The (Lack of) Science behind the Body Mass Index (BMI)

by
Theo Pavlidis (©2007)

(Latest editing 10/20/09)

If you have ever had a medical checkup, you have probably heard about the Body Mass Index (BMI) that it supposed to have an optimal value around 25. Probably you were told to take your weight in pounds, divide it by the square of your height in inches and multiply the result by 703 to find your BMI. If you are over 40 years old your BMI was most likely more than 25 and your doctor told you to lose weight. The multiplication by the mysterious number 703 tends to lend the measure an aura of scientific authority. However if were in Europe you need not worry about that mysterious number. To find your BMI you take your weight in kilograms and divide it by the square of your height in meters. The 703 is needed for converting pounds to kilograms and inches to meters. (You can tell right away the European origin of the measure.)

Of course you can find your ideal weight in kilograms from the formula below, provided the height is expressed in meters. (By the way, this is the equation of a parabola.)

Ideal Weight = 25 * height2
(1)

Let us now look at the results for people 1.60m (5 feet 3 inches), 1.70m (5 feet 7 inches), 1.80m (5 feet 11 inches), 1.90m (6 feet 2 inches) . The weights (in kilograms) we get from the formulas are respectively: 64, 72, 81, and 90. Do you notice that the weight comes to be close to the number expressed by the decimals in your height? When I was growing up in Greece doctors were saying that your ideal weight should be in kilograms equal to the number expressed by the decimals in your height. The mathematical formula for that is a linear equation.

Ideal Weight = 100 * (height - 1)
(2)

The straight line of the linear equation is a tangent to the parabola of the quadratic equation and the two meet for height equal to 2 meters and weight equal to 100 kgs. However they are very close over a large area. For height 1.80m the difference of the equations is only 1kg and for height 1.70m is 2.25kg. Click to see a Diagram showing the relationship between the two with Equ. (1) in black and Equ. (2) in green.

The agreement between the BMI formula (Equ. (1)) and a gross empirical relationship (Equ. (2)) made me suspicious and I started investigating. According to the Wikipedia article the BMI formula was derived by a Belgian "between 1830 and 1850". That seemed strange and I did some research on the internet and indeed the inventor of BMI is the Belgian (Flemish) mathematician Adolphe Quetelet (1796-1874). I also found several biographies of his on the internet (see list at the end of this article). Interestingly, the BMI formula did not become popular amongst physicians until well after 1970.

What is the scientific basis for the formula? We have to go back to Quatelet and read that "in 1846 he published a book on probability and social science that demonstrated as diverse a collection of human measurements as the heights of French conscripts and the chest circumferences of Scottish soldiers could be taken as approximately normally distributed." (sites 2 and 3 listed below). Therefore the most likely explanation is that both the BMI and the linear expression of Equ. (2) were derived as a gross approximation to a set of observed weights and heights of recruits in a Western European army. An additional tiny piece of evidence for such an origin is the fact that my own weight when I was conscripted into the Greek Army was that given by Eqs (1) or (2).

Next time your doctor brings up the BMI measure ask him/her what were the population data that the index was derived from. I find very disturbing to use a statistical measure derived over 150 years ago, most likely, from a group of young men to determine the proper weight for men and women of any age. There have been several publication critical of the BMI (see below) and if your doctor follows the literature, she/he may not mention BMI at all.

There is another disturbing fact in Equ. (1). Why is the weight expressed as the square of the height? Elementary solid geometry tells us that the volume of an object is equal to the third power of its linear dimensions, so the weight should be proportional of the cube of the height. However strength is proportional to the cross section of your arms and legs, so it is proportional to the square of the height. As a result, the ratio of strength over volume is declining function of height and that is why insects are far more mobile than dogs and dogs are more mobile than humans. Because for any given person height is determined by genetics and childhood nutrition, it must be taken as a given. Then the formula for proper weight must contain both a cubic term (to account for the volume) and a quadratic term (to account for the need for strength). I have not seen any such formula, but using the BMI expression because we do not have an accurate expression does not seem to be the smart thing to do.

There have been articles pointing out that BMI gives too low weights for tall people but the public is not aware of them. Another flaw of the formula (also recognized in the literature) is that it does not distinguish between weight due to muscle and weight due to fat. Again that knowledge is not widely available. If you have the patience to read the Wikipedia article to the end you will find a good critique of the BMI in the section "Limitations and shortcomings" where there are also citations to the literature.

Yes, you must be concerned about gaining excess weight, but what is excess weight is not what the formula tells you. Your best bet is to find a health practitioner who takes a realistic view of weight and discuss the problem with that person.

Biographical Information about Adolphe Quetelet

1. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Quetelet.html
2. http://www.mrs.umn.edu/~sungurea/introstat/history/w98/Quetelet.html
3. http://www.famousbelgians.net/quetelet.htm

Scientific Critiques of BMI

Not surprisingly, there have been several scientific studies that point out the weaknesses of the BMI. Below are links or references to some of them. Such studies are usually epidemiological, i.e. they look at mortality or illness of people and see how well that correlated with the BMI.

  1. London School of Hygiene & Tropical Medicine (2006, August 8). Waist-hip Ratio Should Replace Body Mass Index As Indicator Of Mortality Risk In Older People. ScienceDaily. Retrieved November 3, 2007, from http://www.sciencedaily.com­ /releases/2006/08/060808091511.htm
  2. Archives of Internal Medicine Article (Aug. 2008) that includes the conclusion: "Among US adults, there is a high prevalence of clustering of cardiometabolic abnormalities among normal-weight individuals and a high prevalence of overweight and obese individuals who are metabolically healthy" Since "overweight and obese" were defined using the BMI the conclusion is not at all surprising. This study made a big splash in popular the press and I hope that it will put an end to the BMI use.

Several studies led by Dr. Katherine M. Flegal

  1. Abstract of a talk on the "Epidemiology of oveweight and obesity" that contains the following statement: " ... the health consequences of the increases in obesity have not been well delineated and are not well understood."
  2. Methodological Problems in estimating deaths from obesity. The link points to slides from a talk given at the Institute of Medicine. The talk is highly technical, but even if you have no training in mathematical statistics you can see that estimating deaths from a particular cause is no simple matter. (See also the work of Ioannidis.)
  3. News Release Discussion of April 20, 2005 about a study led by Dr. Flegal that demostrated that obesity is only the seventh cause of preventable death rather than second as previously thought.
  4. AP Report of Nov. 11, 2007 reporting on a study by Dr. Flegal. It includes the statement "Specifically, obesity raised the risk of death from heart disease, diabetes and kidney disease, and several cancers previously linked with excess weight, including breast, colon and pancreatic cancer. But being merely overweight — having a BMI between 25 and 30 — did not increase the risk of dying from heart disease or any kind of cancer. Also surprising was that overweight people were up to about 40 percent less likely than normal-weight people to die from several other causes including emphysema, pneumonia, injuries and various infections. The age group that seemed to benefit most from a little extra padding were people aged 25 to 59; older overweight people had reduced risks for these diseases, too." (Emphasis by T.P.) Of course, these results are not surprising at all to those who understand that having (for a given height) the average weight of a French army recruit around 1850 need not be a predictor of health.

Some Publications Related to the Use of BMI in Children

The following citations were provided to me by my daughter Karen Pavlidis, PhD. She also directed my attention to several issues related to false alarms about an "obesity epidemic."

Unfortunately, the journals are accessible through the web only to authorized users. You have to look for them through a University Library. While all four papers use the BMI, they also point out several problems with it.

  1. I. E. Buchan et al "Body mass index has risen more steeply in tall than in short 3-year olds", International Journal of Obesity, 31 (2007), 23-29.
  2. S. E. Moore et al "Ethnic Differences in the relationship between fasting leptin and BMI in children", International Journal of Obesity, 28 (2004), 17-21.
  3. S. K. Bhargava et al "Relation of Serial Changes in Childhood Body-Mass Index to Impaired Glucose Tolerance in Young Adulthood", New England Journal of Medicine, 350 (2004), 865-75.
  4. M. F. Franklin "Comparison of weight and height relations in boys from 4 countries", American Journal of Clinical Nutrition, 70 (1999) 157S-162S,

Collections from the Web

There are several postings that provide critiques to the BMI index. Some of them are listed below in no particular order.

  1. BMI: A critique of its use in human biology and the health professions by William D. Ross and Ottó G. Eiben, 2002. Quote from the abstract: "We contend that the common BMI scale for men and women to ascribe a health weight range is a mathematical artifact."
  2. A critique of the expression of paediatric body composition data by J. C. K. Wells, 2001. Quote from the abstract: "Traditional measurements such as body mass index and skinfold thickness do not measure fat in accurate quantitative terms."
  3. The association of body mass index with health outcomes: causal, inconsistent, or confounded? by Eyal Shahar, Am J Epidemiol. 2009 Oct 15;170(8):957-8.

First Posted: Sept. 23, 2007
Latest version: November 8, 2007
Collections from the Web updated: October 20, 2009.

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