Evidence And Proof

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Any discussion of EBM gives rise to the question, what is evidence? The first concern is with the problem of proof and philosophers have long argued over this. In mathematics, the ancient Greeks demonstrated rigorous proofs of many theorems (literally God-like things), especially in algebra and geometry, and they thought of these as general laws.

Thus, we know for certain that Pythagoras' Theorem is true. The question arises as to whether one can have similar certainty in other areas of human enquiry.

In the natural sciences, Francis Bacon (1561-1626) described the work of scientists as collecting information and adducing natural laws. However, David Hume (1711-1776) concluded that no number of singular observations, however large, could logically entail an unrestricted general statement. Just because event A follows event B on one occasion, it does not follow that event B will be observed the next time we see A. Thus it does not logically follow, in the manner that a mathematical theorem is true, that A will always follow B whether we observe A and B together on two, twenty or two thousand occasions. The point here is that simply observing an association is not proof that an association actually exists.

There may, however, be real reasons why two events are associated, and in general one would hope to discover these. Thus, although we observe that 20 consecutive bedridden patients develop pressure sores, this does not logically imply that the 21st patient will do so. However, it does suggest a pattern that would be foolish to ignore when considering appropriate care for patient 21.

'Hume's problem' troubled philosophers as it seemed to discourage endeavours to make sense of nature. It was not until the last century that Karl Popper (1902-1994) proposed the idea of falsifiability. Falsifiability states that laws cannot be shown to be either true or false but that they can only be held provisionally true. He pointed out that observations cannot be used to prove laws, but can falsify them. Hume's famous example is the universal law 'all swans are white'. This cannot be proven, no matter how many swans one sees that are white, but it would take only a single black swan to refute the law. This has direct bearing on statistical inference, where, as part of the study design, one sets up a null hypothesis and then tries to refute it with the experimental observations. Failure to reject the null hypothesis does not logically imply that one should accept it, rather it implies that we do not have enough evidence to reject it.

Clinical trials which compare treatments are designed with a null hypothesis in mind, namely that the treatments have no differential effect on patient outcome. We try and disprove this null hypothesis using patient data. However, we can never prove a null effect.

The basis of EBM is that any guidance arising from any review of evidence is only provisional, albeit based on the best evidence available at the time. We can collect more evidence and, if this concurs with the existing evidence, it may give us greater confidence in our guidelines, but still cannot prove them. However, later evidence may contradict the existing theories (and hence disprove them), however well founded the past evidence is.

This approach may seem rather negative, but in fact it is liberating. What Popper's philosophy gives scientists is the freedom of 'trying their best'. With this they avoid claiming omnipotence, such as would be implied if their statements were assumed true for all time. It gives scientists a model whereby criticism of existing models is actively encouraged. It enables us to differentiate the good scientific theories from the poor. For good ones, one can devise experiments to attempt to falsify the hypotheses arising from the theories. However, all theories are not equally valid. Thus theories that have withstood attempts to disprove them are to be preferred over those that have not been so tested. It is worth pointing out, however, that often the choice of which experiments

Table 1.1 The Bradford-Hill criteria to assess causality (after Hill, 1965; reproduced by permission of the Royal Society of Medicine)








Strength of association


Biological gradient






Freedom from, or control of, confounding and bias


Analogous results found elsewhere

to conduct are financial, social or political decisions. Thus lack of supporting evidence for a theory may not necessarily be a deficiency of the theory itself, but rather the lack of will to test the theory.

Outside of the realm of mathematics, and in the less predictable fields of the biomedical and clinical sciences, the nature of human variability has meant that universal laws are rare. There are some obvious laws, such as if a person is deprived of oxygen they soon die; but such laws are the exception. Thus if we give a person a large dose of arsenic, they do not inevitably die. Rather than with establishing universal laws, biomedical science is concerned with a number of basic questions such as: Does exposure to substance A increase the risk of disease B? Does treatment C cure more people with disease D than other therapies?

More than a century ago Robert Koch (1843-1910) devised a number of questions the answers to which could be used to try and decide whether a specific bacterium caused a particular disease. These were modified by Bradford Hill (Hill, 1965) to a general examination of whether an event, such as an environmental exposure or smoking, would increase the risk of disease or prescribing a medical treatment improves the chance of cure. The Bradford-Hill criteria are summarised in Table 1.1.

In the Bradford-Hill criteria temporality means that the effect follows the cause and not vice versa. Thus a fall in lung cancer deaths in UK men succeeded a drop in the numbers of male smokers with a lag in time of some 30 years. This lag lends weight to a causal link between smoking and lung cancer. Consistency implies that the same fall in lung cancer deaths has been observed in women, or in other countries where smoking prevalence has fallen. Coherence means that different study types, such as case-control and cohort studies addressing the same issue, lead to similar conclusions. Strength of the association suggests that the stronger the effect the more plausible the causality. For example, smokers have 10 times the risk of lung cancer compared with non-smokers. The idea concerning the biological gradient is that if heavy smokers are found to be at greater risk of lung cancer than light smokers, then the case for causality is strengthened.

Specificity suggests that if the link were causal, the smokers would be mainly at risk from respiratory disease mortality, and not from other unrelated types of mortality such as those arising from road accidents. The relationship appears plausible as cigarette smoke is inhaled into the lungs and autopsy evidence from smokers and non-smokers documents clear differences between their respective lungs. A confounding variable is one that is related to both the exposure and the outcome, but not through a causal pathway. For smoking, genetics has been argued as a confounder on the basis that the impulse to smoke may be genetic - certainly if parents smoke then children are more likely to smoke. Also genes may control the risk of lung cancer. If the genes for smoking and lung cancer were linked then it would appear that smoking and lung cancer were causally related. However, if the genetic theory were true, it would have a hard time to explain away the other causal evidence such as that provided by temporality. Bias could occur in a study or survey because people with lung cancer may be more likely to recall details of their smoking history than people without lung cancer.

Just as in philosophy we cannot prove a universal law, so in medicine we cannot prove absolutely a causal effect. Satisfying the Bradford-Hill criteria increases the likelihood that a causal effect is present, but cannot give an absolute proof of it. Hill (1965) himself admitted: 'none of my nine viewpoints can bring indisputable evidence for or against the cause-and-effect hypothesis and none can be regarded as a sine qua non'.

As one example, this philosophy has considerable implications when epidemiologists try to show that the measles, mumps and rubella (MMR) vaccine does not cause autism. We can never prove the null that that there is no association between the MMR vaccine and autism. All we can do is demonstrate that, if there is a risk, then the risk is very low. It is up to those who advise on public health issues to decide whether the risk of autism is lower and/or less damaging than the competing risks associated with a child having measles. In this respect, temporality was a major issue as in the UK increases in the diagnosis of autism had been linked to the introduction of MMR. However, this increase has not been observed in other countries, none of the other Bradford-Hill criteria are satisfied and there is no clear biological theory linking vaccines to autism.

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