Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T22:56:30.346Z Has data issue: false hasContentIssue false
  • English
  • Français

Respondent-driven sampling and an unusual epidemic

Part of: Mathematical sociology

Published online by Cambridge University Press:  21 June 2016

J. Malmros ,
F. Liljeros  and
T. Britton
J. Malmros*
Affiliation:
Stockholm University
F. Liljeros*
Affiliation:
Stockholm University
T. Britton*
Affiliation:
Stockholm University
*
* Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.
*** Postal address: Department of Sociology, Stockholm University, SE-106 91 Stockholm, Sweden. Email address: [email protected]
* Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.
Get access Rights & Permissions [Opens in a new window]

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 R0, the probability of a major 'outbreak', and the relative size of a major outbreak for c < ∞ 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.

Keywords

Stochastic epidemic modelrespondent-driven samplingconfiguration modelReed–Frost

MSC classification

Primary: 92D30: Epidemiology
Secondary: 91D30: Social networks
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 518 - 530
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Andersson, H. and Britton, T. (2000).Stochastic Epidemic Models and Their Statistical Analysis (Lecture Notes Statist.151).Springer, New York.CrossRefGoogle Scholar
[2]Athreya, K. B. and Ney, P. E. (1972).Branching Processes.Springer, New York.CrossRefGoogle Scholar
[3]Ball, F. and Lyne, O. D. (2001).Stochastic multitype SIR epidemics among a population partitioned into households.Adv. Appl. Prob. 33, 99–123.Google Scholar
[4]Ball, F. and Neal, P. (2002).A general model for stochastic SIR epidemics with two levels of mixing.Math. Biosci. 180, 73–102.CrossRefGoogle ScholarPubMed
[5]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.) Google Scholar
[6]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.Google Scholar
[7]Ball, F. G., Sirl, D. J. and Trapman, P. (2014).Epidemics on random intersection graphs.Ann. Appl. Prob. 24, 1081–1128.CrossRefGoogle Scholar
[8]Barbour, A. D. and Reinert, G. (2013).Approximating the epidemic curve.Electron. J. Prob. 18, 30 pp.Google Scholar
[9]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.CrossRefGoogle ScholarPubMed
[10]Britton, T., Deijfen, M. and Martin-Löf, A. (2006).Generating simple random graphs with prescribed degree distribution.J. Statist. Phys. 124, 1377–1397.Google Scholar
[11]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.CrossRefGoogle Scholar
[12]Csardi, G. and Nepusz, T. (2006).The igraph software package for complex network research.InterJournal Complex Systems 1695.Google Scholar
[13]Gile, K. J. (2011).Improved inference for respondent-driven sampling data with application to HIV prevalence estimation.J. Amer. Statist. Assoc. 106, 135–146.CrossRefGoogle Scholar
[14]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.CrossRefGoogle ScholarPubMed
[15]Heckathorn, D. D. (1997).Respondent-driven sampling: a new approach to the study of hidden populations.Social Problems 44, 174–199.Google Scholar
[16]Heckathorn, D. D. (2002).Respondent-driven sampling II: deriving valid population estimates from chain-referral samples of hidden populations.Social Problems 49, 11–34.Google Scholar
[17]Lu, X., Malmros, J., Liljeros, F. and Britton, T. (2013).Respondent-driven sampling on directed networks.Electron. J. Statist. 7, 292–322.Google Scholar
[18]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.CrossRefGoogle ScholarPubMed
[19]Martin-Löf, A. (1986).Symmetric sampling procedures, general epidemic processes and their threshold limit theorems.J. Appl. Prob. 23, 265–282.CrossRefGoogle Scholar
[20]Molloy, M. and Reed, B. (1995).A critical point for random graphs with a given degree sequence.Random Structures Algorithms 6, 161–179.Google Scholar
[21]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.Google Scholar
[22]Newman, M. E. J. (2002).Spread of epidemic disease on networks.Phys. Rev. E (3) 66, 016128.Google Scholar
[23]Salganik, M. J. and Heckathorn, D. D. (2004).Sampling and estimation in hidden populations using respondent-driven sampling.Sociological Methodol. 34, 193–239.Google Scholar
[24]Van der Hofstad, R. (2014).Random graphs and complex networks. Vol. I. Available at http://www.win.tue.nl/~hofstad/NotesRGCN.html.Google Scholar
[25]Volz, E. and Heckathorn, D. D. (2008).Probability based estimation theory for respondent driven sampling.J. Official Statist. 24, 79–97.Google Scholar
[26]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.CrossRefGoogle ScholarPubMed
[27]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.Google Scholar