Lewis Wolpert: Statistical analysis established that smoking led to lung cancer. Statistics save lives

To suggest that "there are lies, damn lies and statistics" is really outrageously unfair and misleading. Statistical analysis is fundamental to careful interpretation of data in many areas of science, technology and public affairs. It is essential to the unravelling of complex dependencies. In particular, it is fundamental to the study of many aspects of human health.

Children at school should be taught the importance of randomised clinical trials, an essentially statistical idea, which are vital to the establishment of the effectiveness of treatments. Anecdote will not do in these matters. In the 1940s, Bradford Hill and Richard Doll were investigating the incidence of lung cancer and expected to find air pollution to be of primary importance. But after careful statistical analysis, they established that smoking was the overriding factor. Statistics save lives.

The career of the statistician David Cox illustrates improbabilities in life. He went up to Cambridge during the Second World War to study mathematics. He would have preferred physical chemistry but the headmaster of his grammar school in Birmingham, himself a mathematician, virtually insisted that Cox read mathematics. After two years of exemption from national service, he was sent by the recruiting board to the Royal Aircraft Establishment where he worked on statistical quality-control of aircraft components and the statistical distribution of stresses on aircraft in flight.

In particular, he had to study the strengths of spot-welded joints. If two pieces of metal are welded together with 10 spots, then, under load, perhaps two of the spots may fail but the remaining eight may be strong enough to deal with the enhanced load. In other words, what is the relation between the distribution of strengths of the spots and of the joint? Cox produced a crude solution to this problem in the mathematics of applied probability.

One day, in the library, he read a paper by Henry Daniels giving an elegant solution to the same problem, this time, however, in a textile setting relating the strength of a bundle of fibres to that of the individual fibres. Cox was so impressed that he applied to work with Daniels, the wisest scientific decision he ever made, he now feels. This was at the Wool Industries Research Association in Leeds.

Later, at Imperial College, he developed one of his most influential ideas, that of the proportional hazards model. This is essentially a method for disentangling the effects of different explanatory variables on survival times. It was developed initially with medical applications in mind, although it has been applied in fields ranging from physics and engineering reliability to econometrics and sociology. For this work he received, in the US, the Kettering prize and gold medal for contributions to the treatment of cancer, the only non-medical person ever to have been awarded this.

It is a mark of the wide-ranging importance of statistical ideas, and, in a way, of the unifying role of mathematical thinking, that statisticians publish their work not only in specialised journals for other statisticians but in many other fields, too. In Cox's case, these include textiles, agriculture, hydrology, medicine and sociology. He has written not only about statistical analysis but also about the closely related issues of planning of experiments; his book on this theme contains no mathematical formulae and is aimed to convince general investigators of the importance of such issues as randomisation for bias avoidance.

A somewhat controversial aspect of statistical thinking concerns Bayes' method, which involves the incorporation of information into the calculations of what is already believed. It thus involves an element of personal judgement, rather peculiar for a subject so rigorous and mathematical. Whatever the merits of such arguments, there is no doubt about Cox's initial judgement about the probability that he would be knighted and end as the warden of an Oxford college; it would have been that the probabilities involved were so small as to be negligible. But that is what happened. Now in his late seventies, he is travelling the world and has a new research monograph soon to be published.

Lewis Wolpert is Professor of Biology as Applied to Medicine at University College London