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In our earlier discussion of the problems associated with using and interpreting statistical data we described some of the difficulties involved when trying to establish and model causation. As Rothman et al. (2008, p5 [ROT1]) observe:

"such a model should address problems of multifactorial causation, confounding, interdependence of effects, direct and indirect effects, levels of causation, and systems or webs of causation"

In medical statistics the word cause is often used in a probabilistic sense, i.e. by suggesting that factor A is a cause of outcome or disease B, we often mean that A significantly increases the risk or probability of outcome B. This lack of specificity reflects an underlying uncertainty about the detailed processes at work. Hence recognizing that a particular chemical is carcinogenic does not explain the processes that lead from exposure to incidence of the condition — these processes are likely to be extremely complicated involving molecular biology, and may be difficult if not impossible to determine.

In a famous paper delivered by Austin Bradford Hill to the Royal Society of Medicine in 1965 [BH2], he suggested a series of viewpoints (his terminology) by which one might use as guidance when seeking to establish the nature and validity of a suspected causal relation. In this subsection we summarize what has now become known as the Bradford Hill Criteria, although the term criteria was not used in his paper. He commences with the assumption that a clear-cut association (or correlation) of some kind has been observed. This association does not need to be one that is determined as statistically significant — in fact, Bradford Hill argues strongly against the blind use of statistical significance in this context. In addition and as noted above, the causal relationship may in fact be complex, as for example in a causal chain, or in an effect that may be the result of multiple (i.e. different) causal factors or the result of several factors working in combination. Bradford Hill's nine viewpoints for examining possible causal effects are, in summary:

Bradford Hill's (1965) 9 Viewpoints for Causation

1.Strength: if an association is very strong it deserves closer consideration than weaker associations — for example, if we observe that heavy smokers are 30+ times more likely to contract lung cancer than non-smokers, the strength of evidence is more powerful than if we observed that they were only 2x as likely to contract lung cancer. In fact it was Bradford Hill who first brought this particular relationship to public attention. On the other hand, lower strength of evidence does not imply that there is no causal relationship

2.Consistency: is the observed association repeated/repeatable, in different locations, at different times and under differing circumstances? As above, the absence of such repeatability does not imply that there is no causal relationship — for example, it may not be possible to repeat a set of circumstances

3.Specificity: if the observed association appears to be highly specific to a given set of circumstances and/or locations, then it is more likely to be related to these circumstances in some causal manner. For example, the very high incidence of certain diseases amongst individuals working in very specific environments (e.g. chimney sweeps and felt hat makers in the 18th and 19th centuries; Nickel refinery workers in the early 20th century). A somewhat different example is the incidence of pre-menopausal breast cancers where a high number of cases has been observed within particular families across the generations, suggesting a specific genetic effect

4.Temporality: here the question is whether the order is AB or BA. For example, is being extremely overweight causing people to contract a particular disease or condition, or do people with a particular condition become extremely overweight. These kinds of relationships can be quite subtle and inter-connected

5.Biological gradient: if increased exposure to some well-defined hazard is associated with a similarly increase in disease incidence, then this tends to support a causal relationship, as compared with a relationship for which no 'gradient effect' is observed

6.Plausibility: if the suspected causal relationship is plausible, within the scope of current knowledge, then it has (marginally) more merit than a relationship for which no known explanation can be proposed. Having made this observation, it is clearly a relatively weak criterion

7.Coherence: if the suspected causal relationship is consistent with current knowledge about the variables involved, it may help to support (or at least, not to detract from) the possible causal relationship being considered. Again, as with plausibility, this may be regarded as a relatively weak criterion

8.Experiment: if one or more repeatable controlled experiments can be carried out to test the suspected causality, and these tests support the hypothesis, this greatly enhances the strength of evidence case

9.Analogy: if a similar causal relationship has been established, but under different circumstances, it may again provide support for the argument that a causal relationship exists, but again this is a weak criterion

These 9 viewpoints have been taught to students in the biomedical sciences for many years, often as criteria rather than as broad guidance. More recently authors such as Phillips and Goodman [PH1] have re-emphasized the original 'lessons' of Bradford Hill, in particular his skepticism regarding the use of statistical significance. In their commentary they summarize these missing lessons as:

Statistical significance should not be mistaken for evidence of a substantial association

Association does not prove causation (other evidence must be considered)

Precision should not be mistaken for validity (non-random errors may exist)

Evidence (or belief) that there is a causal relationship is not sufficient to suggest action should be taken

Uncertainty about whether there is a causal relationship (or even an association) is not sufficient to suggest action should not be taken

In preparing these bullet points the authors were particularly concerned to address the question of systematic errors or bias, which we have previously seen can be complex and inadvertently introduced, thereby confusing both intuitive and statistical inference. They also emphasize the importance of the relationship between causal analysis and the subsequent decision making regarding policies such as screening, interventions and vaccination. These policies exist in a much broader framework of political and economic considerations, requiring weighted cost-benefit and risk-based assessments, whatever the apparent strength of evidence may be from causal analysis.

Evans (1976, (EVA1]) focused on identification of cause-effect relationships for diseases, rather than the generality of such relations. His "criteria for causation" table, developed as a form of unification of the ideas and research by many authors over the previous century, but curiously without reference to Bradford Hill, is provided below (with his italics):

Evans' (1976, Table 13) 10 Criteria for Causation

1.Prevalence of the disease should be significantly higher in those exposed to the putative cause than in cases [or] controls not so exposed

2.Exposure should be present more commonly in those with the disease than in controls without the disease when all the risk factors are held constant

3.Incidence of the disease should be significantly higher in those exposed than in those not exposed as shown in prospective studies

4.Temporally, the disease should follow exposure with a distribution of incubation periods on a bell shaped curve

5.A spectrum of host responses should follow exposure along a logical biological gradient from mild to severe

6.A measurable host response following exposure should regularly appear in those lacking this before exposure or should increase in magnitude if present before exposure

7.Experimental reproduction of the disease should occur in higher incidence in animals or man appropriately exposed than in those not so exposed; this exposure may be deliberate in volunteers, experimentally induced in the laboratory, or demonstrated in a controlled regulation of natural exposure

8.Elimination or modification of the putative cause or the vector carrying it should decrease the incidence of the disease

9.Prevention or modification of the host's response on exposure should decrease or eliminate the disease (e.g. immunization, application of statins to reduce cholesterol), and

10. Sense: the whole thing should make biologic and epidemiological sense

There are a number of formal and informal tools and procedures that may be utilized to assist in the analysis of the relationships between supposed causes and effects (i.e. in addition to purely statistical approaches). In many fields, including medical research, structured diagrams are often helpful, for example the use of traditional graph theory such as the work of Greenland et al. [GR1, ROT1] which uses the analysis of directed acyclic graphs (DAGs) to help identify and understand cause-effect relationships and confounding. A number of authors in the medical field have also used the Ishikawa or fishbone diagram as an aid to identifying the components and structure of causation particularly in the context of quality management and policy making. Formal structured review procedures, such as brainstorming and Delphi techniques, and of course the entire peer review process for research work and publications, collectively provide a range of mechanisms for obtaining the best possible understanding of possible cause-effect relationships.


[ALT1] Altman D G, Bland J M (1991) Improving Doctors' Understanding of Statistics. J of the Royal Stat. Soc., A, 154(2), 223-267

[BH1] Bradford Hill A (1937) Principles of Medical Statistics. The Lancet, London (issued in various editions until 1971. Then republished as "A Short Textbook of Medical Statistics" in 1977

[BH2] Bradford Hill A (1965) The Environment and Disease: Association or Causation? Proc. of the Royal Soc. of Medicine, 58, 295-300. A copy of this article is reproduced on Tufte's website:

[CAM1] Campbell M J, Machin D, Walters S J (2007) Medical Statistics : A Textbook for the Health Sciences. 4th Ed., John Wiley & Sons Ltd, Chichester

[ERC1] Ercan I, Berna Y, Yang Y, Ozkaya G, Cangur S, Ediz B , Kan I (2007) Misuage of Statistics in Medical research. Eur. J of Gen. Med., 4(3), 128-134

[EVA1] Evans A S (1976) Causation and Disease: The Henle-Koch Postulates Revisited. Yale J Biol Med., 49(2), 175-195

[GR1] Greenland S, Pearl J, Robins J M (1999) Causal Diagrams for Epidemiologic Research, Epidemiology,10(1), 37-48

[MRC1] Medical Research Council (1948) Streptomycin treatment of pulmonary tuberculosis. BMJ, 4582, 769-782

[PH1] Phillips C V, Goodman K J (2004) The missed lessons of Sir Austin Bradford Hill. Epidemiologic Perspectives & Innovations, 1(3)

[ROT1] Rothman K J, Greenland S, Lash T L eds. (2008) Modern Epidemiology. 3rd Ed., Lippincott Williams & Wilkins

[OLS1] Olson S H, Voigt L F, Begg C B, Weiss N S (2002) Reporting participation in case-control studies. Epidemiology,13(2),123-6