Bradford Hill Criteria

The Bradford Hill criteria are a set of nine principles, formulated by Austin Bradford Hill in 1965, for evaluating whether an observed association between an exposure and a disease reflects a genuine causal relationship. Developed in the context of establishing that smoking causes lung cancer — against industry objections that correlation is not causation — the criteria provide a structured framework for causal inference in observational epidemiology.

The nine criteria are: strength of association, consistency, specificity, temporality, biological gradient (dose-response), biological plausibility, coherence, experiment, and analogy. Of these, only temporality is strictly necessary: causes must precede effects. The others are heuristic weights to be balanced against each other, not a checklist or algorithm. Hill himself was explicit that no mechanical procedure replaces scientific judgment about the totality of evidence.

The criteria predate the formal causal graph methods of Pearl's do-calculus and have been criticized for lacking mathematical precision; they remain, nonetheless, the dominant practical framework for causal reasoning in evidence-based medicine and public health policy. Their lasting contribution is not an algorithm but a discipline: insisting that the move from association to causation requires explicit argument rather than implicit assumption.\n\n== Hill vs. Pearl: Two Cultures of Causation ==\n\nThe Bradford Hill criteria and Judea Pearl's do-calculus represent two incompatible approaches to the same problem: how to infer causation from observation. The Hill criteria are heuristic, qualitative, and rooted in medical judgment. The do-calculus is formal, algorithmic, and rooted in graph theory. The criteria ask: does this association look like causation? The calculus asks: what intervention would we need to perform to confirm causation?\n\nThis difference is not merely methodological. It is epistemological. The Hill criteria assume that causation is a property of the world that reveals itself through careful observation and expert judgment. The do-calculus assumes that causation is a structural property of a causal graph that can be extracted from the data-generating process if we can represent it correctly. The criteria are appropriate when the causal structure is unknown and the data are observational; the calculus is appropriate when the causal structure can be hypothesized and tested against data.\n\nBut neither approach is sufficient for the complex causal systems of the 21st century. The Hill criteria break down when confounding variables are unobserved or when the exposure-disease relationship is mediated by networks rather than chains. The do-calculus breaks down when the causal graph is misspecified — when the modeler omits a confounder, adds a collider, or misdirects an arrow. The two approaches are complementary in principle but rarely combined in practice: epidemiologists use Hill, computer scientists use Pearl, and the two communities publish in different journals and attend different conferences.\n\nThe Bradford Hill criteria will remain the dominant framework in public health not because they are superior to the do-calculus but because they are compatible with the institutional structure of medicine. Doctors are trained to exercise judgment, not to draw causal graphs. The criteria legitimate judgment by wrapping it in a checklist. The do-calculus threatens this structure by suggesting that causation can be computed rather than judged. The persistence of the Hill criteria in an era of algorithmic causation is not a testament to their validity but a symptom of a deeper resistance: the medical profession's reluctance to cede epistemic authority to machines. And in this, the doctors may be wiser than the computer scientists. Causation is not merely a computation; it is a responsibility, and responsibility cannot be delegated to a graph.\n\n