Wednesday, January 6, 2010

Spread of Obesity in a Large Social Network

In the July 26, 2007 issue of JAMA Nicholas A. Christakis, M.D., Ph.D., M.P.H., and James H. Fowler, Ph.D wrote The Spread of Obesity in a Large Social Network over 32 Years where they evaluated a densely interconnected social network of 12,067 people assessed repeatedly from 1971 to 2003 as part of the Framingham Heart Study. The animation below is a supplemet to that article. There is also some excellent supplemental material here and I strongly urge you to check out the author's web site.

This dynamic graphic representation of a portion of the Framingham Heart Survey social network depicts the spread of obesity in the network, ties within the network and the change in those ties over 32 years. Since obesity is a multi-centric epidemic, there are many foci with many people influencing each other and forming ties in complex ways.

Each circle or “node” represents one person in the data set. Nodes with red borders are women, and nodes with blue borders are men. The size of each node is proportional to the subject’s BMI. In addition, the interior color indicates the obesity status of the individual subject. Yellow nodes represent obese persons with a BMI greater than 30 kg/m2, and green nodes represent non-obese subjects. Each line between two nodes represents a social connection between two people. Purple lines denote close genetic ties such as parents, children, and siblings. Gray lines denote non-genetic relations such as friends and spouses. Ties between residential neighbors are not shown in this video clip, though such ties are considered in the text. Appendix 1 contains more detailed information about this dynamic graph.

The graph shows only a part of the network because the overall network is quite large and has 12,067 subjects. The nodes shown here are all part of the “giant component” of the network, which is the largest group of connected persons in the network; 2,200 people are present. All subjects shown were tied to this cluster by at least one social relationship at least once during the 32 years that the network was observed.

The starting positions for all subjects were generated by assuming that all ties were permanent and then using a procedure known as the Kamada-Kawai algorithm to optimize the total distance between connected nodes so that each pair is as close to a fixed distance as possible. This way of drawing the network positions nodes so that those that are connected lie near each other and so that ties do not overlap any more than necessary. Nodes at the center of the network are more connected to other people in the Framingham Heart Study Social Network compared to nodes on the periphery, suggesting that they are more “popular” or have more relatives.

At the upper left of the window is a time indicator showing the year. The video clip starts by showing all ties extant at inception (in the period between 1971 and 1972). At the end of each year, we run the Kamada-Kawai algorithm again and re-position the nodes in the network based on the new set of ties observed. Ties, however, can change at any time, according to which precise day they are observed to appear or disappear. Similarly, node size changes on the precise day that a new weight for a person is observed.

Over time new ties can appear and disappear. For example, we might learn about a friendship for the first time during a subject interview in 1973. This friendship might last until a particular date in 1986 when the subject no longer names this person as a friend. Nodes can disappear, too, if people die. When this happens, the tie between the two people would also disappear.

Notice that the network gets more compact as more ties appear, and as people who are socially connected move to the center of the network. The quantitative analyses reported in the paper document a tendency for obese and non-obese people to cluster together in the network, and this movie helps to illustrate this process as the network changes over time. However, because obesity is a multi-centric epidemic, there are many foci and many people influencing each other and also forming ties with each other in complex ways. Hence, multiple parts of this network are becoming obese and clustering together at once.

By the end, however, clustering of obese and non-obese persons can be discerned: for example, there is a densely interconnected cluster towards the left of the image, at 9:00 o’clock, and also another one towards the very middle of the image. One also gets the sense that the prevalence of obesity is lower at the periphery of the network than at the center. Nevertheless, the network is still sufficiently complex that this clustering is also partially obscured, which is the reason for the more formal mathematical tests described in the text of the paper.

And from Pioneer's "Leaders in Change" video series here is Nicholas Christakis:

Finally, it is worth noting that the entire network is getting heavier as time goes on, tracking the obesity epidemic from 1971 to 2003.
Nicholas Christakis is co-author with James Fowler of Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives.