The Annals of Applied Statistics

Estimating within-school contact networks to understand influenza transmission

Gail E. Potter, Mark S. Handcock, Ira M. Longini, and M. Elizabeth Halloran

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Abstract

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than nonfriends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.

Article information

Source
Ann. Appl. Stat. Volume 6, Number 1 (2012), 1-26.

Dates
First available in Project Euclid: 6 March 2012

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1331043386

Digital Object Identifier
doi:10.1214/11-AOAS505

Zentralblatt MATH identifier
06026422

Mathematical Reviews number (MathSciNet)
MR2951527

Citation

Potter, Gail E.; Handcock, Mark S.; Longini, Ira M.; Halloran, M. Elizabeth. Estimating within-school contact networks to understand influenza transmission. The Annals of Applied Statistics 6 (2012), no. 1, 1--26. doi:10.1214/11-AOAS505. http://projecteuclid.org/euclid.aoas/1331043386.


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References

  • Baccam, P., Beauchemin, C., Macken, C. A., Hayden, F. G. and Perelson, A. S. (2006). Kinetics of influenza A virus infection in humans. J. Virol. 80 7590–7599.
  • Basta, N. E., Chao, D. L., Halloran, M. E., Matrajt, L. and Longini, I. M., Jr. (2009). Strategies for pandemic and seasonal influenza vaccination of schoolchildren in the United States. Am. J. Epidemiol. 170 679–686.
  • Cauchemez, S., Donnelly, C. A., Reed, C., Ghani, A. C., Fraser, C., Kent, C. K., Finelli, L. and Ferguson, N. M. (2009). Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States. N. Engl. J. Med. 361 2619–2627.
  • Chao, D. L., Halloran, M. E. and Longini, I. M., Jr. (2010). School opening dates predict pandemic influenza A(H1N1) outbreaks in the United States. J. Infect. Diseases 202 877–880.
  • Conlan, A. J. K., Eames, K. T. D., Gage, J. A., von Kirchbach, J. C., Ross, J. V., Saenz, R. A. and Gog, J. R. (2011). Measuring social networks in british primary schools through scientific engagement. Proceedings of the Royal Society B: Biological Sciences 278 1467–1475.
  • Duerr, H. P., Schwehm, M., Leary, C. C., De Vlas, S. J. and Eichner, M. (2007). The impact of contact structure on infectious disease control: Influenza and antiviral agents. Epidemiology and Infection 135 1124–1132.
  • Eames, K. T. D. (2008). Modelling disease spread through random and regular contacts in clustered populations. Theoretical Population Biology 73 104–111.
  • Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Monographs on Statistics and Applied Probability 57. Chapman and Hall, New York.
  • Elveback, L. R., Fox, J. P., Ackerman, E., Langworthy, A., Boyd, M. and Gatewood, L. (1976). An influenza simulation model for immunization studies. Am. J. Epidemiol. 103 152–165.
  • 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.
  • Ferguson, N. M., Cummings, D. A. T., Fraser, C., Cajka, J. C., Cooley, P. C. and Burke, D. S. (2006). Strategies for mitigating an influenza pandemic. Nature 442 448–452.
  • Fruchterman, T. M. and Reingold, E. M. (1991). Graph drawing by force-directed placement. Software, Practice and Experience 21 1129–1164.
  • Germann, T. C., Kadau, K., Longini, I. M., Jr. and Macken, C. A. (2006). Mitigation strategies for pandemic influenza in the United States. Proc. Natl. Acad. Sci. USA 103 5935–5940.
  • Geyer, C. J. and Thompson, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data. J. Roy. Statist. Soc. Ser. B 54 657–699.
  • Gile, K. J. and Handcock, M. S. (2006). Model-based assessment of the impact of missing data on inference for social networks. Center for Statistics in the Social Sciences, Univ. Washington.
  • Glass, L. and Glass, R. (2008). Social contact networks for the spread of pandemic influenza in children and teenagers. BMC Public Health 8 61.
  • Goodreau, S. M., Kitts, J. A. and Morris, M. (2009). Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks. Demography 46 103–125.
  • Halloran, M. E., Hayden, F. G., Yang, Y., Longini, I. M., Jr. and Monto, A. S. (2007). Antiviral effects on influenza viral transmission and pathogenicity: Observations from household-based trials. Am. J. Epidemiol. 165 212–221.
  • Halloran, M. E., Ferguson, N. M., Eubank, S., Longini, I. M., Jr., Cummings, D. A. T., Lewis, B., Xu, S., Fraser, C., Vullikanti, A., Germann, T. C., Wagener, D., Beckman, R., Kadau, K., Barrett, C., Macken, C. A., Burke, D. S. and Cooley, P. (2008). Modeling targeted layered containment of an influenza pandemic in the United States. Proc. Natl. Acad. Sci. USA 105 4639–4644.
  • Handcock, M. S. (2003). Degreenet: Models for skewed count distributions relevant to networks. Version 1.0-3. Seattle, WA. Available at http://statnetproject.org.
  • Handcock, M. S. and Gile, K. J. (2010). Modeling social networks from sampled data. Ann. Appl. Stat. 4 5–25.
  • Harris, K. M. (2009). The national longitudinal study of adolescent health (add health), waves I and II, 1994–1996; wave III, 2001–2002; wave IV, 2007–2009. [Machine-readable data file and documentation]. Carolina Population Center, Univ. North Carolina at Chapel Hill.
  • Harris, K. M., Halpern, C. T., Whitsel, E., Hussey, J., Tabor, J., Entzel, P. and Udry., J. R. (2009). The national longitudinal study of adolescent health: Research design. Available at http://www.cpc.unc.edu/projects/addhealth/design.
  • Hens, N., Ayele, G. M., Goeyvaerts, N., Aerts, M., Mossong, J., Edmunds, J. W. and Beutels, P. (2009a). Estimating the impact of school closure on social mixing behaviour and the transmission of close contact infections in eight European countries. BMC Infect. Dis. 9 187.
  • Hens, N., Goeyvaerts, N., Aerts, M., Shkedy, Z., Damme, P. V. and Beutels, P. (2009b). Mining social mixing patterns for infectious disease models based on a two-day population survey in Belgium. BMC Infect. Dis. 9 5.
  • Keeling, M. J. and Eames, K. T. D. (2005). Networks and epidemic models. J. R. Soc. Interface 2 295–307.
  • Loeb, M., Russell, M. L., Moss, L., Fonseca, K., Fox, J., Earn, D. J. D., Aoki, F., Horsman, G., Van Caeseele, P., Chokani, K., Vooght, M., Babiuk, L., Webby, R. and Walter, S. D. (2010). Effect of influenza vaccination of children on infection rates in hutterite communities. J. Amer. Med. Assoc. 303 943–950.
  • Miller, J. C. (2009). Spread of infectious disease through clustered populations. Journal of the Royal Society Interface 6 1121–1134.
  • Mossong, J., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., Massari, M., Salmaso, S., Tomba, G. S., Wallinga, J., Heijne, J., Sadkowska-Todys, M., Rosinska, M. and Edmunds, W. J. (2008). Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Medicine 5 0381–0391.
  • Murphy, B. R., Rennels, M. B., Douglas, R. G. Jr., Betts, R. F., Couch, R. B., Cate, T. R. Jr., Chanock, R. M., Kendal, A. P., Maassab, H. F., Suwanagool, S., Sotman, S. B., Cisneros, L. A., Anthony, W. C., Nalin, D. R. and Levine, M. M. (1980). Evaluation of influenza A/Hong Kong/123/77 (H1N1) ts-1A2 and cold-adapted recombinant viruses in seronegative adult volunteers. Infect. Immun. 29 348–355.
  • Potter, G. E., Handcock, M. S., Longini, I. M., Jr. and Halloran, M. E. (2011a). Modeling within-household contact networks from egocentric data. Ann. Appl. Statist. 5 1816–1838.
  • Potter, G. E., Handcock, M. H., Longini, I. M., Jr. and Halloran, M. E. (2011b). Supplement A to “Estimating within-school contact networks to understand influenza transmission. DOI:10.1214/11-AOAS505SUPPA.
  • Potter, G. E., Handcock, M. H., Longini, I. M., Jr. and Halloran, M. E. (2011c). Supplement B to “Estimating within-school contact networks to understand influenza transmission. DOI:10.1214/11-AOAS505SUPPB.
  • R Development Core Team (2008). R: A language and environment for statistical computing.
  • Read, J. M., Eames, K. T. D. and Edmunds, W. J. (2008). Dynamic social networks and the implications for the spread of infectious disease. Journal of The Royal Society Interface 5 1001–1007.
  • Rodriguez, C. V., Rietberg, K., Baer, A., Kwan-Gett, T. and Duchin, J. (2009). Association between school closure and subsequent absenteeism during a seasonal influenza epidemic. Epidemiology 20 787–792.
  • Salathé, M., Kazandjieva, M., Lee, J. W., Levis, P., Feldman, M. W. and Jones, J. H. (2010). A high-resolution human contact network for infectious disease transmission. Proc. Natl. Acad. Sci. USA 107 2202022025.
  • Smieszek, T., Fiebig, L. and Scholz, R. W. (2009). Models of epidemics: When contact repetition and clustering should be included. Theor. Biol. Med. Model 6 11.
  • Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J. F., Quaggiotto, M., Van den Broeck, W., Rgis, C., Lina, B. and Vanhems, P. (2011a). High-resolution measurements of face-to-face contact patterns in a primary school. PLoS ONE 6.
  • Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Colizza, V., Isella, L., Regis, C., Pinton, J. F., Khanafer, N., Van den Broeck, W. and Vanhems, P. (2011b). Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Medicine 9 87.
  • Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S, 4th ed. Springer, New York.
  • Xia, H., Chen, J., Marathe, M. V. and Mortveit, H. S. (2010). Synthesis and embedding of subnetworks for individual-based epidemic models. NDSSL Technical Report 10-139, Univ. North Carolina at Chapel Hill.

Supplemental materials

  • Supplementary material A: Model validation and descriptive analyses of simulated contact networks. We compare our fitted degree distribution to that from an alternate data source, the POLYMOD study. We compare marginal and joint distributions of variables from contact networks simulated from our model to the empirical marginal and joint distributions in the epidemic survey, which was used to estimate model input parameters.
  • Supplementary material B: Sensitivity analysis for targeted antiviral prophylaxis intervention. We perform sensitivity analysis to assess the impact of the assumption of perfect reporting of contacts in the targeted antiviral prophylaxis intervention. Simulations are performed with 90% and 75% of contacts reported.