Some Obesity Math

When I was in graduate school, we had an old book laying around titled something like How to Lie with Statistics.  I don't remember ever actually reading the book but the title says it all: one can tell two entirely different stories depending on how one chooses to report the numbers.

I fear that much of the rhetoric surrounding obesity has fallen into this trap.  According to CDC data, the average weight of men aged 40-49 has increased roughly 15 lbs in the past 10 to 15 years (compare data in this publication to this one showing the average weight going from about 187 lbs in 1988-1994 to about 202 lbs in 2003-2006; I should also note that more recent data shows these weight gains leveling off).  

Fifteen pounds doesn't seem like a huge number to me (I've personally lost and gained much more than this amount in my adult life).  So, how is it that this small to medium sized increase in average weight gets translated into a message that there is an epidemic?  Part of the answer is that when scientists translate averages into prevalence rates, the numbers look a lot scarier.   

Stick with me while I illustrate with an example.  

Let’s take a hypothetical population of men whose average weight is 180 lbs.  Suppose, men’s weights vary in the population according to a normal distribution with a standard deviation of 30 lbs.  This means roughly 68% of the men will have weights between 150 lbs and 210 lbs.  Suppose also, for convenience sake, that all the men are the same height: 5 ft 10 inches. 

Obesity is defined as BMI greater than 30 (BMI is weight in kg divided by height in meters squared).  In our hypothetical example, where everyone is the same height, a man will be obese if he weighs more than 209 lbs.  Moreover, given our assumptions about the normal distribution, we can readily project that 16.6% of men in this population will be obese (1 minus the cdf of a normal distribution with mean 180 and standard deviation of 30 evaluated at the point 209 is 0.166).

What if all men gain a paltry 5 lbs?  The average weight goes from 180 up to 185 lbs.  Yet, (again given the assumption of the normal distribution), obesity prevalence will go up from 16.6% to 21.1%.

Thus, we have what most of us would consider a rather trivial gain in weight (an increase in 5 lbs or a 2.8% increase in weight); however, we have what appears to be a rather dramatic increase in obesity prevalence (prevalence goes up 4.48% or a 27% increase in prevalence of obesity!).

If we run through the same example again assuming men gain an average of 10 lbs, we can find that obesity prevalence goes up almost 58% even though weight only increased 5.5%!

Both statistics are "true" but they tell very different stories.  

Does 1 lb = 3500kcal?

Researchers studying the effect of various food policies on changes in weight often use the simple saying that a change of 3500 kcal via diet or exercise results in a 1 lb change in weight (it is a claim we repeated in our paper in the Journal of Health Economics, which studied the efficacy of fat taxes).

I ran across this interesting post by a Mike Gibney, a public health and nutrition expert, who points out some problems with the 1 lb = 3500 kcal calculation.  Here's what he has to say:

Firstly, a 1lb weight loss will not be 100% fat but will also involve the loss of some lean tissue (muscle and protein elements of adipose tissue and its metabolism). Whereas fat has an energy value of 9 kcal/g, lean tissue has a value of 4 kcal/g. The exact ratio of the loss of lean and fat in weight reduction depends largely on the level of fat in the body at the outset.

and:

The second criticism of this rule is that it ignores time. If you shed 3,500kcal per week every week, that would differ from a deficit of 3,500 kcal per month every month. The former leads to a daily deficit of 500 kcal while the latter is just 117 kcal.

and:

Thirdly, the 3,500 kcal rule assumes complete linearity – in other words the rule equally applies, pound after pound of weight loss. We saw above that progressive weight loss will progressively increase the % of that weight loss as lean tissue but more importantly, the 3,500kcal rule ignores a major adaptation in energy expenditure

and on this topic, he concludes:

Clearly, the continued use of the 3,500 kcal rule in predicting weight loss should cease and the recommendations of the consensus statement of the ASN and ILSI should apply: “Every permanent 10 kcal change in energy intake per day will lead to an eventual weight change of 1lb when the body reaches a new steady state.  It will take nearly a year to achieve 50% and about 3 years to achieve 95%”.

Finally, I'll point out the importance of taking into account these kinds of issues when calculating the effects of fat taxes.  He says that according to one study, a 20% soda tax would lead to;

 a reduction of energy intake of 34-47 kcal per day for adults. Using the 3,500 kcal rule, an average weight loss of 1.60kg would be predicted for year 1 rising to 8kg in year 5 and to 16kg in year 10. However, when the dynamic mathematical model is used, the corresponding figures for years 1, 5 and 10 are, respectively, 0.97, 1.78 and 1.84 kg loss. The % of US citizens that are over-weight is predicted to fall from existing levels of 66.9% over-weight to 51.5% over-weight in 5 years time using the 3,500 kcal rate but using the dynamic mathematical model, the 5-year figure for the over-weight population in the US would be just 62.3%.

 

Greg Gutfeld on the Food Police

Greg Gutfeld at his hilarious and satirical best . . .

My favorite lines:

The LA City Council just adopted a resolution for meatless Mondays.  This is while around most of this awful brutal world they have meatless weeks and months.  They'd be happier with 'please don't let me starve Mondays.'

and

How hilarious is it that the left accuses the right of invading their bedrooms just as they climb onto your plate.

and

This is Solindra for your belly which is why I feel like throwing up.

The Fat Tax that Wasn't

A while back Denmark passed a law to implement one of the first comprehensive "fat taxes."  A year after its implementation, it looks like they've changed their mind.  

One of the biggest drivers of the reversal was apparently public opinion, not to mention the negative economic impacts.  

I am often amazed at how easy many public health professions believe it is to change weight and corral bad behavior simply by just slapping a tax on things they don't like.  Just today, the folks over at Freakonomics discuss a recent conference where fat taxes were thought a really good idea (I've been a many of these kinds of meetings too).  

We economists often come across as uncaring , negative Nellies when we point out that such taxes often have very little effect on weight, have unintended consequences (as Denmark just realized), and are regressive (meaning that food taxes hit the poor the hardest).  

But, at the end of the day, who is more caring?  The folks pushing for costly taxes that wont materially change weight and health or those of us trying to prevent bad policies from affecting those who can least afford to pay the effects?

LA Food Police

If you haven't yet heard, the Los Angeles City council has declared the first day back to work each week to be "Meatless Monday."  According to one source,

Councilwoman Jan Perry, who also supports the banning of new fast food restaurants in South Los Angeles, said  the new resolution is just one part of a new "good food" agenda for the city.

I don't necessarily have a problem with private entities pushing for less meat consumption.  I might disagree with some of their claims (as I did here), but at least we can put all our facts on the table.  One fact that is often forgotten in meat debates is that it isn't sufficient to look at the amount of energy (or crops) expended to get beef.  We also have to look at what we get.  Most people really like the taste of meat.   

Almost no one looks at their iPad and asks, "how much more energy went into producing this than my old Apple II." The iPad is so much better than the Apple II.  We'd be willing to accept more energy use to have a better computer.  Likewise a nice T-bone is so much better than a head of broccoli.  I'm willing to accept more energy use to have a T-bone than a head of broccoli.    

Now, if my T-bone consumption is imposing costs on others, let's talk about that.  But, here the focus would be on the issues causing the externality (e.g., CO2) not on meat per se.  

The real trouble comes when city governments (rather than private entities) start making symbolic gestures (here's my take on what symbolic gestures imply about government).  Even more troubling is when a council-man or -women presumes to know better than a land-owner or restaurant owner how their land and capital should be used.  See this Reason TV video for an interesting account of developments in LA. 

First Lady Michelle Obama hopes to curb childhood obesity by teaching children about nutrition and exercise. "There's no expert on this planet who says that the government telling people what to do actually does any good with this issue," she says.