Are you, or do you know, an undergraduate who has good math, biology and/or computer programming chops wanting to spend some of their summer getting paid to do research in these areas?

My research institute, NIMBioS, is now accepting applications from undergraduates and for its Summer Research Experience program. NIMBioS provides the housing and a stipend and two mentors who will guide students through a research project. The 2014 projects are pretty diverse and include one that I will co-mentor with fellow post-doc Keenan Mack on the Argentine ant supercolony.

As described in this Radiolab story, the massive scale of Argentine ant cooperation is astounding. But, as described in this (gated) commentary by David Queller, probably unstable. Our project, in short, is to model this instability.

If you know an undergraduate with a pretty good grasp of entomology, evolutionary game theory, and/or agent-based modelling skills, please encourage them to apply. If you happen to be an undergraduate who regularly reads this blog, chances are you are the type of person who should apply as well.

Having served on admissions committees for my former graduate program, having these types of research experiences (and strong associated recommendation letters) are a good way to convince admission committees and potential major professors that you know what actual science (as opposed to classroom science) looks like.

For reasons unrelated to my usual research, I have been looking into medical literature concerning diabetes in “normal weight” people. If you read anything about treating diabetes the first steps are to eat better, exercise and lose weight. But what if you already eat healthy, exercise a lot and are at a normal or ideal weight? Well, current medical thinking is that if you are at normal weight with diabetes you are more likely to die than someone who is overweight. This seems counter-intuitive which is why it is called an “obesity paradox.”

Much of this comes from a paper published last year in JAMA (a top medical journal) finding that “[a]dults who were normal weight at the time of incident diabetes had higher mortality than adults who are overweight or obese.” This counter-intuitive finding was reported in the New York Times, the NYT health blog, CNN, Rueters, CBS, and many other places.

The study included 2,625 individuals pooled from five observational datasets. The individuals “were classified as normal weight if their BMI was 18.5 to 24.99 or overweight/obese if BMI was 25 or greater.” BMI, or Body Mass Index, is calculated as one’s weight in kilograms divided by one’s height in meters squared.

BMI is the measurement the media uses when reporting, for example, America’s increasing obesity epidemic. BMI is also often used by doctors as an individual measure of health (even though that was never its intended purpose and it has many well-known limitations). One thing to notice is that BMI does not take body composition into account, just weight – one kilogram of muscle counts the same as a kilogram of fat. A common criticism of using BMI for assessing individual health is that a very muscular person is considered as “obese” as a very fat person.

So do diabetic people with normal weight have higher mortality than obese people with diabetes? The results, as quoted, from the JAMA paper:

After adjustment for demographic characteristics and blood pressure, lipid levels, waist circumference, and smoking status, hazard ratios comparing normal-weight participants with overweight/obese participants for total, cardiovascular, and noncardiovascular mortality were 2.08 (95% CI, 1.52-2.85), 1.52 (95% CI, 0.89-2.58), and 2.32 (95% CI, 1.55-3.48), respectively.

Wait a second! They controlled for WAIST CIRCUMFERENCE?!? (I think this may have been the only time I’ve literally done a double-take while reading a scientific paper.)

To see why this might be a big problem, please consider two fictional characters, Zangief* and E. Honda, from the hit 1987 arcade game Street Fighter II. These gentlemen have about the same BMI (using the stats from the Street Fighter wiki). However, their waist circumferences are radically different.

Who would you consider more obese? Using BMI alone they are equally obese, but I am also going to go out on a limb and say that E. Honda is closer to what most of us would consider “obese” given that a higher percentage of his mass comes from body fat.** But what happens when we control for waist circumference?

Essentially, we are asking “what is the estimated effect of BMI, discounting the estimated effect of abdominal circumference.” I conservatively estimate that Zangief’s waist is about half the circumference of E. Honda’s. So “controlling” for waist circumference discounts E. Honda’s BMI more and thus we effectively count Zangief as more obesethan E. Honda. This is because we have abstracted away the additional abdominal fat that contributes both to E. Honda’s circumference and BMI. The result is that if even if someone built like E. Honda has a higher rate of mortality than someone built like Zangief, we would conclude that less obese people have a higher mortality rate. This “obesity paradox,” though, would just be a statistical artifact of controlling for something we should not have.

But these are video game characters. Would this hold up for real-world data? Let’s see.

R (the statistical software) has an easily downloadable dataset for bodyfat and other body measurements for 253 males. (The documentation suggests that five observations have errors, so I removed them, leaving us with data for 247 males. This is much smaller than the sample in the paper, but good enough to illustrate my point.) For those playing at home, click below for the code to snag the dataset:

#Installs the mfp package - only do this once
install.packages("mfp")
#Load library
library (mfp)
#Load bodyfat dataset
data(bodyfat)
#Copy bodyfat dataset to bf_data
bf_data <- bodyfat
#Add a column of BMIs calculated from weight and height data
bf_data$BMI=703*bf_data$weight/bf_data$height^2
#Remove observations documentation suggests are errors
bf_data <- bf_data[-c(42, 48, 76, 96, 182),]

This data contains body fat percentage (called “brozek”), height and weight (from which we can calculate BMI), and waist circumference. What we are going to do next is a thought experiment where we assume that the common wisdom is exactly true. That is we are going to assume that body fat is an exact predictor for mortality (however measured). In real life this is obviously not true, there will be noise in the data. But this assumption will hurt us in that it should be the hardest case for falsely finding that overweight people have lower mortality than normal weight people. In other words, even assuming that the intuitive result is exactly true, can we erroneously find the counter-intuitive result by controlling for abdominal circumference?

First, lets run a regression of BMI on body fat percentage. If the coefficient of BMI comes out positive, this indicates that there is a positive relationship between BMI and body fat. And, since we assumed that body fat was a perfect predictor of mortality, BMI would have a positive relationship with mortality.

# Fit the regression model (brozek is a measure of body fat percentage)
BMI_fit <- lm(bf_data$brozek ~ bf_data$BMI, data=bf_data)
#Report the coefficients
coefficients(BMI_fit) # model coefficients
#Plot the data and regression line
plot(bf_data$BMI, bf_data$brozek, xlab="BMI", ylab="Body Fat Percentage",main="BMI vs Body Fat")
abline(BMI_fit)

Below are the results. The coefficient for BMI (1.51) is positive, indicating a positive relationship between BMI and mortality. This is consistent with the conventional wisdom.

(Intercept) bf_data$BMI
-19.393723 1.510123

The same can be done with waist circumference.

# Fit the regression model (brozek is a measure of body fat percentage)
WC_fit <- lm(bf_data$brozek ~ bf_data$abdomen, data=bf_data)
#Report the coefficients
coefficients(WC_fit) # model coefficients
#Plot the data and regression line
plot(bf_data$abdomen, bf_data$brozek, xlab="Waist", ylab="Body Fat Percentage",main="Waist vs Body Fat")
abline(WC_fit)

coefficients(WC_fit) # model coefficients
(Intercept) bf_data$abdomen
-34.6493981 0.5791725

Again, the coefficient for waist circumference (0.58) is positive, indicating a positive relationship between waist circumference and mortality. This is, again, consistent with the conventional wisdom.

Finally, lets see what happens when we run the regression for BMI “controlling” for waist circumference.

# Fit the regression model (brozek is a measure of body fat percentage)
BMI_and_WC_fit <- lm(bf_data$brozek ~ bf_data$BMI + bf_data$abdomen, data=bf_data)
#Report the coefficients
coefficients(BMI_and_WC_fit) # model coefficients

The coefficient on BMI came out negative! To a naive observer this would look against the conventional wisdom. BMI correlates negatively with mortality (and remember that this is after we assumed that body fat was a perfect predictor of mortality). This would seem to indicate that obese people are less likely to die than normal people. An “obesity paradox.”

Why does this happen? It happens because when controlling for waist circumference, you are essentially making fat cost less than muscle in your BMI calculations – the same as with E. Honda and Zangief above. In other words, you are counting people who are in better shape as more obese than they really are.

How does this simple thought experiment jibe with the original paper? Pretty well I think.

One thing about the paper is that they actually ran one model where they did not “control” for waist circumference. They did not report finding an “obesity paradox” for that model – which is consistent with my thought experiment. However, they suspiciously did not report any results for that model in the text of the paper -which leads me to suspect that the results did not fit well with their story. [But they did in a Table, see important UPDATE below.] They also found that abdominal circumference was associated with mortality which is consistent with my thought experiment.

So there you go, it seems like people with more muscle relative to fat live longer. Not exactly as counter-intuitive as the study (and press about the study) might make us think.***

I get really mad about bad statistics in medical research. It is one thing to erroneously claim that beautiful people have more daughters. It is not going to literally kill anyone. But medical doctors (most without much statistical training) rely on published medical research to treat patients. When they rely on bad research, it can kill people.

Medical stats people. Am I missing something important here? If not, is this problem worth pointing out in a more formal way? Obviously my thought experiment is simpler than the model in the paper (I consider this a feature) and my dataset is smaller (easily corrected, I think). Send me an email or comment below.

[UPDATE: Thank you for all of the comments thus far, both here and through social media. One of my friends pointed out that Table 2 of the original paper contains the results for the model that did not control for waist circumference that were not reported in the text. He said that this was standard practice in reporting medical research, so it was unfair of me to say this was suspicious.

From the way I read the table normal weight is still associated with higher overall mortality (but in both models not cardiovascular mortality), but difference between normal weight and overweight/obese is much less than in the model adjusting for waist circumference. The confidence interval for normal BMI total mortality does not quite overlap with the mortality for overweight/obese BMI individuals. So outside of something else going on, indications are that controlling for WC may increase the magnitude of the “paradox” but is not the sole explanation.

The table reports the findings in relative risk – which is fairly uninformative. Since the baserate for death in the overweight group was about 1.5%, we are talking about an increased absolute risk of on the order of 0.5-1.5%. Disagreement?]

*- In the Disney movie, Wreck-It-Ralph, Zangief is portrayed as a “bad guy.” However, in the video game he was not a bad guy. He was just Russian. Just because you are Russian doesn’t necessarily mean you are a bad guy.

** – Please note that I don’t want to pick on E. Honda. Despite his size, he is pretty spry. I almost always picked him when challenging my middle school friends (and enemies) at the arcade.

*** – Relatedly, a lot of people tell me that belly fat is an especially bad kind of fat for diabetes. But this oft cited study on the subject does not support that conclusion. It doesn’t compare belly fat to other kinds of fat. In fact, it finds them very highly correlated. What is going on here?

Randy Schekma, upon winning the Nobel Prize in medicine says he will not publish in Science, Nature or Cell (top science journals). Interesting commentary on this move by Michael Eisen and Jon Wilkins.

Why Biology Belongs in the Study of Politics by John Hibbing guest-posting at the Monkey Cage. I find this whole discussion fairly frustrating. Mostly because biology ≠ genetics. Maybe I’ll write a post about this someday.

What’s the deal with inclusive fitness theory? Ben Allen blogs about his new paper with Martin Nowak and E.O. Wilson. I find little to disagree with here (other than calling my very first blog post “heated.”) Models make assumptions. Models are used for different purposes. These assumptions are often wrong, but sometimes useful. Sometimes assumptions useful for one purpose are not useful for another. I think there is still confusion here between inclusive fitness accounting and inclusive fitness theory, so my opinion of the older Nowak/Wilson paper is unchanged. I also like Jon Wilkins’s bear video.

The lack of information flow between disciplines can hardly be underestimated. A brilliant example is the sunk cost fallacy... Hundreds of papers were written in economics and psychology on the sunk cost fallacy, and hundreds of papers were written in evolutionary biology (by some of the most eminent biologists) on the Concorde fallacy — which is the same fallacy. There is not a single cross reference in these hundreds of papers, nor any awareness that both fields came to opposite conclusions: in economics and psychology, it is taken for granted that humans often commit the sunk cost fallacy, in animal biology,
no conclusive evidence has been found that a single animal species would commit the sunk cost fallacy (Arkes and Ayton 1999).