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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: fredrik.liljeros@sociology.su.se
* Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.
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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 

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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