How statistical reasoning entered medicine
Statistical reasoning in medicine developed through comparisons of groups, probability models and methods for controlled experiments. Its history also includes a persistent debate about how population evidence should inform care for an individual patient.
Ancient comparisons and environmental explanations
The Hippocratic treatise On Airs, Waters, and Places, dating to about 400 BCE, examined geographic, environmental and seasonal influences on disease without using statistical methods. Although its disease theory rested on humoral imbalance, its explanations were naturalistic rather than appeals to deities and extended beyond the individual patient.
The Book of Daniel supplies a literary forerunner of a comparative dietary experiment: Daniel and other Jewish children ate legumes and drank water for ten days, were judged healthier than those eating the king's food and were allowed to continue. This was a comparison without the statistical tests or intervals of a modern trial. In modern trial terminology, that account describes an interventional, open-label, active-controlled, parallel-group comparison.
Inoculation and controlled comparison
Eighteenth-century smallpox inoculation deliberately exposed recipients to smallpox material in the hope of inducing a mild infection and subsequent immunity, at the risk of severe or fatal disease. Opponents appealed to avoiding harm, while supporters advanced arguments recognisable as benefit–risk comparisons.
In an anonymous pamphlet of 1722, John Arbuthnot estimated mortality from natural smallpox at one in ten using London's Bills of Mortality, then assumed without evidence a mortality of one in a hundred after inoculation. From that assumed tenfold difference he argued that universal inoculation could save London at least 1,500 lives annually and provide a prudent choice for an individual.
In 1760 Daniel Bernoulli used probability mathematics to compare inoculated and non-inoculated life expectancy and estimate benefits by age. Jean d'Alembert challenged whether the model represented human choice: accepting a risk of death immediately might not be equivalent to gaining years late in life.
James Lind's scurvy comparison took a different approach, deliberately assigning twelve sailors to six groups of two with a common diet but different supplements. The citrus group had one complete and one near recovery, exceeding improvement in the other groups. Lind's documentation in A Treatise of the Scurvy helped establish his reputation as a founder of the controlled clinical trial.
The numerical method and the individual patient
Pierre-Charles-Alexandre Louis promoted the numerical method in medicine during the 1830s, using hospital observations to question bloodletting in his 1835 Recherches sur les effets de la saignée. He argued that numerical comparisons were clearer and more scientific than descriptions such as “more or less” or “rarely or frequently”, and expected them to displace reliance on physicians' intuitive medical judgement.
Critics objected that a physician treated an individual rather than a statistical construct. Benigno Risueño d'Amador compared medical probabilities to maritime insurance: knowing that one hundred of a thousand ships might be lost did not identify which ships would perish, and he considered that limitation fatal to medical usefulness. François Double compared treatment based on a population average to fitting everyone with shoes made to an imaginary average foot. These objections framed a conflict between advancing knowledge through aggregate observations and treating the person needing care.
Jules Gavarret brought probability mathematics to the debate in his 1840 Principes généraux de statistique médicale. Trained as an engineer before becoming a physician, he recognised that averages from repeated samples could vary within “limits of oscillation”. For Louis's 140 typhoid cases, with 52 deaths and 88 recoveries, the observed mortality was about 37%; Gavarret calculated a range of roughly 26–49%, anticipating interval estimation.
Gavarret's approach attracted discussion but no sustained school of followers in nineteenth-century medicine. Statistical evidence remained contested: Joseph Lister used studies to support antiseptic surgery, while critics invoked competing studies for their own theories of safer surgery.
Florence Nightingale used polar-area diagrams, known as Coxcombs, to communicate findings about military-hospital sanitary conditions to Queen Victoria; her statistical work contributed to British health reforms. She became the first female member of the Royal Statistical Society and later joined the American Statistical Association.
Statistical institutions and medical education
Karl Pearson's Biometric School and Laboratory at University College London helped standardise and mathematise the study of biological variation in the late nineteenth and early twentieth centuries. His work included curve fitting, goodness-of-fit tests and correlation, initially motivated by statistical implications of Darwinian natural selection. He also advocated medical applications through contributions to medical journals.
Outside medicine, William Sealy Gosset, a chemist at Guinness in Dublin writing as “Student”, developed the t-test in work on consistent brewing.
Major Greenwood studied under Pearson in 1904–1905 while completing his medical qualification and became a full-time medical statistician at the Lister Institute in 1910. His 1912–1913 Lancet exchange with Almroth Wright began with a blood test used in pneumococcal-vaccine work among South African miners and broadened into debate over credible scientific evidence. In 1927 Greenwood became the first professor of epidemiology and vital statistics at the London School of Hygiene and Tropical Medicine and was elected to the Royal Society the following year.
Austin Bradford Hill trained with Greenwood and attended Pearson's lectures after tuberculosis during the First World War interrupted his intended medical career and he earned an economics degree by correspondence. He became a reader at the London School of Hygiene and Tropical Medicine in 1933 and succeeded Greenwood as head of its Statistics and Epidemiology Unit in 1945. His 1937 Lancet articles became Principles of Medical Statistics, subsequently published in multiple editions and translations.
Randomisation and causal reasoning
In 1946 Hill designed a streptomycin trial in tuberculosis using random sampling numbers to allocate patients to bed rest or streptomycin. In 1965 he articulated the Bradford Hill criteria for considering whether an observed association might suggest causation, including associations between smoking and cancer.
The historian of medicine J. Rosser Matthews interprets this history as continuity in population-based reasoning alongside increasingly sophisticated methods. In his interpretation, the tension between group evidence and individual care persisted despite therapeutic advances and helps explain medicine's reliance on statistical specialists and professional medical writers.