Causal inferences — Hill’s criteria

Despite the adage to the contrary, data analysts often make causal inferences based on correlational data. Epidemiologists have developed several guidelines for this process, one of which is Hill’s nine criteria (Hill, 1965). They are used after “observations reveal an association between two variables, perfectly clear-cut and beyond what we would care to attribute to the play of chance” (i.e. after statistical analysis shows a low probability of the observed effect being caused by random fluctuations).

Hill provides the following list as “points to consider before deciding that the most likely interpretation is causation”. I find them to be a helpful check list for evaluating any claims, not just causality.

Name Examples from Hill’s investigation of smoking and cancer
Relative Death rates
Lung cancer Coronary thrombosis
Smoker 9-10 2
Non Smoker 1 1

Large differences which cannot be explained by other features intimately related to the proposed causal feature. Hill reports a summary of the association between smoking and lung cancer from 15 years of studies (right) as displaying a strong enough association to continue with the following 8 criteria.

Consistency Has it been repeatedly observed by different persons, in different places, circumstances and times? (Replication) Since the 1950 smoking studies cited above, a large number of additional studies have confirmed the result.
Specificity The effects should be narrowly targeted. If other causes of death are raised 10, 20 or even 50% in smokers whereas cancer of the lung is raised 900 – 1000% we have specificity – a specificity in the magnitude of the association.
Temporality Causal agent must happen before effect.
Gradient Are changing levels of the causal agent related to response measure? The smoking studies cited above also found that heavy smokers had a 25 to 1 Relative Death rate.
Plausibility It would help if the suspected causality is plausible given current knowledge.
Coherence Is there supporting tangential information? Hill states, I regard as greatly contributing to coherence the histopathological evidence from the bronchial epithelium of smokers and the isolation from cigarette smoke of factors carcinogenic for the skin of laboratory animals.
Experiment Occasionally it is possible to appeal to experimental, or semi-experimental, evidence.
Analogy Hill states, in some circumstances it would be fair to judge by analogy. With the effects of thalidomide and rubella before us we would surely be ready to accept slighter but similar evidence with another drug or another viral disease in pregnancy.

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