Way back in 1965, Sir Austin Bradford Hill proposed nine criteria that could be used to distinguish causal from noncausal associations in observational studies. Some of these criteria have withstood the test of time better than others, including:
Strength: strong associations are more likely to be causal than weak associations. But strong associations can still be noncausal, as is the case with the association between Down syndrome and birth rank, which is confounded by the relation between Down syndrome and maternal age.
Consistency: repeated observation of an association across several well-designed studies increases the likelihood that the association is due to the same causal factor.
Coherence: a cause-and-effect interpretation of an association is stronger when it does not conflict with established knowledge of how the world works. Hence, we know that measurements of barometric pressure don’t cause the weather even though these measurements and weather conditions are highly correlated.
Dose-Effect: a stimulus-response association in which the magnitude of the response varies as a function of the stimulus magnitude. The relationship between two correlated variables is more likely to be causal when changes in the “dose” of one variable are followed by changes in magnitude of the other*. Hill actually called this the “biologic gradient”.
Hill himself was ambivalent about the utility of these criteria. On the one hand, he asked “in what circumstances can we pass from this observed association to a verdict of causation?” Yet he disagreed that any “hard-and-fast rules of evidence” existed by which to judge causation:
“None of my nine viewpoints [criteria] can bring indisputable evidence for or against the cause-and- effect hypothesis and none can be required as a sine qua non.”
Fifty-six years later, we still lack “hard-and-fast rules of evidence” to make confident claims of causation in observational research, but Hill did provide some useful tips for generating causal hypotheses - to be tested, of course, in subsequent experimental studies.
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* Although Hill was thinking only of linear gradients - e.g., more of x causes more of y - the dose response can also be non-linear, as is the case with threshold, all-or-nothing- and time-dependent dose effects.
References:
Hill, A.B. (1965). The environment and disease: association or causation?, Proceedings of the Royal Society of Medicine 58, 295–300.
“Hill’s Criteria for Causality” (2005) Encyclopedia of Biostatistics. John Wiley & Sons, Ltd. DOI: 10.1002/0470011815.b2a03072. Adapted from Chapter 2 of Modern Epidemiology 2nd Ed., with permission from the publisher.
Hume, D. (1978). A Treatise of Human Nature (originally published in 1739). Oxford University Press edition, with an Analytical Index by L. A. Selby-Bigge, published 1888. 2nd Ed. with text revised and notes by P.H. Nidditch, published 1978.
Rothman, K.J. & Greenland, S. (1997). Modern Epidemiology, 2nd Ed. Lippincott, Philadelphia, Chapter 8.