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_65559686_cupcakes304The Doctor is In.

We—he-heee-ll. What do we have here, mes amis? The BBC’s magazine website has an article asking “BMI: Does the Body Mass Index need fixing?” And answering, yes, it does, and one Nick Trefethen, Professor of Numerical Analysis at Oxford University is suggesting how that might be done. Here it is.

“Pourquoi?” you ask. (You are clearly, feeling somewhat French today. Or maybe that’s just me, so I’ll translate: “Huh?”) What’s this about BMI and it needing fixing?

BMI—that’s Body Mass Index to you good folks—is the measure that has been used since the 1960s as the basis for diagnosing obesity. It is a formula where you take your weight and divide it by your height squared. That is:

BMI = weight / height2

(It’s best if your weight is measured in kilograms and your height in meters because then the values come out at somewhere between about 15ish and 35ish—nice, easy to work with numbers. But if your height and weight are in different units—pounds and feet, say—there are scaling factors that can be used to make the numbers come out nicely. Mathematically speaking, it all works out the same.) You can find any one of a gazillion BMI calculators on the web that will take your height and weight in any units and spit out your BMI and tell you what it means. Here’s one.

BMI 18 to 25? Fine. No problemo. Looking good. BMI 25 to 30? On the plumpish side—technically “overweight”. Above that, you’re in serious “obese” territory. Get thee to a doctor. No, not this one—an MD.

Now, BMI is used as the diagnostic measure for obesity for one very important reason: it correlates with body fat content, and the amount of body fat one has is what medical thinking currently believes is the dangerous thing about being fat.  Note that it doesn’t measure body fat content – it just correlates, meaning if you have a high body fat content, you’re likely to have a high BMI, but the relationship is not exact.

It would be much better to actually measure body fat content and base the diagnosis of obesity on that, but it so happens that measuring body fat content is rather difficult. Rather difficult meaning, in this case, you have to be dead to get an accurate read. That sort of difficult. If you want to know your body fat content and still be alive, you’ll have to settle for an approximation. Which is what BMI is. (There are other ways of getting an approximate measure of body fat content—hydrodensitometry, DEXA, liquid scintillation detection—but if I just threw out there a whole lot of techno-jargon it’d just be showing off. 😉

BMI has a rather august history. Its first mentioned use was by a Belgian statistician, Adolphe Quetelet, in 1836. Adolphe—we’re on first name terms in this blog—was interested in applying mathematics to the study of people—births and deaths, and growth and size and so on. He experimented with using ratios of weight and height as indicators of a person’s heft or bulk and studied how these changed over time. While mostly Adolphe just divided weight by height—a much easier calculation than using powers—he did note that:

[d]’après des recherches nombreuses que j’ai faites sur la corrélation entre les tailles et les poids des homes adults, j’ai cru pouvoir conclure que les poids sont simplement comme les carrés des hauteurs[,]

Following numerous experiments that I have done on the correlation between adults’ height and weight, I have been able to conclude that weight varies simply with the square of height.

(Quetelet, Adolphe. Sur L’homme Et Le Développement De Ses Facultés, Ou Essai De Physique Sociale. Paris: Bachelier, 1835, p.97.)

And for that reason, the ratio of weight divided by the square of the height was given the name Quetelet’s Index. In 1972, the American physiologist Ancel Keys renamed (and depersonalized and denationalized) the index, calling it Body Mass Index (BMI), but every so often you do come across the occasional current reference to Quetelet’s Index, especially if the author is European and knows their history. And perhaps doesn’t like Americans.

BMI is, of course, not the only way you can combine height and weight in an index. You can, as Quetelet usually did, just divide weight by height. You can use weight divided by the cube of the height—called Rohrer’s Index. You can use height divided by the cube root of the weight—called Livi’s Index (which is just the inverse cube root of the Rohrer Index. Naturellement.)

So why, out of these various indices is BMI the one used most often today? It’s not the easiest one to calculate (weight/height is easier). It’s not the one where the dimensions of the top number in the fraction (the numerator) match the dimensions of the bottom number (the denominator). (Mathematicians love that in an index – makes it mathematically prettier. By that count, Livi or Roher’s indexes are prettiest.) So why BMI?

BMI correlates with body fat content and it does it the the best of all the indices. And that’s why it has become the measure for obesity.

Now here’s where the history of BMI becomes very important so that one doesn’t spend god knows how long and how many research dollars like Professor Nick Trefethen, Professor of Numerical Analysis at Oxford University, has done in announcing he has found a better way of measuring obesity than BMI when—sorry Nick—it’s been done before.

Question: Why do you want a better measure than BMI?

Answer: BMI only correlates with body fat content, it doesn’t measure it. So sometimes some funny things happen. People who are very highly muscled also have a very high BMI. That’s because muscle is very dense—it’s heavy, but it doesn’t take up a whole lot of space for that amount of weight. This fact—that BMI would be high for very muscly people as well as very fat people—was known in…wait for it…1942. (That study was done by a doctor working at the US Naval Yard where he tested All-American football players. They were chunky. Cubic. And had high BMI.) Clearly, the fact that BMI can’t pick out the difference between an All-American Football player and genuine butterball is something of a problem if you just want to mechanically measure heaps of people, like for an epidemiological study. Perhaps that so-called obesity epidemic is in fact an epidemic of weight-lifting??!! We’re not getting fatter, we’re getting more cut? Oh, I wish.

Question: Is Professor Nick right in saying you can find a better index than BMI for approximating body fat content?

Answer: Yes, you can, but only if you go with non-whole numbers in the exponents—the powers. Which is what Professor Nick has done. He says that 2.5 works well. (That is weight divided by height to the power 2.5). He may want to have a chat with R.J. Benn from the Medical Research Council who thinks 1.6 or 1.8 might do better. Which he said in 1971.

Sigh. I really am too young and lovely to be thinking that this is all old hat. But…meh.

So, OK, we can find an index that does better than BMI in approximating body fat content. And with computers nowadays, what’s a decimal or two in the exponent? But here’s the big question: should we junk the BMI for another formula that might approximate body fat content better?

Answer: Not much point, really. All the ways we have of measuring body fat content on a living person are approximations. And it is difficult to get consensus on how to measure and diagnose a condition—BMI has achieved this somewhat. Most obesity researchers use BMI to measure obesity. So current research into obesity can at least built on itself, rather than perpetually fumbling about with the question of “how do we measure this?”

And here’s the really critical thing: there is new research being done right now into what makes obesity harmful. The indications are that total body fat content is too gross a measure (ha ha – sorry for the pun) to capture the dangers of being fat. Rather, there are early suggestions that the location of the fat and how it is affecting the body’s metabolism (which are connected) determine how dangerous the fat is. It is more likely that in the future, obesity will be diagnosed with a blood test, looking for markers in the blood connected to the metabolic action of fat. Whether you are diagnosed as obese or not will not depend on your weight. It will depend on a chemical in your blood. It would therefore, be silly to junk BMI and the consensus for using it right now in favour of a measure which is only marginally better, when there is every promise that a measure that is radically better will come along in the next ten or so years.

Interesting things on the horizon, that’s for sure. Now, till then, put down that cookie, turn off the computer (yes, I know you’re on the computer. Right now in fact. Don’t be fibbing to me. Dr Then knows all) and

Stay well,

Doctor Then.

Interested? Want more?

For seminal investigations of the different height-weight indices, see

  • Billewicz, W.Z., W.F.F. Kemsley, and A.M. Thomson. “Indices of Adiposity.” British Journal of Preventative Social Medicine 16 (1962): 183-28.
  • Khosla, T., and C.R. Lowe. “Indices of Obesity Derived from Body Weight and Height.” British Journal of Preventative Social Medicine 21 (1967): 122-28.
  • Benn, R.T. “Some Mathematical Properties of Weight-for-Height Indices Used as Measures of Adiposity.” British Journal of Preventative Social Medicine 25 (1971): 42-50.

Ancel Keys’ paper renaming Quetelet’s Index as the Body Mass Index is Keys, Ancel, Flaminio Fidanza, Martti J. Karvonen, Noboru Kimura, and Henry L. Taylor. “Indices of Relative Weight and Obesity.” Journal of Chronic Diseases 25 (1972): 329-43.

An excellent summary of the use of BMI in government health reports is Kuczmarski, R.J., and Katherine M. Flegal. “Criteria for Definition of Overweight in Transition: Background and Recommendations for the United States.” American Journal of Clinical Nutrition 72 (2000): 1074-81.