Journal of Applied Probability

Respondent-driven sampling and an unusual epidemic

J. Malmros, F. Liljeros, and T. Britton

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

Respondent-driven sampling (RDS) is frequently used when sampling from hidden populations. In RDS, sampled individuals pass on participation coupons to at most $c$ of their acquaintances in the community ($c=3$ being a common choice). If these individuals choose to participate, they in turn pass coupons on to their acquaintances, and so on. The process of recruiting is shown to behave like a new Reed–Frost-type network epidemic, in which `becoming infected' corresponds to study participation. We calculate $R_0$, the probability of a major `outbreak', and the relative size of a major outbreak for $c\lt\infty$ in the limit of infinite population size and compare to the standard Reed–Frost epidemic. Our results indicate that $c$ should often be chosen larger than in current practice.

Article information

Source
J. Appl. Probab., Volume 53, Number 2 (2016), 518-530.

Dates
First available in Project Euclid: 17 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1466172871

Mathematical Reviews number (MathSciNet)
MR3514295

Zentralblatt MATH identifier
1342.92256

Subjects
Primary: 92D30: Epidemiology
Secondary: 91D30: Social networks

Keywords
Stochastic epidemic model respondent-driven sampling configuration model Reed–Frost

Citation

Malmros, J.; Liljeros, F.; Britton, T. Respondent-driven sampling and an unusual epidemic. J. Appl. Probab. 53 (2016), no. 2, 518--530. https://projecteuclid.org/euclid.jap/1466172871


Export citation

References

  • Andersson, H. and Britton, T. (2000). Stochastic Epidemic Models and Their Statistical Analysis (Lecture Notes Statist. 151). Springer, New York.
    Mathematical Reviews (MathSciNet): MR1784822
  • Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, New York.
    Mathematical Reviews (MathSciNet): MR373040
  • Ball, F. and Lyne, O. D. (2001). Stochastic multitype SIR epidemics among a population partitioned into households. Adv. Appl. Prob. 33, 99–123.
    Mathematical Reviews (MathSciNet): MR1825318
    Digital Object Identifier: doi:10.1239/aap/999187899
    Project Euclid: euclid.aap/999187899
  • Ball, F. and Neal, P. (2002). A general model for stochastic SIR epidemics with two levels of mixing. Math. Biosci. 180, 73–102.
    Mathematical Reviews (MathSciNet): MR1950749
    Digital Object Identifier: doi:10.1016/S0025-5564(02)00125-6
  • Ball, F. and Sirl, D. (2013). Acquaintance vaccination in an epidemic on a random graph with specified degree distribution. J. Appl. Prob. 50, 1147–1168. (Correction: 52 (2015), 908.)
    Mathematical Reviews (MathSciNet): MR3161379
    Digital Object Identifier: doi:10.1017/S0021900200013851
    Project Euclid: euclid.jap/1389370105
  • Ball, F., Sirl, D. and Trapman, P. (2009). Threshold behaviour and final outcome of an epidemic on a random network with household structure. Adv. Appl. Prob. 41, 765–796.
    Mathematical Reviews (MathSciNet): MR2571316
    Digital Object Identifier: doi:10.1239/aap/1253281063
    Project Euclid: euclid.aap/1253281063
  • Ball, F. G., Sirl, D. J. and Trapman, P. (2014). Epidemics on random intersection graphs. Ann. Appl. Prob. 24, 1081–1128.
    Mathematical Reviews (MathSciNet): MR3199981
    Digital Object Identifier: doi:10.1214/13-AAP942
    Project Euclid: euclid.aoap/1398258096
  • Barbour, A. D. and Reinert, G. (2013). Approximating the epidemic curve. Electron. J. Prob. 18, 30 pp.
    Mathematical Reviews (MathSciNet): MR3065864
    Digital Object Identifier: doi:10.1214/EJP.v18-2557
  • Bengtsson, L. et al. (2012). Implementation of web-based respondent-driven sampling among men who have sex with men in Vietnam. PLoS ONE 7, e49417.
  • Britton, T., Deijfen, M. and Martin-Löf, A. (2006). Generating simple random graphs with prescribed degree distribution. J. Statist. Phys. 124, 1377–1397.
    Mathematical Reviews (MathSciNet): MR2266448
    Digital Object Identifier: doi:10.1007/s10955-006-9168-x
  • Britton, T., Janson, S. and Martin-Löf, A. (2007). Graphs with specified degree distributions, simple epidemics, and local vaccination strategies. Adv. Appl. Prob. 39, 922–948.
    Mathematical Reviews (MathSciNet): MR2381582
    Digital Object Identifier: doi:10.1239/aap/1198177233
    Project Euclid: euclid.aap/1198177233
  • Csardi, G. and Nepusz, T. (2006). The igraph software package for complex network research. InterJournal Complex Systems 1695.
  • Gile, K. J. (2011). Improved inference for respondent-driven sampling data with application to HIV prevalence estimation. J. Amer. Statist. Assoc. 106, 135–146.
    Mathematical Reviews (MathSciNet): MR2816708
    Digital Object Identifier: doi:10.1198/jasa.2011.ap09475
  • Gile, K. J. and Handcock, M. S. (2015). Network model-assisted inference from respondent-driven sampling data. J. R. Statist. Soc. A 178, 619–639.
    Mathematical Reviews (MathSciNet): MR3348351
    Digital Object Identifier: doi:10.1111/rssa.12091
  • Heckathorn, D. D. (1997). Respondent-driven sampling: a new approach to the study of hidden populations. Social Problems 44, 174–199.
  • Heckathorn, D. D. (2002). Respondent-driven sampling II: deriving valid population estimates from chain-referral samples of hidden populations. Social Problems 49, 11–34.
  • Lu, X., Malmros, J., Liljeros, F. and Britton, T. (2013). Respondent-driven sampling on directed networks. Electron. J. Statist. 7, 292–322.
    Mathematical Reviews (MathSciNet): MR3020422
    Digital Object Identifier: doi:10.1214/13-EJS772
    Project Euclid: euclid.ejs/1359041593
  • Malekinejad, M. et al. (2008). Using respondent-driven sampling methodology for HIV biological and behavioral surveillance in international settings: a systematic review. AIDS Behavior 12, 105–130.
  • Martin-Löf, A. (1986). Symmetric sampling procedures, general epidemic processes and their threshold limit theorems. J. Appl. Prob. 23, 265–282.
    Mathematical Reviews (MathSciNet): MR839984
    Digital Object Identifier: doi:10.2307/3214172
  • Molloy, M. and Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures Algorithms 6, 161–179.
    Mathematical Reviews (MathSciNet): MR1370952
  • Molloy, M. and Reed, B. (1998). The size of the giant component of a random graph with a given degree sequence. Comb. Prob. Comput. 7, 295–305.
    Mathematical Reviews (MathSciNet): MR1664335
    Digital Object Identifier: doi:10.1017/S0963548398003526
  • Newman, M. E. J. (2002). Spread of epidemic disease on networks. Phys. Rev. E (3) 66, 016128.
    Mathematical Reviews (MathSciNet): MR1919737
  • Salganik, M. J. and Heckathorn, D. D. (2004). Sampling and estimation in hidden populations using respondent-driven sampling. Sociological Methodol. 34, 193–239.
  • Van der Hofstad, R. (2014). Random graphs and complex networks. Vol. I. Available at http://www.win.tue.nl/\raise.17ex$\scriptstyle\sim$hofstad/NotesRGCN.html.
  • Volz, E. and Heckathorn, D. D. (2008). Probability based estimation theory for respondent driven sampling. J. Official Statist. 24, 79–97.
  • Wejnert, C. (2009). An empirical test of respondent-driven sampling: point estimates, variance, degree measures, and out-of-equilibrium data. Sociological Methodol. 39, 73–116.
  • Wejnert, C. and Heckathorn, D. D. (2008). Web-based network sampling: Efficiency and efficacy of respondent-driven sampling for online research. Sociological Meth. Res. 37, 105–134.
    Mathematical Reviews (MathSciNet): MR2516739

Applied Probability Trust

Journal of Applied Probability
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more