Wednesday 5 August 2015

The meaning of proof - Hill's criteria and Koch's postulates (2)

People tend to use the word “proof” without understanding what it means. When, in respect of a proposition, someone says: “There is no proof”, the response should be: “What do you mean by proof?”, a question that is usually met by a puzzled silence.


“Proof”, as originally defined in classical geometry, is the fulfillment of predefined criteria. Someone who asks for proof should be asked: “What are your predefined criteria of proof?”

This was understood by the great German pathologist Robert Koch. His challenge was to find the cause of tuberculosis, consumption or phthisis as it was known at the time in the latter half of the nineteenth century. At the time it was thought that tuberculosis was “constitutional” – it ran in families and, in the days before genetics, it was considered to be somehow inherited. Koch felt that the family clustering was the result of the transfer of a micro-organism.

Robert Koch 1943-1910

Much laboratory work led him to define what became known as the Koch Bacillus, what we now know as Mycobacterium tuberculosis. Although he felt that this was the likely cause and had to be certain. He needed proof that would be acceptable not only to himself but also to a scientific community that was clearly sceptical.
Understanding the concept of proof, Koch had to record his predefined criteria that, if fulfilled, would lead to the acceptance of the micro-organism being the cause of tuberculosis. His criteria were called “Koch’s Postulates”, and they are as follows:
1.  The specific organism should be shown to be present in all cases of animals suffering from a specific disease but should not be found in healthy animals.

2.  The specific micro-organism should be isolated from the diseased animal and grown in pure culture on artificial laboratory media.

3.  This freshly grown micro-organism, when inoculated into a healthy laboratory animal, should cause the same disease seen in the original animal.

4.  The micro-organism should be re-isolated in pure culture from the experimental infection.

Koch’s postulates were very demanding, and it can be seen that they required the following reach requirements:

•     the postulated cause must be a micro-organism;
•    the micro-organism must be isolated and grown in laboratory culture;
•    The micro-organism must be inoculated into a healthy animal and produce disease.

Not all micro-organisms can be isolated and grown, this applying to viruses and many recently-discovered bacteria. Not every micro-organism causing human disease will produce that disease in laboratory animals. Is inoculation into human, volunteers or in ignorance, acceptable? The answer to this is an emphatic “No!”

Koch’s Postulates have major limitations and in practice they are only of historic interest. They cannot be applied to non-biological likely causes of disease and a different approach became necessary.

Sir Austin Bradford Hill 1897-1991

The eminent British statistician Sir Austin Bradford Hill felt that proof of causation could be made using different criteria than Koch’s postulates, and he felt these to be necessary in the case of the inanimate causes of disease, for example cigarette smoking as the cause of carcinoma of the lung.  He identified the following criteria as being necessary for “proof” to be established:

1.  Strength of association
2.  Consistency of association
3.  Temporality
4.  Biological gradient
5.  Plausibility
6.  Coherence
7.  Experimentation
8.  Analogy
It is important to note that apart from Experimentation, all the criteria are part of the observational process of scientific investigation. The observations become increasingly controlled so as to avoid other factor. For example death rate must be standardised for age.

It is generally recognised that proof is pragmatic, the fulfillment of predetermined criteria. There is no absolute proof; we are looking for the best story that can be defined using existing knowledge. It might change with the passage of time as new knowledge becomes available.

Koch’s postulates identified absolutes; a bacterium did or did not grow. Hill’s criteria are not absolute and all criteria can be regarded as judgmental.

The strength of association is the association between the disease and the proposed cause. The strength is determined by statistical method.

Consistency is important, being the association being corroborated in several studies.

Temporality indicates that association at one point in time does not indicate cause-effect relationship, but we must look at the association over a time-line. The proposed cause must predate the disease.

The biological gradient indicates that in general the greater the exposure to the proposed cause, the great is the probability of disease (for example number of cigarettes smoked and the development of lung cancer).

All these add up to construct plausibility – does it make sense? Is there a coherent pattern – does it all hang together?

Experimentation is limited by ethical considerations. It might be possible to transmit the disease to others, if not to experimental animals then to other human beings. Such research is not tolerated today. However the effect of elimination of the proposed cause is ethical and highly informative.

Finally there is analogy. Does the proposed cause or something similar (biological or chemical) cause similar diseases?

Hill’s criteria of causation have been reviewed and refined by researchers at the US National Institute of Health (NIH) to look at the possibility of a microbe causing a disease, and in this particular case Crohn’s disease. The principles are equally applicable to the investigation of a possible microbial cause of coronary heart disease, for which there is no obvious cause at present (cholesterol and diet theories are not sustainable when the evidence is reviewed critically).

Hill’s Criteria are very valuable but little known. Most if not all doctors are aware of Koch’s Postulates, but Hill’s Criteria do not seem to be taught. We should all be more aware of them.


  1. outside math and logics a "proof" is just a subjective probability estimate
    that exceeds some (high) level. Above that level you use the word "proof"
    which average people better understand [sigh] than probability numbers.
    [I've been asking in internet for subjective probability estimates
    without much success - people are reluctant.]

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