Chance News 76

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Quotations

"Counting is the religion of this generation. It is its hope and its salvation."

-- Gertrude Stein, as quoted in The Emperor of All Maladies: A Biography of Cancer, Siddhartha Mukherjee.

Submitted by Steve Simon.

Forsooth

Dispute over statistics in social network analysis

Catching Obesity From Friends May Not Be So Easy. Gina Kolata, The New York Times, August 8, 2011.

Social network analysis has led to some rather intriguing findings about your health.

Does obesity spread like a virus through networks of friends and friends of friends? Do smoking, loneliness, happiness, depression and illegal drug use also proliferate through social networks? Over the past few years, a series of highly publicized studies by two researchers have concluded that these behaviors can be literally contagious — passed from person to person.

These findings, published in the New England Journal of Medicine in 2007 have come under attack by statisticians.

I know that many professional statisticians felt it was all bunk from the word go,” said Russell Lyons, a mathematics professor at Indiana University, who recently published a scathing review. of the work on contagion of social behaviors.

The authors of the 2007 publication used a massive cohort study that had

data gathered from 12,067 subjects in a long-running federal study, the Framingham Heart Study. The data included 32 years of medical records, including such routine data as body weight and smoking habits.

The unique feature of the Framingham study was the request from each participant to name a friend who could help locate them if a follow-up exam was missed. This allowed the researchers to apply social network analysis to this data set and to correlate it to measures of health, such as obesity.

In analyzing the Framingham data, Dr. Christakis and Dr. Fowler found that friends, and friends of friends, had similar levels of obesity, but neighbors did not.

There are several explanations for this finding, which the researchers addressed in their article.

One was homophily, the tendency to choose friends like oneself. A second explanation was that people are affected in the same ways by the environments they share with their friends.

The third explanation, and the one that garnered so much attention, was contagion. Dr. Christakis and Dr. Fowler focused on this as a cause of obesity, saying that they could estimate its effect and that it was large. They theorized that a person’s idea of an acceptable weight, or an acceptable portion size, changes when he sees how big his friends are or how much they eat.

How can you disentangle these three possible mechanisms that might produce a correlation of obesity among friends?

In their first study, for example, Dr. Christakis and Dr. Fowler wrote that if person A names person B as a friend and B does not name A, then B’s weight affects A. If B gets fat, the researchers estimated, then A has a 57 percent change of getting fat as well. But if A gets fat, the researchers said, it has no effect on B.

But a careful statistical analysis noted some problems.

But those estimates did not come from the raw data, Dr. Lyons pointed out. They came from the researchers’ statistical model. And the estimates actually showed that when B did not name A as a friend, B was still 13 percent more likely to become obese.

The difference between 57% and 13% was not large enough to achieve statistical significance. Perhaps, countered the authors, but the results they found were consistent across multiple studies.

But those estimates did not come from the raw data, Dr. Lyons pointed out. They came from the researchers’ statistical model. And the estimates actually showed that when B did not name A as a friend, B was still 13 percent more likely to become obese.

Questions

1. Does a result that is not statistically significant, but which is replicated across multiple studies constitute proof of causation?

2. What are the social implications if the results of Christakis and Fowler are true?

Submitted by Steve Simon.

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