The Annals of Applied Statistics

Vaccines, contagion, and social networks

Elizabeth L. Ogburn and Tyler J. VanderWeele

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Consider the causal effect that one individual’s treatment may have on another individual’s outcome when the outcome is contagious, with specific application to the effect of vaccination on an infectious disease outcome. The effect of one individual’s vaccination on another’s outcome can be decomposed into two different causal effects, called the “infectiousness” and “contagion” effects. We present identifying assumptions and estimation or testing procedures for infectiousness and contagion effects in two different settings: (1) using data sampled from independent groups of observations, and (2) using data collected from a single interdependent social network. The methods that we propose for social network data require fitting generalized linear models (GLMs). GLMs and other statistical models that require independence across subjects have been used widely to estimate causal effects in social network data, but because the subjects in networks are presumably not independent, the use of such models is generally invalid, resulting in inference that is expected to be anticonservative. We describe a subsampling scheme that ensures that GLM errors are uncorrelated across subjects despite the fact that outcomes are nonindependent. This simultaneously demonstrates the possibility of using GLMs and related statistical models for network data and highlights their limitations.

Article information

Source
Ann. Appl. Stat., Volume 11, Number 2 (2017), 919-948.

Dates
Received: November 2014
Revised: February 2017
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1500537729

Digital Object Identifier
doi:10.1214/17-AOAS1023

Mathematical Reviews number (MathSciNet)
MR3693552

Zentralblatt MATH identifier
06775898

Keywords
Causal inference social networks contagion peer effects

Citation

Ogburn, Elizabeth L.; VanderWeele, Tyler J. Vaccines, contagion, and social networks. Ann. Appl. Stat. 11 (2017), no. 2, 919--948. doi:10.1214/17-AOAS1023. https://projecteuclid.org/euclid.aoas/1500537729


Export citation

References

  • Ali, M. M. and Dwyer, D. S. (2009). Estimating peer effects in adolescent smoking behavior: A longitudinal analysis. J. Adolesc. Health 45 402–408.
  • Anderson, R. M. and May, R. M. (1985). Vaccination and herd immunity to infectious diseases. Nature 318 323–329.
  • Aronow, P. M. and Samii, C. (2013). Estimating average causal effects under general interference. Technical report, arXiv:1305.6156.
  • Bowers, J., Fredrickson, M. M. and Panagopoulos, C. (2013). Reasoning about interference between units: A general framework. Polit. Anal. 21 97–124.
  • Breslow, N. E. (1996). Generalized linear models: Checking assumptions and strengthening conclusions. Stat. Appl. 8 23–41.
  • Cacioppo, J. T., Fowler, J. H. and Christakis, N. A. (2009). Alone in the crowd: The structure and spread of loneliness in a large social network. J. Pers. Soc. Psychol. 97 977.
  • Choi, D. S. (2014). Estimation of monotone treatment effects in network experiments. ArXiv Preprint, arXiv:1408.4102.
  • Christakis, N. A. and Fowler, J. H. (2007). The spread of obesity in a large social network over 32 years. N. Engl. J. Med. 357 370–379.
  • Christakis, N. A. and Fowler, J. H. (2008). The collective dynamics of smoking in a large social network. N. Engl. J. Med. 358 2249–2258.
  • Christakis, N. A. and Fowler, J. H. (2010). Social network sensors for early detection of contagious outbreaks. PLoS ONE 5 e12948.
  • Christakis, N. A. and Fowler, J. H. (2013). Social contagion theory: Examining dynamic social networks and human behavior. Stat. Med. 32 556–577.
  • Cohen-Cole, E. and Fletcher, J. M. (2008). Is obesity contagious? Social networks vs. environmental factors in the obesity epidemic. J. Health Econ. 27 1382–1387.
  • Eames, K. T. D. and Keeling, M. J. (2002). Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proc. Natl. Acad. Sci. USA 99 13330–13335.
  • Eames, K. T. D. and Keeling, M. J. (2004). Monogamous networks and the spread of sexually transmitted diseases. Math. Biosci. 189 115–130.
  • Earn, D. J. D., Dushoff, J. and Levin, S. A. (2002). Ecology and evolution of the flu. Trends Ecol. Evol. 17 334–340.
  • Eckles, D., Karrer, B. and Ugander, J. (2014). Design and analysis of experiments in networks: Reducing bias from interference. ArXiv Preprint, arXiv:1404.7530.
  • Eubank, S., Guclu, H., Kumar, V. S. A., Marathe, M. V., Srinivasan, A., Toroczkai, Z. and Wang, N. (2004). Modelling disease outbreaks in realistic urban social networks. Nature 429 180–184.
  • Fine, P. E. M. (1993). Herd immunity: History, theory, practice. Epidemiol. Rev. 15 265–302.
  • Fowler, J. H. and Christakis, N. A. (2008). Estimating peer effects on health in social networks: A response to Cohen-Cole and Fletcher; and Trogdon, Nonnemaker, and Pais. J. Health Econ. 27 1400–1405.
  • Gill, J. (2001). Generalized Linear Models: A Unified Approach. Quantitative Applications in the Social Sciences 134. Sage Publications, Thousand Oaks, CA.
  • Halloran, M. E. and Hudgens, M. G. (2012). Causal inference for vaccine effects on infectiousness. Int. J. Biostat. 8 Art. 6.
  • Halloran, M. E. and Struchiner, C. J. (1991). Study designs for dependent happenings. Epidemiology 2 331–338.
  • Halloran, M. E. and Struchiner, C. J. (1992). Modeling transmission dynamics of stage-specific malaria vaccines. Parasitol. Today (Regul. Ed.) 8 77–85.
  • Halloran, M. E. and Struchiner, C. J. (1995). Causal inference in infectious diseases. Epidemiology 6 142–151.
  • Imai, K., Keele, L. and Tingley, D. (2010). A general approach to causal mediation analysis. Psychol. Methods 15 309–334.
  • John, T. J. and Samuel, R. (2000). Herd immunity and herd effect: New insights and definitions. Eur. J. Epidemiol. 16 601–606.
  • Keeling, M. J. and Eames, K. T. (2005). Networks and epidemic models. J. R. Soc. Interface 2 295–307.
  • Keller, M. A. and Stiehm, E. R. (2000). Passive immunity in prevention and treatment of infectious diseases. Clin. Microbiol. Rev. 13 602–614.
  • Klovdahl, A. S. (1985). Social networks and the spread of infectious diseases: The AIDS example. Soc. Sci. Med. 21 1203–1216.
  • Klovdahl, A. S., Potterat, J. J., Woodhouse, D. E., Muth, J. B., Muth, S. Q. and Darrow, W. W. (1994). Social networks and infectious disease: The Colorado Springs study. Soc. Sci. Med. 38 79–88.
  • Latora, V., Nyamba, A., Simpore, J., Sylvette, B., Diane, S., Sylvere, B. and Musumeci, S. (2006). Network of sexual contacts and sexually transmitted HIV infection in Burkina Faso. J. Med. Virol. 78 724–729.
  • Lazer, D., Rubineau, B., Chetkovich, C., Katz, N. and Neblo, M. (2010). The coevolution of networks and political attitudes. Polit. Commun. 27 248–274.
  • Lyons, R. (2011). The spread of evidence-poor medicine via flawed social-network analysis. Statistics, Politics, and Policy 2.
  • Noel, H. and Nyhan, B. (2011). The unfriending problem: The consequences of homophily in friendship retention for causal estimates of social influence. Soc. Netw. 33 211–218.
  • O’Brien, K. L. and Dagan, R. (2003). The potential indirect effect of conjugate pneumococcal vaccines. Vaccine 21 1815–1825.
  • Ogburn, E. L. and VanderWeele, T. J. (2014). Causal diagrams for interference. Statist. Sci. 29 559–578.
  • Ogburn, E. L., VanderWeele, T. J. and Christakis, N. A. (2017). Supplement to “Vaccines, contagion, and social networks.” DOI:10.1214/17-AOAS1023SUPP.
  • Osterholm, M. T., Kelley, N. S., Sommer, A. and Belongia, E. A. (2012). Efficacy and effectiveness of influenza vaccines: A systematic review and meta-analysis. Lancet, Infect. Dis. 12 36–44.
  • Pearl, J. (2001). Direct and indirect effects. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence 411–420.
  • Robins, J. M. and Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology 3 143–155.
  • Robins, J. M. and Richardson, T. S. (2010). Alternative graphical causal models and the identification of direct effects. In Causality and Psychopathology: Finding the Determinants of Disorders and Their Cures (P. Shrout, ed.). Oxford Univ. Press.
  • Rosenbaum, P. R. (2007). Interference between units in randomized experiments. J. Amer. Statist. Assoc. 102 191–200.
  • Rosenquist, J. N., Murabito, J., Fowler, J. H. and Christakis, N. A. (2010). The spread of alcohol consumption behavior in a large social network. Ann. Intern. Med. 152 426–433.
  • Shalizi, C. R. (2012). Comment on “Why and when ‘flawed’ social network analyses still yield valid tests of no contagion.” Statistics, Politics, and Policy 3.
  • Shalizi, C. R. and Thomas, A. C. (2011). Homophily and contagion are generically confounded in observational social network studies. Sociol. Methods Res. 40 211–239.
  • Toulis, P. and Kao, E. (2013). Estimation of causal peer influence effects. In Proceedings of the 30th International Conference on Machine Learning 1489–1497.
  • Ugander, J., Karrer, B., Backstrom, L. and Kleinberg, J. (2013). Graph cluster randomization: Network exposure to multiple universes. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 329–337. ACM.
  • Valeri, L. and VanderWeele, T. J. (2013). Mediation analysis allowing for exposure-mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychol. Methods 18 137–150.
  • VanderWeele, T. J. (2011). Sensitivity analysis for contagion effects in social networks. Sociol. Methods Res. 40 240–255.
  • VanderWeele, T. J., Ogburn, E. L. and Tchetgen Tchetgen, E. J. (2012). Why and when “flawed” social network analyses still yield valid tests of no contagion. Statistics, Politics, and Policy 3 1–11.
  • VanderWeele, T. J. and Tchetgen Tchetgen, E. J. (2011a). Bounding the infectiousness effect in vaccine trials. Epidemiology 22 686–693.
  • VanderWeele, T. J. and Tchetgen Tchetgen, E. J. (2011b). Effect partitioning under interference in two-stage randomized vaccine trials. Statist. Probab. Lett. 81 861–869.
  • VanderWeele, T. J., Tchetgen Tchetgen, E. J. and Halloran, M. E. (2012). Components of the indirect effect in vaccine trials: Identification of contagion and infectiousness effects. Epidemiology 23 751–761.
  • van der Laan, M. J. (2012). Causal inference for networks. U.C. Berkeley Division of Biostatistics Working Paper Series, Working Paper 300.
  • Yang, Y., Sugimoto, J. D., Halloran, M. E., Basta, N. E., Chao, D. L., Matrajt, L., Potter, G., Kenah, E. and Longini, I. M. (2009). The transmissibility and control of pandemic influenza A (H1N1) virus. Science 326 729–733.

Supplemental materials

  • Application of methods from “Vaccines, contagion, and social networks” to Harvard flu data. In the supplementary material, we describe an analysis of the Harvard flu network data using our methods.