Tuesday, August 20, 2013

Why BMI is not accurate for taller populations

Lisa Wade (at SocImages) links to a really good, publicly accessible run-down on the various environmental reasons why human (and animal) populations have been growing heavier. The author makes a pretty quick equivalence between obesity and BMI by (effectively) just equating the two, thusly:
And so we appear to have a public consensus that excess body weight (defined as a Body Mass Index of 25 or above) and obesity (BMI of 30 or above) are consequences of individual choice.
Now, I believe that there are two germane debates when it comes to the issue of BMI, obesity, and health: (1) the validity of applying a population metric to individuals (which I contend is categorically, logically, and methodologically incorrect) and (2) the question of whether BMI is actually a useful metric of our population. I would contend that the author focuses mainly on studies that presume that #2 is true, which then allows him to focus on answering #1. (I will admit that it's far more juicy and fun to look into #1, but is epistemologically lazy.)

Before continuing, let me first state that we cannot disagree with the fact that the average weight-to-height ratio (otherwise known as the BMI) has been increasing over time. This is a fact. It has countless reams of documentation that support it. Arguing that it hasn't happened is akin to shouting imprecations of denial against the existence of the sun while standing in the middle of a desert at high noon. In short, the numbers are irrefutable: the BMI ratio is increasing. Indeed, the article agrees that this is happening, and does an excellent job of examining the potential causes of the increase in BMI. But what the article misses is the very question of whether BMI itself (and therefore the mechanical definition of "obesity is when BMI>30" that no doubt underlie most of the studies in this area) is actually a useful metric to use on our current population.

The reason why I bring this up (almost once each year on my blog) is that many people breeze past the fundamental question of whether BMI actually is doing the job we assume it is (supposed) to be doing, which is (at the very least) providing a description of the relative height-to-weight ratio of the study population. Indeed, to the issue of the misapplication of the BMI, I will only repeat my position that it's categorically, logically, and methodologically incorrect. (I'll let Devlin explain why.) Instead, below, I'm going to point out one fundamental flaw in the BMI itself: height.

Taller people have a bigger BMI than shorter people of the same build. This is an important (but unsurprising) statement. Also important (but also unsurprising) is that a person can gain weight (or lose weight) without gaining (or losing) height. All this means that height is the independent variable in the description of BMI.

Furthermore, looking at the formula for BMI (weight/[height^2]) it's easy to note that increases in height (say 6 inches/~15 cm) will have a far greater impact to the BMI than an increase in weight (say 6 lbs/~2.5 kg), since height is squared, while weight is not. This means that - as the population gets taller - in order to remain below a BMI of 30, the population must weigh relatively less than a shorter population. Why? It's because the relationship of height-to-weight that forms the BMI was derived from data about 19th century Belgians (who were 5'5" tall, and for whom the formula of wt/[ht^2] was adequate).

But things have changed - a lot - in the height department.

Specifically, humans have become taller than those 5'5"-tall, mid-19th century Belgians. Unfortunately, though, the BMI calculation we use is still that same one derived over 150 years ago (which, btw, was not meant to be a measure of health). But what does this mean? It means that - as a population gets taller - it must become relatively lighter in weight (i.e., far thinner) in order to remain at the same BMI. For example, let's see what happens when we compare the two 2008 US presidential contenders: Barack Obama and John McCain:

Barack Obama: 6' 1.5", 180 lbs = 23.4 BMI
John McCain: 5' 7", 165 lbs = 25.8 BMI

True, Obama was (and remains) thinner than McCain, but - to show how much height influences the BMI calculation, compare, McCain to (then) outgoing president, George W. Bush: at 5' 11" and 190 lbs, George W. Bush had a 26.5 BMI, which is 0.7 higher than McCain's, but was (without much argument) thinner than McCain. So, if Bush was thinner than McCain, but had a higher BMI, and Obama has a slightly lower BMI than McCain, but is a LOT thinner, why is this the case?

The reason why the BMI fails at predicting taller populations is that BMI is fundamentally measuring the relationship incorrectly. For people who are around 5'5" tall (like those mid-19th century Belgians for whom the BMI was calculated originally), then the relationship is actually pretty good. However, with significantly taller (and significantly shorter) populations, the BMI falls apart, because - at these heights - the BMI is no longer acting as an accurate measure.

As Devlin (over at Devlin's Angle) writes:
The BMI was formulated, by a mathematician, not a medical physician, to provide a simple, easy-to-apply mathematical formula to give a broad, society-level measure of weight issues. It has absolutely no scientific or medical basis. It is based purely on a crude statistical analysis. It measures a general society trend, it does not predict.
I would put it one further: saying that "it measures a general society trend, based on the assumption that we can extrapolate from a statistical relationship found among mid-19th century Belgians; it does not predict."

And - in general - populations have been growing taller than mid-19th century Belgians. Especially in Asia. For an example of the change of Japanese average height over time, see here. And this means that these populations are moving away from that range of heights at which BMI was calculated, and for which - at the population level - BMI is/was relatively descriptive.

I'm not even going to get into a discussion about how screwed up BMI gets when you look at populations of athletes. (Hint: the US Olympic team is almost definitely in the "overweight" or "obese" categories, since most of them have a higher-than-average muscle density.)

My other entries on BMI (many of which were motivated from reading SocImages) are here

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