Calculating body mass index (BMI)

Summary: Body Mass Index is a statistically useful index of a person’s relative weight.

Body mass index (BMI) is an index of the relative weight of a person. In other words, it is an estimate of a person’s weight, adjusted for height. The formula for calculating BMI is

Weight in kilograms/(Height in Meters)2.

The equation implies that, holding other factors constant, weight is proportional to height squared, at each level of height. This equation is counterintuitive because of the common assumption that to calculate mass or volume, a cubic function is necessary. In fact, dividing mass by height cubed was historically a popular method, called the “Ponderal index.” However, Adolphe Quetelet (1796–1874) observed that, for an “average man,” a squared function was a better fit to the data. With increasing age, humans’ height increases at a faster rate than width. Taller adults tend to be slimmer—waistlines do not usually grow in proportion to increasing height. Quetelet observed that people do not expand equally in all three dimensions. If they did, then the Ponderal index would still be valid. In reality, he noted that, “weight increases nearly as the square of the height”—particularly between puberty and age 25. Before puberty, the Ponderal index does increase more proportionally to width. Quetelet stressed that there was considerable variance in body shape and size, which are determined by biological, psychological, and social factors. For example, he noted that “young persons who apply themselves to study, and persons in the affluent classes generally, are taller than others.”

The Quetelet Index

The popularity of the Quetelet index increased following World War II, when epidemiological evidence began to accumulate that excess weight was a risk factor for premature mortality and morbidity. Historically, and in several cultures today, excess weight (corpulence) was considered healthy and desirable. Given this new evidence, actuaries needed a quick and reliable way to predict who might be most at risk, so that insurance premiums could be loaded against those with excess weight. They creating height-weight charts, based on Quetelet’s data, which provided the typical weights expected at various levels of height for the average person—assuming that they were age 25. The index was later termed “body mass index.”

Insurance companies, clinicians, and researchers began using BMI as a proxy variable for measuring excess weight at all ages, not simply as an index of relative weight at age 25, as originally intended. The popularity of BMI remains today. For example, the World Health Organization uses BMI in its definition of obesity, where “overweight” is defined as BMI equal to or greater than 25, and obesity is defined as a BMI more than 30. There are no agreed BMI cutoffs for childhood obesity in the same way that there are for adults. The categorization of continuous data (for example, overweight, obese) is controversial because it results in a loss of information. BMI is indeed a risk factor for chronic diseases, despite its usage deviating from the original intended purpose. In clinical settings, BMI is usually supplemented with other information regarding disease risk, such as blood pressure or lifestyle factors including cigarette smoking. Additionally, it may be necessary to take into account whether the person has an ectomorphic, mesomorphic, or endomorphic body type.

The Quetelet index was first formally evaluated by epidemiologists working on data from a large cohort study, called the Framingham Heart Study. They noticed that Quetelet’s index was being widely used as an indicator of excess weight, not simply weight adjusted for height as it was originally intended. The epidemiologists wanted to evaluate the validity of this assumption, by comparing different methods for measuring relative weight against three criteria:

• 1. The proxy should not correlate with height.
• 2. The proxy should correlate highly with skinfold thickness measurements, since these are valid proxies for the thickness of the subcutaneous fat layers in different parts of the body, in turn.
• 3. The proxy should be easy to calculate.

After analyzing the data, they concluded that Quetelet’s index was indeed the best available measure, and renamed it the Body Mass Index. However, it should be noted that correlations between BMI and skinfold thickness measurements varied considerably, and the highest was 0.8. The researchers noted that if height and weight are the only data available, excess body fat is unlikely to be measured in a satisfactory way. The lower a correlation between a proxy variable and the variable it is intended to measure, the less well that proxy will correlate with health outcomes. It should also be noted that the third criterion (the ease of calculation) is not statistical—the validity of an index or test should be based on how well it performs against a gold standard, not simply because it is easy to use.

Criticisms

Researchers have since argued that valid proxies for excess body fat should take into account its distribution in the body. Excess fat in the abdominal region (visceral fat) is a risk factor for metabolic diseases, regardless of total fat volume in the body. Waist circumference correlates highly with visceral fat, leading some researchers to suggest that waist circumference is a better proxy for excess weight than BMI. Similar alternatives include the ratio of waist circumference to hip circumference (waist-to-hip ratio). Because waist circumference is associated with increased morbidity and mortality risk, holding BMI constant, it provides additional information that is not captured by BMI. Both are considered independent risk factors, such that it may be necessary to measure both BMI and waist circumference. In fact, a consensus statement from Shaping America’s Health concluded that waist circumference predicted cardiometabolic outcomes, and should therefore be measured in clinical settings as a matter of routine. However, waist circumference is difficult to measure reliably. BMI remains a useful index for many purposes.

Bibliography

Eknoyan, Garabed. “Adolphe Quetelet (1796–1874): The Average Man and Indices of Obesity.” Nephrology Dialysis Transplantation 23, no. 1 (2008).

Ferrera, Linda A. Body Mass Index and Health. Hauppauge, NY: Nova Biomedical Books, 2005.

Friedlander, Joel. Body Types. San Rafael, CA: Marin Bookworks, 2010.

Keys, A., F. Fidanza, M. J. Karvonen, N. Kimura, and H. Taylor. “Indices of Relative Weight and Obesity.” Journal of Chronic Diseases 25 (July 1972).

National Institutes of Health. “Calculate Your Body Mass Index.” http://www.nhlbisupport.com/bmi/.

Quetelet, Adolphe. A Treatise on Man and the Development of His Faculties. Edinburgh, UK: W. and R. Chambers, 1842.