统计学文献10

170december2004

a life in statisticsa life in statistics

Purposes, methods,

philosophies

Peter Armitage has enjoyed a long and distinguished career in biostatistics, and has also given considerable thought to the way in which statistics is taught to non-mathematicians, perhaps because, he says jokingly, he always found maths a bit difficult himself. Now in retirement, he is still communicating statistical ideas in his rôle as Editor of the Encyclopedia of Biostatistics1.

Th ere was a research section in SR17, headed by George Barnard, who had previously been an applied statistician with the engineering fi rm Plessey and who therefore already had a strong background in engineer-ing statistics. “He was a very suitable person to start training people on doing work on sampling inspection and quality control, about which we all knew nothing. We really didn’t even know a great deal about statistics; we had been to these courses, but we didn’t have much of a feeling for the hands-on aspect of the subject; to some extent we were teaching each other, giving little seminars and arguing with each other.”Some of Armitage’s fi rst work concerned problems of sampling inspection, and early attempts to make some progress with sequential analysis. “Th ere was a general feeling that sequential inspection was the way ahead in “A lot of people who would be able to understand the purposes of statistical methods, and would be able to use them sensibly, are wasting their time if they really try to go deeply into the maths”The war yearsAfter specialising in maths at school in Huddersfi eld, Yorkshire, Armitage left in January 1941, at the age of 17, to go to Cambridge. “Th ere was a tendency at the time to push people into starting college at awkward times in the academic year, because they weren’t sure how long you were going to be able to stay there. So I did two terms of Part I, and then another year taking Prelims.”Th ere was a drive in the summer of 1943 to recruit people into industrial statistics as part of the war ef-fort, and in the early autumn of 1943 Armitage began work in a unit called SR17 in the Ministry of Supply alongside numerous other novice statisticians, includ-ing, for example, Dennis Lindley. At that point, he felt no particular affi nity for statistics, having originally intended to be a schoolteacher. “I had taken a course on statistics during Part I of no particular interest, and then another with J. O. Irwin—he had been working in London for the Medical Research Council before the war and moved to Cambridge during the war. Th at was moderately interesting, but really rather impractical, over-theoretical.” a life in statistics171december2004

quality control, but no over-riding theory, so we were playing about with ad-hockery. In the middle of this, Abraham Wald developed his theory of sequential analysis2, and before it was

published in scientifi c journals it came over in technical reports; we realised that there was an overall powerful approach which we started to take over and work on.”Work continued for the next 2 years and then during the following year some of the unit, including Armitage, were transferred to the National Physical Laboratory. “Th at intro-duced me to some other areas of applied work, not just industrial, and in particular to some biological work as the National Physical Labo-ratory was part of a larger government group-ing of scientifi c work.”

Medical statisticsIn 1946, having fi nished his war service, Ar-mitage was able to return to Cambridge to continue his studies and he completed Part II of the Tripos. Although he had originally intended to return to the National Physical Laboratory, when he was asked to apply for a job in medical statistics in the London School of Hygiene and Tropical Medicine, he said yes. “Th is was a very fortuitous sort of thing as I had no real interest in medical statistics and I only knew one or two of the people working in the fi eld. I was off ered a job and started in December 1947, in a unit of the Medical Re-search Council (MRC) housed in the School of Hygiene under the honorary directorship of A. [later Sir Austin] Bradford Hill. Bradford Hill was a Professor of Medical Statistics, and he had a small group of people employed by the School, but a rather larger group employed by the MRC.”“Bradford Hill had a great ability to develop excellent research in new areas, and, although he was not a highly sophisticated mathematical statistician, he was a very good research strategist”Armitage was appointed as an assist-ant to J. O. Irwin and worked on problems of biological assay, which was a strong interest of Irwin’s. He also looked at some problems from microbiology and it was one of these that he developed into a PhD thesis. It concerned the dynamics of a bacterial population subject to mutation. “You had a population of bacteria that could mutate to a diff erent form and mu-tate back, so you had these two forms growing, and you had to estimate the mutation rates from experimental observations.”He also recalls work estimating the overlap of dust particles in samples of pol-luted air: “If you’re sampling polluted air, you want to count the concentrated dust particles. Now, if you concentrate the sample too much and put it out on plates, the dust particles overlap, and you can’t tell whether a particular image is one dust particle, or two or three. So, for a given density of particles, how much overlapping is there likely to be, and how do you adjust for that? It was re-ally a matter of making models of particles of various shapes falling on an area and ask-ing how much overlap there would be. And it was related to problems that other people, in operations research, had worked on with saturation bombing during the war. If you have tremendously saturated bombing, some of it is going to be wasted because it’s over-lapping.”At that time, Bradford Hill was initiating two major developments in medical statistics. One was to promulgate randomised clinical trials, and the other was to develop aetiological surveys—surveys to study the possible causa-tive eff ects of agents on disease. “Th is led to the fi rst study on smoking and lung cancer, with Richard Doll, which took subjects with cancer and controls and asked them how much they smoked. Th ey then went on to do a large co-hort study, looking at a population of people, discovering how much they smoked, and then looking forward over the years to see which diseases they died from. Hill had a great ability to develop excellent research in new areas, and, although he was not a highly sophisticated mathematical statistician, he was a very good research strategist.“Th ere was a great deal of interest in clini-cal trials, and I thought there was a connection which linked back to my work on sequential analysis in industrial statistics. I felt it would be useful to see whether you could carry out