Hill’s Criteria for
Causality
Despite philosophic criticisms of inductive inference,inductively oriented causal criteria have commonly
been used to make such inferences. If a set of necessary and sufficient causal criteria could be used
to distinguish causal from noncausal associations
in observational studies, the job of the scientist
would be eased considerably. With such criteria,
all the concerns about the logic or lack thereof incausal inference could be forgotten: it would only benecessary to consult the checklist of criteria to see if
a relation were causal. We know from philosophy
that a set of sufficient criteria does not exist [3,6]. Nevertheless, lists of causal criteria have become
popular, possibly because they seem to provide a roadmap through complicated territory.
A commonly used set of criteria was proposedby Sir Austin Bradford Hill [1]; it was an expansion of a set of criteria offered previously in thelandmark Surgeon General’s report on Smoking and
Health [11], which in turn were anticipated by the
inductive canons of John Stuart Mill [5] and therules of causal inference given by Hume [3]. Hillsuggested that the following aspects of an association be considered in attempting to distinguish causal
from noncausal associations: strength, consistency,
specificity, temporality, biologic gradient, plausibility, coherence, experimental evidence, and analogy.
The popular view that these criteria should be used
for causal inference makes it necessary to examine
them in detail:Strength
Hill’s argument is essentially that strong associations
are more likely to be causal than weak associations
because, if they could be explained by some otherfactor, the effect of that factor would have to beeven stronger than the observed association and therefore would have become evident (see Cornfield’s
Inequality). Weak associations, on the other hand,
are more easily explained by undetected biases. To
some extent this is a reasonable argument, but, as
Hill himself acknowledged, the fact that an association is weak does not rule out a causal connection. A commonly cited counterexample is therelation between cigarette smoking and cardiovascular disease.
Counterexamples of strong but noncausal associations are also not hard to find; any study withstrong confounding illustrates the phenomenon. For
example, consider the strong but noncausal relation
between Down syndrome and birth rank, which is
confounded by the relation between Down syndrome
and maternal age. Of course, once the confounding
factor is identified, the association is diminished byadjustment for the factor. These examples remind
us that a strong association is neither necessary nor
sufficient for causality, nor is weakness necessary nor
sufficient for absence of causality. In addition to thesecounterexamples, we have to remember that neither
relative risk nor any other measure of association isa biologically consistent feature of an association; as
described by many authors [4, 7], it is a characteristicof a study population that depends on the relative
prevalence of other causes. A strong association
serves only to rule out hypotheses that the associationis entirely due to one weak unmeasured confounderor other source of modest bias.

Consistency
Consistency refers to the repeated observation of an
association in different populations under different
circumstances. Lack of consistency, however, does
not rule out a causal association, because some effects
are produced by their causes only under unusual circumstances. More precisely, the effect of a causal
agent cannot occur unless the complementary component causes act, or have already acted, to completea sufficient cause. These conditions will not always
be met. Thus, transfusions can cause HIV infection
but they do not always do so: the virus must also bepresent. Tampon use can cause toxic shock syndrome,
but only when other conditions are met, such as presence of certain bacteria. Consistency is apparent only
after all the relevant details of a causal mechanism areunderstood, which is to say very seldom. Even studies of exactly the same phenomena can be expected
to yield different results simply because they differ
in their methods and random errors. Consistency
serves only to rule out hypotheses that the association is attributable to some factor that varies acrossstudies.

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DOI: 10.1002/0470011815.b2a03072

2

Hill’s Criteria for Causality

Specificity
The criterion of specificity requires that a cause leads
to a single effect, not multiple effects. This argument
has often been advanced to refute causal interpretations of exposures that appear to relate to myriad effects, especially by those seeking to exoneratesmoking as a cause of lung cancer. The criterion iswholly invalid, however. Causes of a given effectcannot be expected to lack other effects on any
logical grounds. In fact, everyday experience teaches
us repeatedly that single events or conditions may
have many effects. Smoking is an excellent example:
it leads to many effects in the smoker. The existenceof one effect does not detract from the possibility that
another effect exists. Thus, specificity does not confer
greater validity to any causal inference regarding theexposure effect. Hill’s discussion of this criterion
for inference is replete with reservations, and many
authors regard this criterion as useless and misleading[8, 9].

Temporality
Temporality refers to the necessity that the cause precede the effect in time. This criterion is unarguable,
insofar as any claimed observation of causation must
involve the putative cause C preceding the putative
effect D. It does not, however, follow that a reversetime order is evidence against the hypothesis that C
can cause D. Rather, observations in which C followed D merely shows that C could not have caused
D in these instances; they provide no evidence for oragainst the hypothesis that C can cause D in thoseinstances in which it precedes D.

Biologic Gradient
Biologic gradient refers to the presence of a monotone (unidirectional) dose–response curve. We often
expect such a monotonic relation to exist. For example, more smoking means more carcinogen exposureand more tissue damage, hence more carcinogenesis.
Such an expectation is not always present, however.
The somewhat controversial topic of alcohol consumption and mortality is an example. Death rates
are higher among nondrinkers than among moderatedrinkers, but ascend to the highest levels for heavy
drinkers. Because modest alcohol consumption canhave beneficial effects on serum lipid profiles, sucha J-shaped dose–response curve is at least biologically plausible.
Conversely, associations that do show a monotonic
trend in disease frequency with increasing levels of
exposure are not necessarily causal; confounding canresult in a monotonic relation between a noncausal
risk factor and disease if the confounding factor
itself demonstrates a biologic gradient in its relation
with disease. The noncausal relation between birthrank and Down syndrome mentioned above shows abiologic gradient that merely reflects the progressive
relation between maternal age and the occurrence of
Down syndrome.
Thus the existence of a monotonic association isneither necessary nor sufficient for a causal relation.
A nonmonotonic relation only conflicts with thosecausal hypotheses specific enough to predict a monotonic dose–response curve.

Plausibility
Plausibility refers to the biologic plausibility of the
hypothesis, an important concern but one that is far
from objective or absolute. Sartwell [9], emphasizing
this point, cited the remarks of Cheever, in 1861, who
was commenting on the etiology of typhus before its
mode of transmission (via body lice) was known:
It could be no more ridiculous for the stranger who
passed the night in the steerage of an emigrant ship
to ascribe the typhus, which he there contracted, tothe vermin with which bodies of the sick might beinfested. An adequate cause, one reasonable in itself,must correct the coincidences of simple experience.

What was to Cheever an implausible explanation
turned out to be the correct explanation, since it was
indeed the vermin that caused the typhus infection.
Such is the problem with plausibility: it is too often
not based on logic or data, but only on prior beliefs.
This is not to say that biological knowledge should
be discounted when evaluating a new hypothesis,but only to point out the difficulty in applying thatknowledge.
The Bayesian approach to inference attempts todeal with this problem by requiring that one quantify, on a probability (0 to 1) scale, the certainty that
one has in prior beliefs, as well as in new hypotheses.
This quantification displays the dogmatism or openmindedness of the analyst in a public fashion, withcertainty values near 1 or 0 betraying a strong commitment of the analyst for or against a hypothesis. It

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Hill’s Criteria for Causality
can also provide a means of testing those quantified
beliefs against new evidence [2]. Nevertheless, theBayesian approach cannot transform plausibility into
an objective causal criterion.

Coherence
Taken from the Surgeon General’s report on Smoking and Health [11], the term coherence implies thata cause and effect interpretation for an association
does not conflict with what is known of the natural history and biology of the disease. The examples
Hill gave for coherence, such as the histopathologic
effect of smoking on bronchial epithelium (in reference to the association between smoking and lungcancer) or the difference in lung cancer incidence
by sex, could reasonably be considered examplesof plausibility as well as coherence; the distinction
appears to be a fine one. Hill emphasized that theabsence of coherent information, as distinguished,apparently, from the presence of conflicting information, should not be taken as evidence against an
association being considered causal. On the other
hand, presence of conflicting information may indeed
undermine a hypothesis, but one must always remember that the conflicting information may be mistaken
or misinterpreted [12].

Experimental Evidence
It is not clear what Hill meant by experimental evidence. It might have referred to evidence from laboratory experiments on animals, or to evidence fromhuman experiments. Evidence from human experiments, however, is seldom available for most epidemiologic research questions, and animal evidence
relates to different species and usually to levelsof exposure very different from those that humans
experience. From Hill’s examples, it seems that what
he had in mind for experimental evidence was theresult of removal of some harmful exposure in anintervention or prevention program, rather than the
results of laboratory experiments [10]. The lack ofavailability of such evidence would at least be apragmatic difficulty in making this a criterion for
inference. Logically, however, experimental evidence
is not a criterion but a test of the causal hypothesis, atest that is simply unavailable in most epidemiologic
circumstances.

3

Although experimental tests can be much stronger
than other tests, they are not as decisive as often
thought, because of difficulties in interpretation. For
example, one can attempt to test the hypothesis thatmalaria is caused by swamp gas by draining swamps
in some areas and not in others to see if the malaria
rates among residents are affected by the draining.
As predicted by the hypothesis, the rates will drop in
the areas where the swamps are drained. As Popper emphasized, however, there are always many
alternative explanations for the outcome of every
experiment. In this example, one alternative, whichhappens to be correct, is that mosquitoes are responsible for malaria transmission.

Analogy
Whatever insight might be derived from analogy ishandicapped by the inventive imagination of scientists who can find analogies everywhere. At best,
analogy provides a source of more elaborate hypotheses about the associations under study; absence ofsuch analogies only reflects lack of imagination or
experience, not falsity of the hypothesis.

Conclusion
As is evident, the standards of epidemiologic evidence offered by Hill are saddled with reservations
and exceptions. Hill himself was ambivalent about theutility of these “standards” (he did not use the word
criteria in the paper). On the one hand he asked “inwhat circumstances can we pass from this observed
association to a verdict of causation?” (originalemphasis). Yet, despite speaking of verdicts on causation, he disagreed that any “hard-and-fast rules ofevidence” existed by which to judge causation:
None of my nine viewpoints [criteria] can bringindisputable evidence for or against the cause-andeffect hypothesis and none can be required as a sinequa non.

Actually, the fourth criterion, temporality, is a sinequa non for causality: If the putative cause did
not precede the effect, that indeed is indisputableevidence that the observed association is not causal(although this evidence does not rule out causality inother situations, for in other situations the putativecause may precede the effect). Other than this one
condition, however, which may be viewed as part

Encyclopedia of Biostatistics, Online © 2005 John Wiley & Sons, Ltd.
This article is © 2005 John Wiley & Sons, Ltd.
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DOI: 10.1002/0470011815.b2a03072

4Hill’s Criteria for Causalityof the definition of causation, there is no necessaryor sufficient criterion for determining whether anobserved association is causal.

Acknowledgment
This article is adapted from Chapter 2 of Modern Epidemiology 2nd Ed. [8], with permission from the publisher.

References
[1]

[2]
[3]

[4]

[5]
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published 1888. 2nd Ed. with text revised and notes by
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MacMahon, B. & Pugh, T.F. (1967). Causes and entities
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Mill, J.S. (1862). A System of Logic, Ratiocinative andInductive, 5th Ed. Parker, Son and Bowin, London.
Popper, K.R. (1968). The Logic of Scientific Discovery.
Harper & Row, New York.

[7]

Rothman, K.J. (1976). Causes, American Journal of
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[8] Rothman, K.J. & Greenland, S. (1997). Modern Epidemiology, 2nd Ed. Lippincott, Philadelphia, Chapter 8.
[9] Sartwell, P. (1960). On the methodology of investigations of etiologic factors in chronic diseases – further
comments, Journal of Chronic Diseases 11, 61–63.
[10] Susser, M. (1988). Falsification, verification and causal
inference in epidemiology: reconsiderations in the lightof Sir Karl Popper’s philosophy, in Causal Inference, K.J. Rothman, ed. Epidemiology Resources, Inc.,
Boston.
[11] US Department of Health, Education and Welfare(1964). Smoking and Health: Report of the Advisory
Committee to the Surgeon General of the Public HealthService, Public Health Service Publication No. 1103.
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[12] Wald, N.A. (1985). Smoking, in Cancer Risks andPrevention, M.P. Vessey & M. Gray, eds. Oxford
University Press, New York, Chapter 3.

(See also Causation)

Encyclopedia of Biostatistics, Online © 2005 John Wiley & Sons, Ltd.
This article is © 2005 John Wiley & Sons, Ltd.
This article was published in the Encyclopedia of Biostatistics in 2005 by John Wiley & Sons, Ltd.
DOI: 10.1002/0470011815.b2a03072

KENNETH J. ROTHMAN &SANDER GREENLAND