Obesity is one of the major health issues facing America today. Affecting over one third of all Americans , obesity-related conditions are estimated to cost over $150 billion and cause the premature deaths of an estimated 300,000 people each year . Obesity prevention efforts generate lots of press, whether it be Mayor Michael Bloomberg outlawing the sale of large, sugary beverages in New York City or Michelle Obama’s “Let’s Move!” campaign. Given the stakes, it makes sense that people are searching for effective ways to prevent obesity.
Despite all of the public attention to obesity, more people become obese each year. One of the challenges to fighting obesity is that while we have some understanding of the biological processes that lead to obesity, we have an imperfect understanding of the psychological and social causes of obesity. In a controversial study published in the New England Journal of Medicine , Nicholas Christakis of Harvard and James Fowler of the University of California at San Diego used statistical techniques to examine how people’s networks of friends affected their chances of becoming obese. A remarkable finding of their paper is that obesity appears to be contagious among friends. That is, if one of your friends becomes obese, your chances of becoming obese will increase as a result. The results have been widely reported in the media (for instance, in  and ). The controversy surrounding this study highlights some of the challenges involved in using statistical methods to interpret real-world data.
Environmental Factors, Homophily or Contagion?
Christakis and Fowler observe that obese people tend to have friends who are also obese. However, there are at least three very plausible reasons why this would be the case: shared environment, homophily, and contagion. To understand what these terms mean, let us consider the case of Matt and his friend Oscar: (1) Shared environment – Because Matt and Oscar are friends, it is more likely than average that they are from the same neighborhood, which means that they will have been exposed to similar environmental risk factors (such as not living near a grocery store that sells produce). Thus, if Oscar is obese, Matt is more likely to be obese. (2) Homophily – People tend to find friends who are similar to themselves, so if Oscar is obese and seeks out similar friends, his friend Matt is also likely to be obese. (3) Contagion – Oscar’s obesity has a psychological effect on Matt that makes him more likely to become obese himself.
In their research, Christakis and Fowler examine data from the Framingham Heart Study. This study collected data about 5000 participants’ height and weight over the course of 32 years. Additionally, participants provided the name of a friend who would know how to reach them in case the scientists running the study had trouble getting in touch with the participant. Christakis and Fowler used this data on friendships to get an idea of the friendship ties between the people in the study. They then combined the friendship information with obesity patterns over time among the participants of the study to examine the causes of obesity.
Figure 1. A picture representing part of the data from the Framingham Heart Study. Circles correspond to people, and the size of the circle indicates the size of the Body Mass Index (BMI), a commonly used measure for estimating body fat. Lines between circles represent friendship or family ties. Image from Christakis’ website .
They argue against environmental factors (explanation 1) by looking carefully at asymmetries among who lists whom as a friend in the study. Because participants were only asked to list their closest friend for the survey, it is not always the case that if Oscar listed Matt as a friend, then Matt also listed Oscar as a friend. Suppose Oscar is obese. Then according to a statistical model that Christakis and Fowler created based on the data, if Oscar lists Matt as a friend, Matt is 13% more likely to become obese, whereas if Matt lists Oscar as a friend, then Matt is 57% more likely to become obese. If they both list each other as friends, then Matt is 171% more likely to become obese. Christakis and Fowler argue that if shared environment were truly the only explanation, then these probabilities should all be roughly the same, since Matt and Oscar are equally likely to share the same environment if Matt lists Oscar as a friend or if Oscar lists Matt as a friend.
Christakis and Fowler then examine homophily (explanation 2). Suppose Matt lists Oscar as a friend. Then, according to the model created by Christakis and Fowler, Matt’s chances of becoming obese are greater if Oscar starts out at a healthy weight and later becomes obese than if Oscar were obese all along. If homophily were the only explanation, then we would expect Matt and Oscar to both start out at a similar weight, but we wouldn’t expect a change in Oscar’s weight to have a particularly large impact on Matt the way Christakis and Fowler argue it did in the study.
Christakis and Fowler’s work has come under criticism from other scientists. Statisticians have identified many different issues in Christakis and Fowler’s work, some of which are fairly straightforward and some of which are subtle. We will discuss two of them here.
Russell Lyons writes an extremely critical paper  describing many things he perceives as drawbacks of their study. One of his simplest critiques is that he doesn’t think Christakis and Fowler rule out explanation 1 in a sufficiently thorough way. While 13% and 57% sound like very different numbers, by their own estimation Christakis and Fowler are less than 95% confident that the difference is not due to random chance. Having enough statistical certainty is important for having an authoritative scientific study, and 95% is usually chosen as the cut-off number. To see why this issue is important, imagine Christakis and Fowler ran ten different studies, and they were 90% confident that the results in each study were not due to random chance. Then on average they would expect one of their studies to be completely false! Thus, Lyons thinks that Christakis and Fowler need to be more confident before making such strong claims.
On a practical level, Cohen-Cole and Fletcher  also argue that Christakis and Fowler’s techniques need improvement. They use Christakis and Fowler’s statistical techniques on a set of survey data of high school teens (called the National Longitudinal Study of Adolescent Health) to show that height, acne, and headaches are “contagious” in the same sense that Christakis and Fowler claim for obesity. Since most people do not expect any of those things to be contagious, Cohen-Cole and Fletcher argue that Christakis and Fowler’s techniques need to be revisited.
In a recent paper , Christakis and Fowler respond to critiques leveled against their work. For many of the critiques, they partially accept the validity of the concerns while arguing that their results still present some evidence for obesity spreading through social networks. They acknowledge that they are less than 95% confident that their results are not due to random chance, yet argue that their data suggest that their conclusions are likely. In response to Cohen-Cole and Fletcher’s work, they argue that Cohen-Cole and Fletcher do not exactly replicate the statistical techniques of Christakis and Fowler and that if they were to change their assumptions to be precisely in line with Christakis and Fowler’s, then they would find little to no evidence of contagion for these traits. Moreover, they point out that since all of Cohen-Cole and Fletcher’s data comes from a survey, it would not be unreasonable for people’s friends to have a small influence on how they report their acne, headaches and height. Christakis and Fowler say that they would be very open to using a different statistical technique to analyze the data if someone else were to suggest a reasonable one.
Too often experimental science is thought of as a single burst of brilliance, where a single paper completely answers a specific question. However, many scientific questions are complicated, and complex discussions such as the one taking place regarding obesity in social networks are both common and crucial for the advancement of science. Applying statistics to real-world data, especially data that doesn’t come from a carefully controlled experiment, is particularly difficult. As work in this area continues, hopefully scientists will be able to understand more about the causes of obesity, which could be a crucial step in our ongoing effort to fight this disease.
Eric Riedl is a graduate student in the Harvard Mathematics Department.
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