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Stat Med. 2018 Jul 30;37(17):2561-2585. doi: 10.1002/sim.7658. Epub 2018 Apr 29.

Exposure, hazard, and survival analysis of diffusion on social networks.

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Department of Biostatistics, University of Washington, Seattle, WA 98105, USA.
Department of Biostatistics, Yale School of Public Health, New Haven, CT 06510, USA.
Yale School of Management, New Haven, CT 06511, USA.
Department of Ecology & Evolutionary Biology, Yale University, New Haven, CT 06511, USA.
Department of Emergency Medicine, Stanford University, Stanford, CA 94305, USA.
Department of Political Science, University of Michigan, Ann Arbor, MI 48109, USA.
Department of Sociology, Yale University, New Haven, CT 06511, USA.
Department of Medicine, Yale School of Medicine, New Haven, CT 06510, USA.
Department of Biomedical Engineering, New Haven, CT 06511, USA.


Sociologists, economists, epidemiologists, and others recognize the importance of social networks in the diffusion of ideas and behaviors through human societies. To measure the flow of information on real-world networks, researchers often conduct comprehensive sociometric mapping of social links between individuals and then follow the spread of an "innovation" from reports of adoption or change in behavior over time. The innovation is introduced to a small number of individuals who may also be encouraged to spread it to their network contacts. In conjunction with the known social network, the pattern of adoptions gives researchers insight into the spread of the innovation in the population and factors associated with successful diffusion. Researchers have used widely varying statistical tools to estimate these quantities, and there is disagreement about how to analyze diffusion on fully observed networks. Here, we describe a framework for measuring features of diffusion processes on social networks using the epidemiological concepts of exposure and competing risks. Given a realization of a diffusion process on a fully observed network, we show that classical survival regression models can be adapted to estimate the rate of diffusion, and actor/edge attributes associated with successful transmission or adoption, while accounting for the topology of the social network. We illustrate these tools by applying them to a randomized network intervention trial conducted in Honduras to estimate the rate of adoption of 2 health-related interventions-multivitamins and chlorine bleach for water purification-and determine factors associated with successful social transmission.


competing risks; diffusion of innovations; social network


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