth having. Moderate drinking appeared to be associated with better health outcomes in many observational studies, and a substantial part of that pattern is attributed to the comparison group including people who had stopped drinking because they were already unwell, which is confounding by prior health. Coffee was associated with disease for decades before the association was traced substantially to smoking, since smokers drank more coffee. Studies of vitamin supplements repeatedly found benefits that randomised trials did not reproduce, with the difference attributed to people who take supplements differing systematically in other health behaviours. In each case the original studies were competently conducted and the confounder was either unmeasured or handled inadequately, which is the point rather than a criticism.

Statistical adjustment is not automatically improving and can introduce bias that was not there. Adjusting for a mediator removes part of the genuine effect, which understates the result. Adjusting for a common consequence of the exposure and the outcome creates a spurious association where none existed, which is a counterintuitive result that follows from the arithmetic and is a known source of error. Adjusting for a variable measured with substantial error leaves residual confounding while giving the appearance of having handled it. And adjusting for many variables chosen because they improve the model fit, rather than because the subject matter implies they are confounders, produces results that cannot be interpreted causally at all. The current recommendation is to decide what to adjust for from an explicit diagram of assumed causal relationships before looking at the data.

A confounder is associated with the exposure, independently affects the outcome and does not lie on the path between them, and only subject knowledge distinguishes it from a mediator. Adjustment handles only measured factors, which is why observational associations support causal claims weakly. Adjusting for a mediator removes real effect and adjusting for a common consequence creates a spurious link.