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certain gambling problems [e.g. Pacioli (1494), Car- Health , dano (1539), and Forestani (1603)] which were first of solved definitively by (1601–1665) and (1623–1662). These efforts gave rise to the mathematical basis of , The field of statistics in the twentieth century statistical distribution functions (see Dis- (see Statistics, Overview) encompasses four major tributions), and . areas; (i) the theory of probability and mathematical The of and of mea- statistics; (ii) the analysis of uncertainty and errors surement had its foundations in the field of astron- of (see Measurement in omy which, from antiquity until the eighteenth cen- Epidemiologic Studies); (iii) design of tury, was the dominant area for use of numerical (see Experimental Design) and surveys; based on the most precise measure- and (iv) the collection, summarization, display, ments that the technologies of the times permit- and interpretation of observational (see ted. The fallibility of their was evident ). These four areas are clearly to early astronomers, who took the “best” obser- interrelated and have evolved interactively over the vation when several were taken, the “best” being centuries. The first two areas are well covered assessed by such criteria as the quality of obser- in many of while vational conditions, the fame of the observer, etc. the third area, being essentially a twentieth- But, gradually an appreciation for averaging observa- century development, has not yet been adequately tions developed and various techniques for fitting the summarized. Although the fourth area has been going observational data to parametric models evolved. on since man first learned to think inductively, it Many of the founders of modern statistics contributed relies on the state of the art in the first three areas. to the early development of the theory of measure- In this brief survey of health statistics during the ment errors including Jacob Bernoulli (1654–1705), past five centuries, emphasis will be given to the (1667–1754), Pierre Simon development of official health statistics systems in Laplace (1749–1827), and Europe and the US. (1777–1855). A systematic approach to the collection of data and tabulating observations in a rational manner began Early Interest in Statistics with the teachings of Francis Bacon (1561–1626). In his influential treatise Novum Organum (1620), At the end of the fifteenth century, he attacked the scholastic philosophy which had was at a rather primitive stage and the threshold of developed in the Middle Ages on the basis of the “scientific revolution” was still two generations the methods of Aristotle. One of the first areas away. The mathematics of the Greeks had only re- influenced by Bacon’s approach was entered European thinking in the twelfth century, and and vital statistics and the social utility of systematic although some progress had been made in practical observations is clearly reflected in these early efforts. applications in navigation and commercial , The utilitarian nature of statistics is evident in the the burgeoning of was only beginning. origins of the word from the Italian stato (state), and Mathematicians still did not recognize the number the original meaning of statistics was a collection zero or know how to deal with negative numbers. of facts of interest to a statesman. Initially such Except for a few examples of probabilistic thinking facts were not primarily numerical, but included such as that in the talmudic literature [10], there was information on , , and customs of scant evidence of the use of a mathematical approach a region. The compilers of such facts were called to to estimate risks or assess the statists, a term which survived into the nineteenth of until the mid-seventeenth century, when the word statistics came to be used century. for numerical data only, replacing the term “political Most historians of statistics trace the origins of arithmetic”, and the word “” came into modern to the efforts to solve vogue. 2 Health Statistics, History of

The Origins of Demography and Vital the first life ever published, perhaps his most Statistics famous contribution. Owing to the widespread influence of Graunt’s Since ancient times, sporadic surveys of people and work, bills of mortality similar to the bills property were done to set tax assessments and levies were introduced in Paris in 1667, and soon after in for military service. But after the fall of the Roman other cities in Europe. empire, regular covering an entire state Graunt’s was brought to the attention did not occur until the eighteenth century. However, of (1629–1695) and his brother there were intermittent attempts to keep track of Ludwig (1631–1699) who proceeded to develop a the births and deaths in some areas through church probabilistic interpretation of the life table, which was records of weddings, christenings, and burials. The rediscovered independently by Nicholas Bernoulli City of London was one of the first to regularize (1687–1759). These investigations, together with the maintenance of such records in 1538, but only the more applied techniques of Edmond Halley within the Church of England. Also at about this (1656–1742) based on the births and funerals in the time a or early warning system of City of Breslau (1693), and the work of Deparcieux plague deaths was started in London. To detect the (1703–1768) in who used data from tontines onset of a plague , parish clerks submitted to construct the first correct life tables, formed the weekly reports on the numbers and causes of deaths. foundation of the actuarial for life These weekly Bills of Mortality were noted by the and annuities. These were developed further by authorities who were to take actions if they detected Abraham DeMoivre (1667–1754), Thomas Simpson the onset of an epidemic, and by the wealthier citizens (1710–1761), (1779–1865), and for “an indication of when to leave the city for William Makeham (1826–1891). the fresh air of the country” [7]. The weekly bills It was not until 1766 in Sweden that Per Wargentin were published regularly from 1604 until 1842 when (1717–1783) published the first mortality tables for they were superseded by reports from the Registrar a whole country based on enumerations of the living General. as well as on deaths. These mortality In 1662, (1620–1674), a London tables demonstrated for the first time in a general tradesman who had been active in local politics population that the of females was less and intellectual society, published his Natural and than that of males. Political Observations Made Upon the Bills of Graunt’s methods of statistical analysis were Mortality, which historians of statistics have referred widely adopted by seventeenth-century statists. William Petty to as “a remarkable book [12]”, “one of the (1623–1687), who was a proteg´ e´ great classics of [6]”, and “a paragon for of Graunt, and after Graunt’s financial bankruptcy in 1666, his patron, coined the term “political descriptive statistical analysis of demographic data arithmetick” and was one of the founders of the field [7]”. Hald summarizes Graunt’s contributions to the of political economy. Gregory King (1648–1712) origins of statistics thus: and Charles Davenant (1656–1714) contributed to Graunt’s critical appraisal of the rather unreliable improvements in the estimates of the population data, his study of mortality by cause of death, of England. Sebastien de Vauban (1633–1707) his estimation of the same quantity by several described the extent of poverty in France, for different methods, his demonstration of the stability which he suffered public disgrace because of its of statistical ratios, and his life table set up embarrassment of the royal government. Nicholas new standards for statistical reasoning. Graunt’s Struyck (1678–1769) instituted town censuses in the work led to three different types of investigations: political arithmetic; testing the stability of statistical Netherlands and improved the recording of births ratios; and calculation of expectations of life and and deaths. The revelations of statistical data were survivorship probabilities [7]. also used to support religious positions such as the claim of John Arbuthnott (1667–1735), who was a At a time when denominator data on the size of vigorous proponent of political arithmetic, that the the population by age were not available, Graunt stability of the sex ratio “is not the effect of chance used several ingenious lines of reasoning to generate but divine providence”. Somewhat later, Johann Peter Health Statistics, History of 3

Suessmilch (1707–1767) in Germany gathered vital Applying Statistics to Medical and from virtually every source then available Issues as evidence of certain tenets of orthodox Lutheran theology. He maintained that the life span (see Life Just as demographic and began Expectancy ) was constant and that little could be with the name of “political arithmetic” in the seven- done to improve mortality rates. His work directly teenth century, began with the name influenced the thinking of Thomas Robert Malthus of “the numerical method” early in the nineteenth (1766–1834). These diverse endeavors eventually century. Although some of his methods were evident led to the establishment of governmental statistical in the works of Phillipe Pinel (1745–1826) and other offices in the nineteenth century. French physicians, Pierre-Charles-Alexandre Louis Among the developments in mathematical statis- (1787–1872) has been described “as the first modern tics that occurred during the eighteenth century, two clinician, the man who made bedside a sci- had special relevance for health statistics. Daniel ence as well as an art, and who established the princi- Bernoulli (1700–1782), who first developed the nor- ple of learning medicine from thoughtful mal approximation to the and of patients [1].” His studies on the inefficacy of blood used it in studies of the stability of the sex ratio letting were the beginning of quantitative medicine at birth, applied the methods of to mortal- and earned him the title of “father of medical statis- ity rates by treating them as continuous functions. This enabled him to obtain a solution in 1760 to tics” [12]. Louis’s hopes for his numerical method an important question of his day: to were echoed by Giacomo Tommasini (1768–1846) in estimate the impact on life expectancy of eliminating Italy, and F. Bisset Hawkins (1796–1894) in Eng- through a proposed program of mandatory land, who published in 1829 the first English textbook vaccination. His invention of the method of com- on medical statistics with the rather grand title of peting risks, with some improvement by d’Alembert Elements of Medical Statistics; Containing the Sub- (1761) and by Makeham (1874), still forms the basic stance of the Gulstonian Lectures Delivered at the tool for such analyses. Royal College of Physicians with Numerous Additions A second development expanded the techniques Illustrative of the Comparative Salubrity, Longevity, used by Vauban. Laplace proposed a nonrandom sam- Mortality, and of Diseases in the Principal pling method to estimate the size of the population Countries and Cities of the Civilized World. Although in 1786. It was based on a notion similar to that of by later standards Louis’s statistical attempts were current ratio estimates, i.e. that the size of the pop- often inadequate, suffering particularly from sparse ulation of a region was proportional to the annual numbers, he had a crucial influence on number of births in that region and that the constant who attended his lectures during his two years in of proportionality could be determined from a purpo- Paris, as did several American physicians who were sive sample of subregions. Graunt had used a similar influential in the early development of public health assumption implicitly a century earlier. and . Laplace’s method was severely criticized, most Louis’s methods were not immediately accepted notably by Baron de Keverberg (1827) [11, p. 164]. for many of the same reasons that Laplace’s methods These criticisms clearly reflected an appreciation that were not: the variability between cases was thought there were a multitude of factors that could influ- to be highly individualistic and not subject to statis- ence any chosen characteristic of a population, that tical summarization. For example, William A. Guy subgroups of the population were not homogeneous (1810–1885), who contributed much to public health with regard to the array of factors influencing the and occupational statistics, felt “the formulae of the characteristic, and, therefore, purposive samples of mathematician have a very limited application to the the population could not reflect the total population. of observation” [12, p. 151]. Only complete censuses of the population would do, The Belgian, (1796–1874), and these would have to amass immense amounts of who dominated the field of social statistics for half information. At this time there was not yet an appre- a century, may have gone too far in the other direc- ciation for the power of random sampling methods tion. Impressed by the central theorem and (see Probability Sampling). believing that based on large numbers of 4 Health Statistics, History of observations from a population had remarkable sta- Medicine, , Vital Statistics, and General bility, he introduced the concept of the “ man” Science, which lasted only eight months, January to (l’homme moyen) which had considerable popular August 1837, but allowed him to write major arti- appeal. He was also enamored of the normal distribu- cles on medical reform and vital statistics. The Births tion and fitted it to many characteristics, marvelling and Deaths Registration Act of 1836 had inaugurated at the statistical of large bodies of data the modern system of civil registration and led to which detracted from further exploration of valid het- the establishment of the General Register Office in erogeneities. However, he influenced a large number 1837. Farr joined the staff of the General Register of including Louis Adolphe Bertillon Office in 1839, serving forty years, first as compiler (1821–1883), Wilhelm Lexis (1837–1914), Francis of abstracts and then as superintendent of the Statis- Galton (1822–1911), (1857–1936), tical Department. and Ronald A. Fisher (1890–1962) [11]. Farr “insisted that the statistician adopt a criti- cal approach, investigating the accuracy of his data, questioning the appropriateness of the units used, Development of Health Statistics in and attempting with the help of ratios, , England and the calculus of probabilities to discover relation- ships and regularity in order to make ” During the eighteenth century many physicians and [5, p. 29]. Farr’s philosophy had an almost immedi- registrars in England recognized the inadequacies of ate impact on improving British statistics. The first the bills of mortality. There were frequent calls for four censuses were fraught with many problems. The reforms but because of concerns about personal liber- 1841 was the first conducted under the super- ties, religious arguments, and beliefs that population vision of the General Register Office and Farr was figures were crucial state secrets, it was not until 1800 one of the key advisors. It was a great improvement that Parliament passed a population act that set up over its predecessors and, together with the annual the census of 1801. By the 1830s, as in the mid- vital statistics data, enabled Farr to put together tables seventeenth century (with Graunt and Petty), London and analyses which placed England at the forefront “witnessed a flash of enthusiasm for vital statistics of this discipline. Between 1836 and the Registra- and political arithmetic” [5, p. 13]. The Statistical tion Act of 1874, Farr was largely responsible for Society of London was founded in 1834 by the same establishing the procedures for collecting and ana- group that had founded the statistics section (Section lyzing the official mortality statistics. He introduced F) of the British Association for the Advancement the standard death certificate in 1845 which saw of Science in 1833, and started publication of its almost no change until 1902. Through Farr’s influ- Journal in 1838. These and other early statistical ence the census of 1851 introduced questions on societies in England were greatly concerned with physical disabilities and other medical items which social problems, conducting several surveys to doc- were continued through 1911. ument conditions in England and continuing to push Farr was greatly interested in statistical nosology, for social reforms long after the surveys proved too introducing his first classification of diseases in 1839. expensive to continue. Although they claimed scien- The first International Statistical Congress in 1853 tific objectivity, these statists were superficial in their took up the issue, but Farr’s nosology did not win the use of mathematical methods, paid little attention to support of other European countries. It was not until the validity or accuracy of their data, but were aware 1893 that Jacques Bertillon (1851–1922) proposed a that using numeric data gave credibility to political system that became the International List of Causes of arguments [5]. Death (see International Classification of Diseases A more balanced contribution was made by (ICD)). William Farr (1807–1883) in the area of vital Problems noted in the vital registration system statistics. Starting his career as an unsuccessful in the mid-nineteenth century are still of concern London clinician, he quickly became an acknowl- at the end of the twentieth, namely accuracy of edged authority on vital and health statistics with diagnoses was not reliable, selection of a single a strong interest in medical and social reform. He underlying cause of death (see Cause of Death, founded his own weekly journal, British Annals of Underlying and Multiple) from among several listed Health Statistics, History of 5 conditions, “the temptation of practitioners to obscure the reports were decidedly deficient. The second or falsify the cause of death to save respectable precedent was when the US became the first nation to families embarrassment in certain sorts of death” establish by constitutional mandate a periodic census [5, p. 62]. Henry Wyldbore Rumsey (1809–1876), requiring complete enumeration of the entire popula- one of the chief proponents of sound vital statistics, tion, conducting its first census in 1790. was vigorous in pointing out statistical fallacies At about this time death reports were being used and shortcomings of the existing systems that bear on occasion in port cities to institute quarantine rereading today. measures in efforts to control of , Many of Farr’s statistical methods have had a yellow fever, and typhus. As the Benthamite social lasting impact: defining mortality rates precisely and reform interests reached America and evidence for basing them on person-years at risk, establishing the the harmful effects of poverty, industrialization, and standard expression of mortality as “deaths per thou- unsanitary conditions was sought from vital statis- sand”, using the life table and life expectancy as key tics, the inadequacies of the city and local registration instruments to assess mortality, using the method of systems became evident. In 1826, Walter Channing indirect standardization (see Standardization Meth- (1786–1876) in Boston outlined some of the require- ods) to compare mortality rates of localities (although ments for valid data on causes of death, including the he seems to have made little use of the direct method requisite for medical certification. In 1827 Nathaniel first demonstrated by F.G.P. Neison in his refutation Niles and John D. Russ published the first report on of the proposal of (1800–1890) to public health statistics in a comparison of mortality use average age at death as a criterion for the health data from New York, Philadelphia, Baltimore, and of communities), recommending the establishment Boston. Other analyses soon followed which became of longitudinal cohort studies [9], and proposing a models for the quantitative health reports produced paradigm for the estimation of the economic value by subsequent generations of health officials which of human life at each age and social class. Farr’s led to increasing pressures for improving the qual- association with (1820–1910) ity of the information. In 1842 Massachusetts again also resulted in contributions to the use of statistical achieved a first by establishing a statewide vital regis- information for health policy purposes, particularly tration system. The effort to establish similar systems in respect to the graphic presentation of data (see in other states marked the beginning of an orga- Graphical Displays). nized public health movement and contributed to the professionalization of statisticians in this coun- Development of Vital Statistics in the try [2, 3]. United States Following on the foundation of the Statistical Society of London, statistical societies were started As interest in statistical information burgeoned in in New York and other American cities. Most did Europe in the first third of the nineteenth century, not last very long but the American Statistical a similar phenomenon was occurring on the other Association, founded in Boston in 1839, proved to side of the Atlantic [4]. Although medicine, statis- be enduring. It is significant that 14 of the original 54 tics, and science generally, in the US lagged behind local members were physicians. But it was a publisher that in Europe, America had actually preceded other and bookseller, Lemuel Shattuck (1793–1859), who countries in two important respects. Whereas other was the Society’s key “statist” for health-related areas relied on church-maintained records of chris- issues. He consulted with, among others, Quetelet and tenings and burials as the basis for vital statistics, was a prime mover for the Massachusetts Registration the Massachusetts Bay Colony enacted a in 1639 Act of 1842. He also played a role in the origins of requiring the reporting of every birth and death within national vital statistics by having mortality queries its jurisdiction, thus establishing the collection of included in the 1850 census. vital statistics as a governmental function covering In 1846, the first national medical convention the entire population. The other colonies gradually (which led to the founding of the American Med- adopted similar regulations but for at least the next ical Association) formed two committees relevant two hundred years the quality and completeness of to health statistics: (i) a committee on registration 6 Health Statistics, History of whose report “provided for the convention to for- that would better describe the current health status mally petition every state government to enact effec- of the population (see Quality of Life and Health tive registration legislation and to request state and Status) and shed some light on health-associated local medical societies to take the lead in lobbying behaviors and use of health care services (see Health for such ” [3, p. 201], and (ii) a committee on Services in the US). The National disease nomenclature which adopted a modification Health Survey was the first continuous nationwide of Farr’s classification. Neither of these recommen- survey to gather information from randomly drawn dations was widely adopted for at least 50 years. representative samples (see Probability Sampling) Although there were many attempts, these efforts of the noninstitutionalized population of the coun- were often failures since “the registration movement try to accomplish these aims (see Surveys, Health had moved too far ahead of its base of community and Morbidity). It consists of two distinct surveys: support” [3, p. 204]. At the end of the century, no the National Health Interview Survey (NHIS) and the state had a system as good as those in several Euro- National Health Examination Survey, the latter sub- pean countries. sequently expanded to the National Health and Nutri- During the last two decades of the nineteenth cen- tion Examination Survey (NHANES). The NHIS tury, the initiative for improving vital statistics shifted conducts interviews in about 1000 households each to the Federal government [8]. Under Dr John Shaw week to obtain information on acute illnesses, chronic Billings (1838–1913), who directed vital statistics in conditions, health-related and behaviors, the 1880 and 1890 US censuses, improvements were and use of health services. The NHANES involves made in gathering mortality data. The American detailed standardized medical examinations, includ- Public Health Association joined with the Census ing laboratory studies and special tests such as ECGs Bureau, which was established in 1902, in drafting a and X-rays, and extensive on nutri- model vital statistics law and standard birth and death tion and previous health conditions. The NHANES certificates that each state could adopt. Because of the is a periodic survey and NHANES III (actually the early efforts of Cressy L. Wilbur (1865–1928), Chief sixth cycle of these surveys), being carried out from Statistician for Vital Statistics from 1906 to 1914, 1988 to 1994, examined a sample of about 30 000 the birth- and death-registration areas grew, reaching persons aged 6 months and over. Health interview completeness in 1933, nearly a century after several surveys have now been conducted in many countries European countries. The Division of Vital Statistics of and examination surveys have been used effectively the Bureau of the Census was transferred to the Pub- in several developing countries to assess the popula- lic Health Service in 1946, becoming the National tion’s health. Office of Vital Statistics, with Dr Halbert L. Dunn These surveys would not have been feasible with- (1896–1975) as Director. In 1960, NOVS was com- out the development of survey methodologies which bined with the National Health Survey to become the occurred in the twentieth century. Anders N. Kiaer National Center for Health Statistics with Forrest (1838–1919), the first director of the Norwegian E. Linder (1906–1988) as its first Director. Central Bureau of Statistics, reintroduced the idea of a survey sample in what he called the “rep- resentative method”, in which the sample was to Development of Health Surveys in the be selected purposively as Laplace had suggested a United States century earlier, rather than randomly. (1869–1957) is credited with being the first The establishment of the National Health Survey in statistician to use random sampling (1906). The sem- 1957 marked a milestone in health statistics. With inal breakthrough for sampling methodology came only a few exceptions, previous data relating to health in 1934 when (1894–1981) estab- came from vital statistics or from diagnosed diseases lished the theoretical basis for stratified sampling seen in hospitals or included in various notifiable dis- with unequal inclusion probabilities. He made another eases registers. As public health concerns in the US major contribution when he introduced the use of shifted from the surveillance and control of acute cost functions into theory (1938). communicable diseases to the prevention of chronic In the early 1940s, Morris Hansen (1910–1990) diseases, it was necessary to develop data systems and William Hurwitz (1908–1969) at the Bureau of Health Statistics, History of 7 the Census perfected the methodologies for complex [3] Cassedy, J.H. (1984). American Medicine and Statistical designs that are the basis for Thinking 1800–1860. Harvard University Press, Cam- most modern large-scale surveys. bridge, Mass. [4] Cohen, P.C. (1982). A Calculating People. The Spread of Numeracy in Early America. University of Chicago Conclusion Press, Chicago. [5] Eyler, J.M. (1979). Victorian Social Medicine: The Ideas At the end of the twentieth century, most industrial- and Methods of William Farr. Johns Hopkins University ized countries have effective vital statistics systems Press, Baltimore. [6] Greenwood, M. (1941–1943). Medical statistics from in place and many have established periodic inter- Graunt to Farr. 32, (1941), 101–127; 32 view surveys to assess the health status and needs of (1942), 203–225; 33 (1943), 1–24. Published by Cam- their citizens. Much remains to be done in develop- bridge University Press, Cambridge, 1948, as the Fitz- ing countries to institute health services information patrick Lectures for 1941 and 1943. systems (see Administrative ) that can [7] Hald, A. (1990). A and Statistics guide public policies and programs. As the pub- and Their Applications Before 1750. Wiley, New York. lic health burden continues to shift from infectious [8] Lawrence, P.S. (1976). The health record of the Amer- ican People, in Health in America: 1776–1976.US diseases to problems of an aging population, to con- Department of Health, Education, and Welfare, DHEW cerns about health promotion and disease prevention, Pub. No. (HRA)76–616. and to assuring adequate health care for all citi- [9] Nissel, M. (1987). People Count. A History of the zens, the needs for reliable, relevant, and timely General Register Office. Office of Population Censuses health statistics become ever greater. Fortunately, the and Surveys, HMSO, London. methodologies developed over several centuries and [10] Rabinovitch, N.L. (1973). Probability and Statistical the data systems that have been established can, if Inference in Ancient and Medieval Jewish Literature. University of Toronto Press, Toronto. appropriate resources are provided, meet these needs. [11] Stigler, S.M. (1968). The . The Mea- surement of Uncertainty Before 1900. Harvard Univer- References sity Press, Cambridge, Mass. [12] Westergaard, H. (1932). Contributions to the History of [1] Bollet, A.J. (1973). Pierre Louis: the numerical method Statistics. King, London. and the foundation of quantitative medicine, American Journal of Medical Science 266, 92–101. MANNING FEINLEIB [2] Cassedy, J.H. (1969). Demography in Early America. Beginning of the Statistical Mind. 1600–1800.Harvard University Press, Cambridge, Mass.