Causation and Causal Inference

Canonical Inference

The oldest and most common systematic approach to causal inference in epidemiology was the comparison of observations to characteristics expected of causal relations. The characteristics might derive from subject-matter judgments or from consideration of causal models, and the comparisons might employ formal statistical methods to estimate and test those characteristics. Perhaps the most widely cited of such an approach is based on the considerations of Sir Austin Bradford Hill, which are discussed critically in numerous sources as well as by Hill himself.

The canonical approach usually leaves terms such as cause and effect as undefined concepts around which the self-evident canons are built, much like axioms are built around concepts such as set and is an element of in mathematics. In his famous 1965 article on association and causation, Hill noted that he did not want to undertake a philosophical discussion of causation. Only proper temporal sequence (cause must precede effect) is a necessary condition for a cause-effect relation to hold. The remaining considerations are more akin to diagnostic symptoms or signs of causation—that is, they are properties an association is assumed more likely to exhibit if it is causal than if it is not. Furthermore, some of these properties (such as specificity and dose response) apply only under specific causal models. Thus, the canonical approach makes causal inference most closely resemble clinical judgment than experimental science, although experimental evidence is listed among the considerations. Some of the considerations (such as temporal sequence, association, dose-response or predicted gradient, and specificity) are empirical signs and thus subject to conventional statistical analysis. Others (such as plausibility) refer to prior belief, and thus (as with disease symptoms) require elicitation from experts, the same process used to construct prior distributions for Bayesian analysis.

The canonical approach is widely accepted in epidemiology, subject to many variations in detail. Nonetheless, it has been criticized for its incompleteness and informality, and the consequent poor fit it affords to the deductive or mathematical approaches familiar to classic science and statistics. [Page 157]Although there have been some interesting attempts to reinforce or reinterpret certain canons as empirical predictions of causal hypotheses, there is no generally accepted mapping of the entire canonical approach into a single analytic methodology. One simply uses standard statistical techniques to test whether empirical canons are violated. For example, if the causal hypothesis linking X to Y predicts a strictly increasing trend in Y with X, a test of this statistical prediction may serve as a statistical criterion for determining whether the hypothesis fails the dose-response canon. Such usage falls squarely in the falsificationist/frequentist tradition of 20th-century statistics, but it leaves unanswered most of the policy questions that drive causal research; this gap led to the development of methodologic modeling.

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