Anne Hardy, M. Eileen Magnello Wellcome Trust Centre for the History of Medicine at UCL, London Statistical methods in epidemiology: Karl Pearson, Ronald Ross, Major Greenwood and Austin Bradford Hill, 1900���1945 Soz.- Pr��ventivmed. 47 (2002) 80���89 0303-8408/02/020080-10 $ 1.50 + 0.20/0 �� Birkh��user Verlag, Basel, 2002 Summary The tradition of epidemiological study through observation and the use of vital statistics dates back to the 18th century in Britain. At the close of the 19th century, however, a new and more sophisticated statistical approach emerged, from a base in the discipline of mathematics, which was even- tually to transform the practice of epidemiology. This paper traces the evolution of that new analytical approach within English epidemiology through the work of four key contribu- tors to its inception and establishment within the wider disci- pline. Keywords: Epidemiology ��� History ��� Statistics. ���The object of the present Grammar���, wrote Karl Pearson (1900: 515) towards the end of the second edition of The grammar of science, ���has been chiefly to show how a want of clear definition has led to the metaphysical obscurities of modern science���. Pearson did not explicitly delineate a statistical methodology in his text, but his call for clear definition provoked an enthusiastic response among many young, scientifically-minded men in the last decade of the 19 th century, not least in a medical student named Major Greenwood (1880���1947), who had rather have studied either history or mathematics, but whose family tradition had com- pelled him into medicine (Hogben 1950���51). It has long been recognised among historians of epidemiology that the quantitative methods and statistical philosophy of Karl Pearson (1857���1936) with W.F.R.Weldon (1860���1906), and Francis Galton (1822���1911) generated the processes by which the modern discipline emerged after World War II. The extent of the metaphysical confusion within which the process was generated has generally been underestimated: bacteriology, it is assumed, effectively displaced the existing tradition of epidemiological study, which was only gradual- ly rediscovered in the years after 1910. This perspective overlooks the obduracy of epidemiology, however. Despite the challenge of bacteriology, despite the historicism and metaphysical obscurity re-introduced into the discipline by Charles Creighton, whose monumental History of epi- demics appeared in the mid-1890s, despite the Pearsonian conviction that every biological event could be reduced to a mathematical formula, epidemiology retained a distinct identity, and consciously maintained and debated that entity, in the years between 1900 and 1940. In that debate, a crucial preparation for the development of the subject after 1945, Major Greenwood played a central part. Before the 1890s, Victorian epidemiology had been a large- ly observational, environmentally-oriented science, which employed fairly simple statistical methods. The year 1894 proved something of a watershed, with the publication, on the one hand, of Creighton���s History, which sought to illu- minate disease causation and behaviour through the exami- nation of past epidemics, and on the other of Emil Roux��� successful anti-toxin therapy for diphtheria. The historical approach induced some epidemiological practitioners to go back to older sources, and to develop, from a reading of Hippocrates, Baillou, and especially Sydenham, a more metaphysical approach to problems of disease. The enticing technologies of bacteriology, by contrast, appeared likely to dispense with the need for epidemiology altogether as one observer noted, once the germ had been found, ���The next step is either to exterminate the germ or devise an antidote. This step having been taken, the epidemic disease ��� is, or ought to be, of only historical interest��� (Anonymous 1921). The metaphysical approach developed, no doubt, in part Series: History of epidemiology

81 Series: History of epidemiology Hardy A, Magnello ME Statistical methods in epidemiology Soz.- Pr��ventivmed. 47 (2002) 80���89 �� Birkh��user Verlag, Basel, 2002 as a reaction against epidemiology: those who espoused it tended to be sharp critics both of bacteriology and of the new statistical methods. For statistics also played a part in this confusing equation. Between the devil of metaphysics and the deep blue sea of bacteriology lay a small band of practitioners who sought the general laws of disease through the application of mathe- matics, a discipline at once more rigorous and less reduc- tionist than either. Victorian epidemiology had made judi- cious use of others��� expert knowledge ��� of meteorology, of geology, chemistry, bacteriology, and statistics ��� but rather as consultant than as integral methodologies. It was, in the tradition of William Farr, a highly pragmatic epidemiology, dealing with the best available data and not straying far from them, using average death-rates, simple methods of statis- tical induction, and common sense, to draw conclusions ��� relationships ��� between illness and insanitary conditions (Greenwood 1935). It was focused largely on local disease outbreaks, on patterns of disease on the ground, and entered into little speculation about issues such as epidemic waves, or the periodicity between outbreaks. Mathematics was not made use of in these investigations, nor were complex statis- tical analyses: there were few medical men ��� let alone epi- demiologists ��� with the ability to deal in mathematical issues. Mathematics did not feature in the curriculum of the Victo- rian medical school, and the only ���epidemiological��� training then available was vital statistics taught on the Diploma in Public Health courses. Like the great majority of any given population, early twentieth-century medical men shied away from anything at all complex to do with figures. There were, however, a handful of medical men who were attracted by mathematics as a means of epidemiological analysis, who were interested in trying to establish ���natural laws��� for the behaviour of disease. The near-universal move- ment towards new standards of scientific rigour, which had been gathering pace through the 19 th century, invited criticism of epidemiology, which, bacteriology apart, con- tained little that could be described as scientific method. Statistical methods offered an alternative to bacteriology ��� and a methodology which could be integrated into the exist- ing explanatory models without too evidently relegating the whole discipline to the mathematical practitioners. Indeed, the idea of supplying statistical methods to measure biolog- ical variation derived from Francis Galton, whose work influenced the Darwinan zoologist W.F.R. Weldon who, in turn, provided the impetus to Karl Pearson���s development of the modern theory of mathematical statistics. Their work represented a new and challenging method of scientific ver- ification and exploration (Magnello 1996). For statistically- minded epidemiologists, the statistical tools which Pearson had created for curve-fitting and goodness of fit tests (for asymmetrical and symmetrical distributions), in addition to the series of correlation methods he devised, had a partic- ular attraction. Having created the Biometric School at University College London (UCL) in 1893, by 1900 Pearson had devised the foundations to the mathematical theory of statistics and the journal Biometrika had also been founded by Weldon, Pearson, and Galton. Some three years later, Pearson established the Drapers��� Biometric Laboratory at UCL. It was in the first years of the new century that Greenwood approached Pearson for guidance on using statistics in medi- cal research, so initiating one of two slender contemporary strands of interest in statistical epidemiology. At about this time also the second strand emerged, independently of the biometric stable, in the redoubtable person of Ronald Ross (1857���1932), discoverer of the mosquito transmission theory of malaria. Like Greenwood, Ross was a reluctant medical man, and also like Greenwood, pressurised by his father into the profession. Ross had wanted to be a painter, but he was also multi-talented: painter, musician, physician, and mathematician. Arriving in India in 1881, he spent most of his first six years in the Bengal Medical Service studying mathematics. Writing to G.H.F. Nuttall in 1899, just before he returned home, he asked, ���Can you tell me whether immunity has been ever studied mathematically?��� A few years later, as external examiner for the Diploma in Tropical Medicine and Hygiene at Cambridge University, he spent his spare time buying maths books in the town (Nuttall 1932���35). Ross had no affiliation with the biometric school, although he appreciated its standing, and sought Pearson���s assistance on quantitative matters regarding his work. In 1908, tackling the problem of the relationship between mos- quito density and malarial infection in Mauritius, he used a simple difference equation in illustration, later developing applications of the technique in the second edition of his Prevention of malaria. Ross���s essay into quantitative epidemiology was closely associated with his interest in malaria. The discovery of the mosquito vector had, inevitably, resulted in unpopular attempts to reduce mosquito numbers as a preventive. It was, however, frequently observed that there was little apparent relationship between numbers of mosquitoes and numbers of malaria victims in a given locality an observa- tion which was used to argue that the amount of malaria did not depend on the number of mosquitoes, and that as an anti-malarial measure mosquito control was redundant. Experimental investigation being impractical, Ross set him- self to examine the question by ���a carefully reasoned analy- sis of the relations between the amount of disease and the