Causal Inference & Bradford Hill Criteria

From association to causation

Rule out the usual suspects. An observed association between an exposure and an outcome is only a starting point. Before it can be judged causal, three explanations must be excluded: chance (assessed with p-values and confidence intervals), bias (systematic error in how subjects are selected or measured), and confounding (a third factor associated with both the exposure and the outcome).

Reverse causality. Sometimes the outcome, or its early phase, changes the exposure. In the "sick quitter" effect, people stop drinking or smoking because they are already ill, so former drinkers appear sicker than moderate drinkers and recent quitters appear to die sooner than continuing smokers. Occult cancer lowering serum cholesterol, making low cholesterol look like a cancer risk factor, is another example. Designs that measure exposure well before the outcome develops protect against this error.

Ecological fallacy. Ecological studies compare groups, such as nations or counties, rather than individuals. A correlation between national salt intake and national stroke mortality cannot show that the particular people who ate more salt are the ones who had strokes; assuming it does is the ecological fallacy.

The Bradford Hill criteria

Once alternatives are addressed, the nine criteria proposed by Austin Bradford Hill help weigh whether an association is causal. They are guides rather than a checklist; only temporality is strictly required.

Temporality is the only indispensable criterion. Cross-sectional and ecological studies measure exposure and outcome at the same moment, so they cannot establish it; cohort studies and randomized trials can.

Weighing the criteria. A strong association is hard to explain away by confounding, whereas a weak one (a relative risk near 1.2) can still be causal but is more easily produced by residual confounding or bias. Plausibility is limited by what is currently known, so a true cause may lack a recognized mechanism when first observed. Experimental evidence also comes from public health interventions: folic acid fortification of grain reduced neural tube defects.

Necessary, sufficient, and component causes

Necessary cause. The disease cannot occur without it. Mycobacterium tuberculosis is necessary for tuberculosis, yet most infected people never develop active disease; high-risk HPV is necessary for virtually all invasive cervical cancer, yet most infections clear without cancer. Both are necessary but not sufficient.

Sufficient cause. A set of factors that, together, inevitably produces disease. Single factors are rarely sufficient on their own. Most risk factors are neither necessary nor sufficient: never-smokers develop lung cancer, and most smokers do not.

The causal-pie model. In Rothman's component-cause model, each sufficient cause is drawn as a pie whose slices are component causes. Disease occurs when every slice of any one pie is in place. A component found in every pie is a necessary cause. Removing any single slice blocks that pie, so disease can be prevented without identifying every component, and because components act jointly, the fractions of disease attributed to different components can sum to more than 100%.

Study design and strength of causal evidence

Designs differ in how well they exclude alternative explanations. Systematic reviews and meta-analyses of well-conducted trials sit at the top of most hierarchies.