Body Mass Index is commonly used as an indicator of obesity, and thus as a sign that a person might be a risk for various health problems (including worse health effects from contracting COVID-19).  But where did the measure come from? 
The definition is straightforward. As the Centers for Disease Control notes: \”Body Mass Index (BMI) is a person’s weight in kilograms divided by the square of height in meters.\” For adults (of any age or gender), the usual guideline is that below 18.5 is \”underweight\” 18.5-24.9 is \”normal or healthy weight,\” 25.0-29.9 is \”overweight,\” and 30 or above is \”obese.\” For an adult is who is 5\’ 9\” (or 1.8 meters), the range for a normal or healthy weight would be 125-168 pounds (or 57 to 76 kilograms). 
The original formula dates back to a Belgian statistician named Adolphe Quetelet (1796–1874). Garabed Eknoyan provides an overview of his story in \”Adolphe Quetelet (1796–1874)—the average man and indices of obesity\” (Nephrology Dialysis Transplantation, January 2008, 23: 1,  pp. 47-51). 

Quetelet was quite a guy. Eknoyan reports that while still a teenager: \”But it was his love of the humanities that dominated his early years. He published poetry, exhibited his paintings, studied sculpture, co-authored the libretto of an opera and translated Byron and Schiller into French.\” At age 23, he was the first recipient of a doctorate in science from the newly founded University of Gent. He became fascinated with probability theory after spending time in Paris with  Joseph Fourier (1768–1830), Simeon Poisson (1781–1840) and Pierre Laplace (1749– 1827). He became interested in seeking out probability distributions of the human form, including the creation of the first height-and-weight tables. Eknoyan continues: 

His subsequent conceptual evolution in the study of man evolved from the study of averages (physical characteristics), to rates (birth, marriage, growth) and ultimately distributions (around an average, over time, between regions and countries) [12]. The latter was the basis of one of his contributions to statistics; the demonstration that the normal Gaussian distribution, typical throughout nature, applied equally to physical attributes of humans, including body parts, derived from large-scale population studies. … 

In developing his index, Quetelet had no interest in obesity. His concern was defining the characteristics of ‘normal man’ and fitting the distribution around the norm. Much like Dublin a century later, he encountered difficulty in fitting the weight to height relationship into a Gaussian curve and began his quest for a solution. In 1831–1832, he conducted what has been considered the first cross-sectional study of newborns and children based on height and weight, and extended it to the study of adults. …

[I]n an 1835 book, A Treatise on Man and the development of his aptitudes, Quetelet wrote: ‘If man increased equally in all dimensions, his weight at different ages would be as the cube of his height. Now, this is not what we really observe. The increase of weight is slower, except during the first year after birth; then the proportion we have just pointed out is pretty regularly observed. But after this period, and until near the age of puberty, weight increases nearly as the square of the height. The development of weight again becomes very rapid at puberty, and almost stops after the twenty-fifth year.\’ 

Quetelet was famous in his own time, and a major influence on other pioneer statisticians like Francis Galton. A statue of him stands on one corner of the  Places des Palais in Brussels, at the entrance to the
Palais des Academies. A century after his death, Belgium put his picture on a postage stamp. But although Quetelet originated the formula, he did not discuss or draw conclusions about obesity. 

However, the Quetelet index was not re-baptized as the Body Mass Index until 1971, in research by a physiologist named Ancel Keys (1904-2004). Nicolas Rasmussen tells this story in \”Downsizing obesity: On Ancel Keys, the origins of BMI, and the neglect of excess weight as a health hazard in the United States from the 1950s to 1970s\” (Journal of the History of the Behavioral Sciences, Autumn 2019, pp. 299-318). Rasmussen also tells the story of efforts by life insurance companies in the early 20th century to pool their data and try to find out if causes of death like heart disease, cancer, and stroke could be predicted based on individual characteristics and behaviors.  Rasmussen writes: 
Big insurance companies began pooling data in quasiprospective collaborative studies around the turn of the century, in which length of life was correlated to a range of risk factors recorded on initial health examinations (Bouk, 2015; Czerniawski, 2007). These intercompany studies were massive, far larger than anything public sector epidemiologists could do at the time. In the landmark Medico‐Actuarial Mortality Investigation (MAMI) of the early teens, over 440,000 insured individuals were examined (representing equal numbers of men and women) for a span of 10–25 years up to 1909—millions of life‐years of observation (Association of Life Insurance Medical Directors & Actuarial Society of America, 1912). MAMI was followed by the similarly designed and executed Medical Impairment Study, which included data on 667,000 men issued policies since 1909, followed through 1928 (Actuarial Society of America & Association of Life Insurance Medical Directors, 1931). Both studies mainly looked at overall mortality rates associated with physical “impairments” and occupations, rarely attempting to identify predictors of particular causes of death (prudently, given the variability in how doctors completed death certificates). Insurance actuaries had tried a number of measures to gauge obesity such as girth for spine length, but the statisticians found that weight for height had the best predictive power for longevity (Czerniawski, 2007; Marks, 1956). And the association between weight and mortality was strong and consistent, changing very little between the generations represented by the two big studies (for people older than 25). In the Medical Impairment Study, for example, men categorized as 25% or more above average weight for their height suffered 30–40% higher mortality rates (depending on age). Similar findings were reported for women, although the mortality penalties of high weight were not quite as severe (Marks, 1956).
By 1900, insurance firms were already screening out applicants well above or below the average weight for their height and, unsurprisingly, after the big intercompany studies, the firms revised their rates and standard height‐weight tables to reflect greater mortality penalties for overweight (and smaller mortality penalties for underweight, as tuberculosis was in retreat). Tables of a normal or healthy weight for each height category were widely distributed by insurance companies and ubiquitous in doctors’ offices during the early 20th century (Weigley, 1984). Thus, the insurance industry informed the understanding of proper body weight among doctors and patients alike, during the period when it first became a matter of popular concern (evidenced, for instance, by rapid diffusion of weighing scales; Jutel, 2001). …
Life insurance firms stiffened their price discrimination; that is, the overweight paid more for their “substandard” policies, if they could get them at all (Czerniawski, 2007; Weigley, 1984). Later, by 1930s, it was something like a universally accepted medical fact that obesity contributed to early death, especially from heart disease. …
The National Heart Institute was created in 1948 to promote research in this area. But perhaps surprisingly, Ancel Keys–who would originate the label for Body Mass Index–was an opponent of the conventional wisdom about the linkage from weight to health. Instead, he argued that concerns about being overweight were often just moralistic lectures (what some today would call \”body-shaming\”). 
As Rasmussen explains it,  Keys agreed that obesity was unhealthy. However, he argued that measurements of excess weight-for-height were not a reliable measure of obesity. \”Based on the observation that, because muscle is denser than fat, extraordinarily lean and  muscular men like varsity football players (and apparently, himself) registered as overweight on standard tables despite being unusually fit, he launched around 1950 into a campaign to replace relative weight measures of obesity with a measure of body fatness or adiposity.\” In addition, Keys argued that fat in one\’s diet was the key predictor of negative health consequences like coronary heart disease: \”Thus, in the 1950s Keys took a strong position arguing that dietary fat intake, not caloric intake or its weight gain consequence, was the cause of high serum cholesterol and therefore a major driver of coronary disease. So he sought to discount weight as a heart disease predictor.\”
Keys thus explored other methods of measuring body fatness. For example, one approach was to submerge someone in water to calculate their volume, then divide by weight to get their density, and then infer body fat from this density. However, this approach was tricky. You had to take into account factors like residual air in the lungs. The extrapolation from density to fat content was at that time based on data from guinea pig dissection experiments. And it was hard to imagine a really large-scale study (or a life insurance policy) that involved dunking all the subjects. 
Another possible approach involves \”skinfold measures,\” which basically  involved using certain calipers and pressures of pinching at specific places around the body. After experimenting with many pinching practices, the concensus seems to be that \”the best sites for measuring skinfolds were the
back of the upper arm when extended 90° and just below the scapula, on the back.\”

Keys led a famous \”Seven Countries\” study that looked at how obesity might predict coronary heart disease, and when the study was published in 1972, it included three measure of obesity: skinfold measures, weight-for-height, and what Rasmussen calls \”a heretofore obscure measure—BMI (weight in kilograms divided by height in meters squared, first proposed a century earlier by Quetelet).\” The statistics suggested that the skinfold measures offered no difference in predictive power over the weight measures: \”So at this point, after more than 20 years of conspicuous efforts to showcase skinfold and the body fatness it measured as a more rigorously scientific and predictively effective index of obesity than relative weight, Keys just dropped the topic of skinfold and adiposity and embraced BMI …\” However, in his study, BMI had only a very mixed record in predicting coronary heart disease. 

Simple measures, like the Body Mass Index, are going to be imperfect. There are longstanding concerns that dividing by height isn\’t quite right, and can lead to short people seeming thinner and tall people seeming fatter. There are other methods. Skinfold techniques are still used. There have been studies that suggest looking at waist-for-height measures, either alone or perhaps together with BMI. 
There are also methods that seek to measure body fat more directly. The approach of submerging someone in water, calculating density, and inferring body fat now rejoices in the name of \”air displacement plethysmography.\” There are also approaches which involve shining infrared light (\”near-infrared interactance\”) or different levels of photons (\”dual energy X-ray absorptiometry\”) through the body, and then calculating body fat based on the idea that fatty tissues absorb more infrared light or attenuate photons differently than lean muscle.
For studies of large populations, Body Mass Index is a useful measure in part because height and weight are relatively easy to collect. There are also historical records of height-and-weight, which were often kept for large population groups like soldiers being drafted into a nation\’s armed forces. Also, the research since Keys has established strong linkages that groups with higher rates of obesity as measured by BMI do on average have a higher rate of adverse health outcomes. But individuals can and do vary considerably, the specific numbers and labels that the Centers for Disease Control place on BMI should be viewed as useful guidelines for groups, not as a firm judgement applying to every person. 

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