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Re: BMI: the theory? [and some evidence]

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Mon, 7 Feb 2005 22:31:32 +0000

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 ```Dear Ted You are correct to conclude that BMI (Weight divided by square of height ) is not a rational index of obesity. However your suggestion of using the cube of the height would make it an even poorer index. The reason is simple: Suppose a person grows 1 foot taller. He does not automatically become 1 foot wider and 1 foot deeper like a cube. If he does, he is obviously getting obese. Sincerely Jacob Puliyel MD MRCP M Phil Consultant Pediartician West Middlesex University Hospital London TW8 8QN On Sun, 6 Feb 2005 16:56:07 -0000, Ted Harding <[log in to unmask]> wrote: > On 06-Feb-05 Ted Harding wrote: > > Hi Folks, > > > > I'm encountering conceptual problems in trying to think > > about Body Mass Index (BMI). > > [...] > > > > BMI is defined as body weight (in kgm) divided by the > > square of the height (in metres), and it is trotted out > > blandly as an important index of whether one's weight > > is excessive. > > > > But: why not the cube of the height? This is my theoretical > > question! > > > > Consider two women, say, of identical geometrical shapes, > > and with exactly the same mass-proportions of different > > tissue types, etc (which themselves are geometrically > > exactly similar and distributed in exactly the same ways). > > Then in particular their bodies will have identical > > densities, and their weights will be in the ratio of the > > cubes of their heights. > > > > But say one is 5ft (1.52m) tall, and the other is 6ft (1.83m) > > tall. Therefore the BMI of the taller one will be 20% > > greater (6/5) than the BMI of the shorter one: > > > > (BMI tall)/(BMI short) = (D*hT^3/hT^2)/(D*hS^3/hS^2) > > = hT/hS = 6/5 = 1.2 > > > > where hT and hS are the heights of the Taller and Shorter, > > and D is proportional to their density. > > [...] > > I have now come across some relevant data on the web: > > http://www.spirxpert.com/quetelet.htm > > Since this does not state how the data were gathered, I cannot > comment for their representativeness. But, on the face of it, > the two graphs shown on this website indicate quite clear support > for the above conclusions. > > In the graph for boys, by eyeball the BMI increases from a > modal value of about 15.0 at a standign height of about 120cm > to a modal value of about 22 at a standing height of 180cm > (though the latter is difficult to perceive clearly in view > of the density of the points). > > This corresponds, roundly, to a 50% increase of BMI for a 50% > increase in standing height, which is just what my "theoretical" > considerations above would predict. > > It is very similar for the girls: BMI=15 at 120cm, > BMI=21 at 165cm (40% BMI increase for 38% height increase). > > I'll keep looking, but if anyone can point to accessible > data of a similar kind I'd be interested and very grateful. > > Best wishes to all, > Ted. > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <[log in to unmask]> > Fax-to-email: +44 (0)870 094 0861 > Date: 06-Feb-05 Time: 16:56:06 > ------------------------------ XFMail ------------------------------ > -- ___________________________ Jacob M. Puliyel MD MRCP MPhil Sara Varughese FRCS eFax UK 07092-124285```