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Correlation, causation and obesity

September 5, 2011

More data is becoming available about all aspects of human behavior. Along with the data comes an ever-increasing number of studies that seek to relate different aspects of human behavior.  It is therefore more important than ever to keep in mind the Statistician’s Mantra: “Correlation does not equal causation.” Simply because two quantities increase or decrease in tandem does not mean that one causes the other.

I think that journalists are particularly guilty of overinterpreting studies.  Here’s just the one from USA Today that popped up after a quick Google search: “Students drink more and more often if living in coed dorms.”  The author of the USA Today report takes it for granted that the study implies that living in coed dorms causes students to drink more.  While finding a relationship between drinking and living in a coed dorm may not be all too difficult, establishing that one causes the other would require quite a bit more effort.  For instance, one could try to recruit a homogeneous group of students, randomly assign them to either single sex or coed dorms, and then track their alcohol consumption over the next few years.  This would require time, expense and effort.  So instead the study quoted in USA Today relied on a survey  – and from the results we can only conclude that perhaps people who drink more choose to live in coed dorms, or that there is a third, unknown factor that influences both drinking and living in coed dorms.   Or that students in coed dorms are more likely to respond truthfully to a question on a survey.

A series of very influential papers by N.A. Chritakis and J.H. Fowler (CF) using data from the Framingham Heart Study should be treated more seriously.  Perhaps the most famous of the CF papers implied that obesity can spread like a contagious disease.  If your spouse becomes overweight, you are 37% more likely to become obese over the next 2 to 4 years – and these percentages become even higher when your close friend becomes obese.  CF concluded that obesity can spread like an epidemic through a social network, and followed this up with a number of studies showing that happiness, loneliness, depression and smoking can behave similarly.

An immediate reaction is that this could be due to homophily – our tendency to befriend people who are in many aspects similar to us. However, the authors of the study tried carefully to rule out this effect.  But, I am still somewhat skeptical of the interpretation – in particular when it takes this form (quoting from this Washington Post article):

“Fowler, speculating that friends could influence one another just by getting together once or twice a year, said, “We were stunned to find that people who were hundreds of miles away had just as much impact on a person’s weight status as friends who are next door. This is not due to people eating or exercising together.”

I don’t know, but I find this a bit hard to swallow.

Indeed, an article by H. Noela and B. Nyhan (here is the free ArXiv version) suggests that there may be effects that were not taken into account in the original CF studies.  In particular, friendships are dynamics, and are formed and dissolved (people get “unfriended” in real life as they do on Facebook).  By not taking into account these effects, the CF studies may have overestimated the effects of social influences.

In the end, it seems that it is still unclear whether obesity, or depression, are communicable through social contacts.  It certainly makes for a good story in the newspaper.  But I am not sure whether we have sufficient evidence to base policies on it.  To find out I would actually have to read the studies, and fully understand the statistical methods that were used.   But that would involve actual work….


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  1. There has been lots of push back on these papers. Andrew Gelman summarizes some of it on his blog

    My take is that like many clinical results, e.g. see, it is likely to be noise.

    • josic permalink

      Thanks Carson – I should have looked at Andy Gelman’s blog. I actually took a quick look at the Lyons paper – I think that should be required reading for graduate students about how not to critique other peoples work. It seems that Lyons brings up a lot of good points, but he does not do himself any favors by sounding so much like a crank.

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