Hidden Population Size Estimation From Respondent-Driven Sampling: A Network Approach

References

• Abdala, N., Carney, J. M., Durante, A. J., Klimov, N., Ostrovski, D., Somlai, A. M., Kozlov, A., and Heimer, R. (2003), “Estimating the Prevalence of Syringe-Borne and Sexually Transmitted Diseases Among Injection Drug Users in St Petersburg, Russia,” International Journal of STD and AIDS, 14, 697–703.
   PubMed Web of Science ®Google Scholar
• Abdul-Quader, A. S., Baughman, A. L., and Hladik, W. (2014), “Estimating the Size of Key Populations: Current Status and Future Possibilities,” Current Opinion in HIV and AIDS, 9, 107–114.
   PubMed Web of Science ®Google Scholar
• Balabanova, Y., Coker, R., Atun, R., and Drobniewski, F. (2006), “Stigma and HIV Infection in Russia,” AIDS Care, 18, 846–852.
   PubMed Web of Science ®Google Scholar
• Bao, L., Raftery, A. E., and Reddy, A. (2010), “Estimating the Size of Populations at High Risk of HIV in Bangladesh Using a Bayesian Hierarchical Model,” Technical Report 573, Department of Statistics, University of Washington.
   Google Scholar
• ——— (2015), “Estimating the Sizes of Populations at Risk of HIV Infection From Multiple Data Sources Using a Bayesian Hierarchical Model,” Statistics and Its Interface, 8, 125–136.
   PubMed Web of Science ®Google Scholar
• Berchenko, Y., and Frost, S. D. (2011), “Capture-Recapture Methods and Respondent-Driven Sampling: Their Potential and Limitations,” Sexually Transmitted Infections, 87, 267–268.
   PubMed Web of Science ®Google Scholar
• Berchenko, Y., Rosenblatt, J., and Frost, S. D. (2017), “Modeling and Analysing Respondent Driven Sampling as a Counting Process,” Biometrics, available at http://onlinelibrary.wiley.com/doi/10.1111/biom.12678/full.
   Google Scholar
• Bernard, H. R., Hallett, T., Iovita, A., Johnsen, E. C., Lyerla, R., McCarty, C., Mahy, M., Salganik, M. J., Saliuk, T., Scutelniciuc, O., Shelley, G. A., Sirinirund, P., Weir, S., and Stroup, D. F. (2010), “Counting Hard-to-Count Populations: The Network Scale-Up Method for Public Health,” Sexually Transmitted Infections, 86, ii11–ii15.
   PubMed Web of Science ®Google Scholar
• Bernard, H. R., Killworth, P. D., Johnsen, E. C., Shelley, G. A., and McCarty, C. (2001), “Estimating the Ripple Effect of a Disaster,” Connections, 24, 18–22.
   Google Scholar
• Bickel, P. J., Nair, V. N., and Wang, P. C. (1992), “Nonparametric Inference Under Biased Sampling From a Finite Population,” The Annals of Statistics, 20, 853–878.
   Web of Science ®Google Scholar
• Broadhead, R. S., Heckathorn, D. D., Weakliem, D. L., Anthony, D. L., Madray, H., Mills, R. J., and Hughes, J. (1998), “Harnessing Peer Networks as an Instrument for AIDS Prevention: Results From a Peer-Driven Intervention,” Public Health Reports, 113, 42–57.
   PubMed Web of Science ®Google Scholar
• Burke, S. E., Calabrese, S. K., Dovidio, J. F., Levina, O. S., Uusküla, A., Niccolai, L. M., Abel-Ollo, K., and Heimer, R. (2015), “A Tale of Two Cities: Stigma and Health Outcomes Among People With HIV Who Inject Drugs in St. Petersburg, Russia and Kohtla-Järve, Estonia,” Social Science and Medicine, 130, 154–161.
   PubMed Web of Science ®Google Scholar
• Cepeda, J. A., Odinokova, V. A., Heimer, R., Grau, L. E., Lyubimova, A., Safiullina, L., Levina, O. S., and Niccolai, L. M. (2011), “Drug Network Characteristics and HIV Risk Among Injection Drug Users in Russia: The Roles of Trust, Size, and Stability,” AIDS and Behavior, 15, 1003–1010.
   PubMed Web of Science ®Google Scholar
• Crawford, F. W. (2016), “The Graphical Structure of Respondent-Driven Sampling,” Sociological Methodology, 46, 187–211.
   PubMed Web of Science ®Google Scholar
• Dávid, B., and Snijders, T. A. (2002), “Estimating the Size of the Homeless Population in Budapest, Hungary,” Quality and Quantity, 36, 291–303.
   Web of Science ®Google Scholar
• Draper, N., and Guttman, I. (1971), “Bayesian Estimation of the Binomial Parameter,” Technometrics, 13, 667–673.
   Web of Science ®Google Scholar
• Erdős, P., and Gallai, T. (1960), “Gráfok Előírt Fokszámú Pontokkal,” Matematikai Lapok, 11, 264–274.
   Google Scholar
• Erdős, P., and Rényi, A. (1959), “On Random Graphs,” Publicationes Mathematicae Debrecen, 6, 290–297.
   Google Scholar
• Erdős, P., and Rényi, A. (1960), “On the Evolution of Random Graphs,” Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17–61.
   Google Scholar
• Ezoe, S., Morooka, T., Noda, T., Sabin, M. L., and Koike, S. (2012), “Population Size Estimation of Men Who Have Sex With Men Through the Network Scale-Up Method in Japan,” Plos One, 7, e31184.
   PubMed Web of Science ®Google Scholar
• Feehan, D. M., and Salganik, M. J. (2016), “Generalizing the Network Scale-Up Method: A New Estimator for the Size of Hidden Populations,” Sociological Methodology, 46, 153–186.
   PubMed Web of Science ®Google Scholar
• Feehan, D. M., Umubyeyi, A., Mahy, M., Hladik, W., and Salganik, M. J. (2016), “Quantity Versus Quality: A Survey Experiment to Improve the Network Scale-Up Method,” American Journal of Epidemiology, 183, 747–757.
   PubMed Web of Science ®Google Scholar
• Félix-Medina, M. H., and Monjardin, P. E. (2009), “Link-Tracing Sampling With an Initial Sequential Sample of Sites: Estimating the Size of a Hidden Human Population,” Statistical Methodology, 6, 490–502.
   Google Scholar
• Félix-Medina, M. H., and Thompson, S. K. (2004), “Combining Link-Tracing Sampling and Cluster Sampling to Estimate the Size of Hidden Populations,” Journal of Official Statistics, 20, 19–38.
   Google Scholar
• Fienberg, S. E. (1972), “The Multiple Recapture Census for Closed Populations and Incomplete 2k Contingency Tables,” Biometrika, 59, 591–603.
   Web of Science ®Google Scholar
• Frank, O., and Snijders, T. (1994), “Estimating the Size of Hidden Populations Using Snowball Sampling,” Journal of Official Statistics 10, 53–53.
   Google Scholar
• Gile, K. J. (2011), “Improved Inference for Respondent-Driven Sampling Data With Application to HIV Prevalence Estimation,” Journal of the American Statistical Association, 106, 135–146.
   Web of Science ®Google Scholar
• Gile, K. J., and Handcock, M. S. (2010), “Respondent-Driven Sampling: An Assessment of Current Methodology,” Sociological Methodology, 40, 285–327.
   PubMed Web of Science ®Google Scholar
• Gile, K. J., Johnston, L. G., and Salganik, M. J. (2015), “Diagnostics for Respondent-Driven Sampling,” Journal of the Royal Statistical Society, Series A, 178, 241–269.
   Google Scholar
• Goodman, L. A. (1961), “Snowball Sampling,” The Annals of Mathematical Statistics, 32, 148–170.
   Google Scholar
• Guo, W., Bao, S., Lin, W., Wu, G., Zhang, W., Hladik, W., Abdul-Quader, A., Bulterys, M., Fuller, S., and Wang, L. (2013), “Estimating the Size of HIV Key Affected Populations in Chongqing, China, Using the Network Scale-Up Method,” PloS One, 8, e71796.
   PubMed Web of Science ®Google Scholar
• Habecker, P., Dombrowski, K., and Khan, B. (2015), “Improving the Network Scale-Up Estimator: Incorporating Means of Sums, Recursive Back Estimation, and Sampling Weights,” PloS One, 10.
   PubMed Web of Science ®Google Scholar
• Hall, W. D., Ross, J. E., Lynskey, M. T., Law, M. G., and Degenhardt, L. J. (2000), “How Many Dependent Heroin Users are There in Australia?” Medical Journal of Australia, 173, 528–531.
   PubMed Web of Science ®Google Scholar
• Handcock, M. S., Fellows, I. E., and Gile, K. J. (2014), RDS Analyst: Software for the Analysis of Respondent-Driven Sampling Data, Los Angeles, CA. Version 0.42. Available at http://hpmrg.org
   Google Scholar
• Handcock, M. S., Gile, K. J., and Mar, C. M. (2014), “Estimating Hidden Population Size Using Respondent-Driven Sampling Data,” Electronic Journal of Statistics, 8, 1491–1521.
   PubMed Web of Science ®Google Scholar
• Handcock, M. S., Gile, K. J., and Mar, C. M. (2015), “Estimating the Size of Populations at High Risk for Hiv Using Respondent-Driven Sampling Data,” Biometrics, 71, 258–266.
   PubMed Web of Science ®Google Scholar
• Heckathorn, D. D. (1997), “Respondent-Driven Sampling: a New Approach to the Study of Hidden Populations,” Social Problems, 44, 174–199.
   Web of Science ®Google Scholar
• Heimer, R., and White, E. (2010), “Estimation of the Number of Injection Drug Users in St. Petersburg, Russia,” Drug and Alcohol Dependence, 109, 79–83.
   PubMed Web of Science ®Google Scholar
• Hickman, M., Hickman, M., Hope, V., Platt, L., Higgins, V., Bellis, M., Rhodes, T., Taylor, C., and Tilling, K. (2006), “Estimating Prevalence of Injecting Drug Use: A Comparison of Multiplier and Capture-Recapture Methods in Cities in England and Russia,” Drug and Alcohol Review, 25, 131–140.
   PubMed Web of Science ®Google Scholar
• Hunter, D. R., and Handcock, M. S. (2006), “Inference in Curved Exponential Family Models for Networks,” Journal of Computational and Graphical Statistics, 15, 565–583.
   Web of Science ®Google Scholar
• Johnston, L. G., McLaughlin, K. R., El Rhilani, H., Latifi, A., Toufik, A., Bennani, A., Alami, K., Elomari, B., and Handcock, M. S. (2015), “Estimating the Size of Hidden Populations Using Respondent-Driven Sampling Data: Case Examples From Morocco,” Epidemiology, 26, 846–852.
   PubMed Web of Science ®Google Scholar
• Johnston, L. G., McLaughlin, K. R., Rouhani, S. A., and Bartels, S. A. (2017), “Measuring a Hidden Population: A Novel Technique to Estimate the Population Size of Women With Sexual Violence-Related Pregnancies in South Kivu Province, Democratic Republic of Congo,” Journal of Epidemiology and Global Health, 7, 45–53.
   PubMed Web of Science ®Google Scholar
• Kadushin, C., Killworth, P. D., Bernard, H. R., and Beveridge, A. A. (2006), “Scale-up Methods as Applied to Estimates of Heroin Use,” Journal of Drug Issues, 36, 417–440.
   Web of Science ®Google Scholar
• Kahn, W. D. (1987), “A Cautionary Note for Bayesian Estimation of the Binomial Parameter n,” The American Statistician, 41, 38–40.
   Web of Science ®Google Scholar
• Kaplan, E. H., and Soloshatz, D. (1993), “How Many Drug Injectors are There in New Haven? Answers From AIDS Data,” Mathematical and Computer Modelling, 17, 109–115.
   Google Scholar
• Khalid, F. J., Hamad, F. M., Othman, A. A., Khatib, A. M., Mohamed, S., Ali, A. K., and Dahoma, M. J. (2014), “Estimating the Number of People Who Inject Drugs, Female Sex Workers, and Men Who Have Sex With Men, Unguja Island, Zanzibar: Results and Synthesis of Multiple Methods,” AIDS and Behavior, 18, 25–31.
   Web of Science ®Google Scholar
• Killworth, P. D., McCarty, C., Bernard, H. R., Shelley, G. A., and Johnsen, E. C. (1998), “Estimation of Seroprevalence, Rape, and Homelessness in the United States Using a Social Network Approach,” Evaluation Review, 22, 289–308.
   PubMed Web of Science ®Google Scholar
• Kozlov, A. P., Shaboltas, A. V., Toussova, O. V., Verevochkin, S. V., Masse, B. R., Perdue, T., Beauchamp, G., Sheldon, W., Miller, W. C., Heimer, R. Ryder, R. W., and Hoffman, I. F. (2006), “HIV Incidence and Factors Associated with HIV Acquisition Among Injection Drug Users in St Petersburg, Russia,” AIDS, 20, 901–906.
   PubMed Web of Science ®Google Scholar
• Larson, A., Stevens, A., and Wardlaw, G. (1994), “Indirect Estimates of ‘Hidden’ Populations: Capture-Recapture Methods to Estimate the Numbers of Heroin Users in the Australian Capital Territory,” Social Science and Medicine, 39, 823–831.
   PubMed Web of Science ®Google Scholar
• Laska, E. M., Meisner, M., and Siegel, C. (1988), “Estimating the Size of a Population From a Single Sample,” Biometrics, 44, 461–472.
   Web of Science ®Google Scholar
• Malmros, J., Liljeros, F., and Britton, T. (2016), “Respondent-Driven Sampling and an Unusual Epidemic,” Journal of Applied Probability, 53, 518–530.
   Web of Science ®Google Scholar
• Maltiel, R., Raftery, A. E., McCormick, T. H., and Baraff, A. J. (2015), “Estimating Population Size Using the Network Scale Up Method,” The Annals of Applied Statistics, 9, 1247–1277.
   PubMed Web of Science ®Google Scholar
• McCormick, T. H., Salganik, M. J., and Zheng, T. (2010), “How Many People Do You Know?: Efficiently Estimating Personal Network Size,” Journal of the American Statistical Association, 105, 59–70.
   PubMed Web of Science ®Google Scholar
• Niccolai, L. M., Toussova, O. V., Verevochkin, S. V., Barbour, R., Heimer, R., and Kozlov, A. P. (2010), “High HIV Prevalence, Suboptimal HIV Testing, and Low Knowledge of HIV-Positive Serostatus Among Injection Drug Users in St. Petersburg, Russia,” AIDS and Behavior, 14, 932–941.
   PubMed Web of Science ®Google Scholar
• Niccolai, L. M., Verevochkin, S. V., Toussova, O. V., White, E., Barbour, R., Kozlov, A. P., and Heimer, R. (2011), “Estimates of HIV Incidence Among Drug Users in St. Petersburg, Russia: Continued Growth of a Rapidly Expanding Epidemic,” The European Journal of Public Health, 21, 613–619.
   PubMed Web of Science ®Google Scholar
• Nikfarjam, A., Shokoohi, M., Shahesmaeili, A., Haghdoost, A. A., Baneshi, M. R., Haji-Maghsoudi, S., Rastegari, A., Nasehi, A. A., Memarian, N., and Tarjoman, T. (2016), “National Population Size Estimation of Illicit Drug Users Through the Network Scale-Up Method in 2013 in Iran,” International Journal of Drug Policy, 31, 147–152.
   PubMed Web of Science ®Google Scholar
• Paz-Bailey, G., Jacobson, J., Guardado, M., Hernandez, F., Nieto, A., Estrada, M., and Creswell, J. (2011), “How Many Men Who Have Sex With Men and Female Sex Workers Live in El Salvador? Using Respondent-Driven Sampling and Capture–Recapture to Estimate Population Sizes,” Sexually Transmitted Infections, 87, 279–282.
   PubMed Web of Science ®Google Scholar
• Pokrovsky, V., Ladnaya, N., and Buravtsova, E. (2010), HIV Infection: Information Bulletin # 34, Moscow, RF: Russian Federal AIDS Center.
   Google Scholar
• Quaye, S., Raymond, H. F., Atuahene, K., Amenyah, R., Aberle-Grasse, J., McFarland, W., El-Adas, A., and Ghana Men Study Group, (2015), “Critique and Lessons Learned From Using Multiple Methods to Estimate Population Size of Men Who Have Sex With Men in Ghana,” AIDS and Behavior, 19, 16–23.
   Web of Science ®Google Scholar
• Raftery, A. E. (1988), “Inference for the Binomial N Parameter: A Hierarchical Bayes Approach,” Biometrika, 75, 223–228.
   Web of Science ®Google Scholar
• Rhodes, T., Sarang, A., Bobrik, A., Bobkov, E., and Platt, L. (2004), “HIV Transmission and HIV Prevention Associated With Injecting Drug Use in the Russian Federation,” International Journal of Drug Policy, 15, 1–16.
   Google Scholar
• Robins, G., Elliott, P., and Pattison, P. (2001), “Network Models for Social Selection Processes,” Social Networks, 23, 1–30.
   Web of Science ®Google Scholar
• Sabin, K., Zhao, J., Calleja, J. M. G., Sheng, Y., Garcia, S. A., Reinisch, A., and Komatsu, R. (2016), “Availability and Quality of Size Estimations of Female Sex Workers, Men Who Have Sex With Men, People Who Inject Drugs and Transgender Women in Low-and Middle-Income Countries,” PloS One, 11, e0155150.
   PubMed Web of Science ®Google Scholar
• Salganik, M. J., Fazito, D., Bertoni, N., Abdo, A. H., Mello, M. B., and Bastos, F. I. (2011), “Assessing Network Scale-Up Estimates for Groups Most at Risk of HIV/AIDS: Evidence From a Multiple-Method Study of Heavy Drug Users in Curitiba, Brazil,” American Journal of Epidemiology, 174, 1190–1196.
   PubMed Web of Science ®Google Scholar
• Salganik, M. J., and Heckathorn, D. D. (2004), “Sampling and Estimation in Hidden Populations Using Respondent-Driven Sampling,” Sociological Methodology, 34, 193–240.
   Web of Science ®Google Scholar
• Sarang, A., Rhodes, T., and Sheon, N. (2012), “Systemic Barriers Accessing HIV Treatment Among People Who Inject Drugs in Russia: A Qualitative Study,” Health Policy and Planning, 28, 681–691.
   PubMed Web of Science ®Google Scholar
• Shaboltas, A. V., Toussova, O. V., Hoffman, I. F., Heimer, R., Verevochkin, S. V., Ryder, R. W., Khoshnood, K., Perdue, T., Masse, B. R., and Kozlov, A. P. (2006), “HIV Prevalence, Sociodemographic, and Behavioral Correlates and Recruitment Methods Among Injection Drug Users in St. Petersburg, Russia,” Journal of Acquired Immune Deficiency Syndromes, 41, 657–663.
   PubMed Web of Science ®Google Scholar
• Shelley, G. A., Bernard, H. R., Killworth, P., Johnsen, E., and McCarty, C. (1995), “Who Knows Your HIV Status? What HIV+ Patients and Their Network Members Know About Each Other,” Social Networks, 17, 189–217.
   Web of Science ®Google Scholar
• Shelley, G. A., Killworth, P. D., Bernard, H. R., McCarty, C., Johnsen, E. C., and Rice, R. E. (2006), “Who Knows Your HIV Status II?: Information Propagation Within Social Networks of Seropositive People,” Human Organization, 65, 430–444.
   Web of Science ®Google Scholar
• Shelton, J. F. (2015), “Proposed Utilization of the Network Scale-Up Method to Estimate the Prevalence of Trafficked Persons,” Forum on Crime and Society: Special Issue Researching Hidden Populations: Approaches to and Methodologies for Generating Data on Trafficking in Persons, 8, 85–94.
   Google Scholar
• Shokoohi, M., Baneshi, M. R., and Haghdoost, A. (2012), “Size Estimation of Groups at High Risk of HIV/AIDS Using Network Scale up in Kerman, Iran,” International Journal of Preventive Medicine, 3, 471–476.
   PubMedGoogle Scholar
• Snidero, S., Corradetti, R., and Gregori, D. (2004), “The Network Scale-Up Method: A Simulation Study in Case of Overlapping Sub-Populations,” Metodoloski Zvezki, 1, 395–405.
   Google Scholar
• Thein, S. T., Aung, T., and McFarland, W. (2015), “Estimation of the Number of Female Sex Workers in Yangon and Mandalay, Myanmar,” AIDS and Behavior, 19, 1941–1947.
   PubMed Web of Science ®Google Scholar
• Thompson, S. K. (2006), “Adaptive Web Sampling,” Biometrics, 62, 1224–1234.
   PubMed Web of Science ®Google Scholar
• Tripathi, A., and Vijay, S. (2003), “A Note on a Theorem of Erdős and Gallai,” Discrete Mathematics, 265, 417–420.
   Web of Science ®Google Scholar
• UNAIDS (2010a), Global Report: UNAIDS Report on the Global AIDS Epidemic 2010, Geneva: UNAIDS. Available at http://www.unaids.org/globalreport/
   Google Scholar
• ———. (2010b), Guidelines on Estimating the Size of Populations Most at Risk to HIV, Geneva, Switzerland: UNAIDS/WHO Working Group on Global HIV/AIDS and STI Surveillance.
   Google Scholar
• van der Heijden, P. G., de Vries, L., Böhning, D., and Cruyff, M. (2015), “Estimating the Size of Hard-to-Reach Populations Using Capture-Recapture Methodology, With a Discussion of the International Labour Organization’s Global Estimate of Forced Labour,” Forum on Crime and Society: Special Issue Researching Hidden Populations: Approaches to and Methodologies for Generating Data on Trafficking in Persons, 8, 109–136.
   Google Scholar
• Vincent, K., and Thompson, S. (2016), “Estimating Population Size With Link-Tracing Sampling,” Journal of the American Statistical Association, accepted.
   Web of Science ®Google Scholar
• Volz, E., and Heckathorn, D. D. (2008), “Probability Based Estimation Theory for Respondent Driven Sampling,” Journal of Official Statistics, 24, 79–97.
   Web of Science ®Google Scholar
• Wang, J., Yang, Y., Zhao, W., Su, H., Zhao, Y., Chen, Y., Zhang, T., and Zhang, T. (2015), “Application of Network Scale Up Method in the Estimation of Population Size for Men Who Have Sex With Men in Shanghai, China,” PLoS ONE, 10, 1–12.
   Web of Science ®Google Scholar
• Watts, D. J., and Strogatz, S. H. (1998), “Collective Dynamics of ‘Small-World’ Networks,” Nature, 393, 440–442.
   PubMed Web of Science ®Google Scholar
• Wejnert, C., and Heckathorn, D. (2011), “Respondent-Driven Sampling: Operational Procedures, Evolution of Estimators, and Topics for Future Research,” in The SAGE Handbook of Innovation in Social Research Methods, eds. M. Williams and W. P. Vogt, London: SAGE Publications, Ltd’, Thousand Oaks, CA: SAGE Publications, Inc., pp. 473–497.
   Google Scholar
• Wesson, P., Handcock, M. S., McFarland, W., and Raymond, H. F. (2015), “If You are Not Counted, You Don’t Count: Estimating the Number of African-American Men Who Have Sex With Men in San Francisco Using a Novel Bayesian Approach,” Journal of Urban Health, 92, 1052–1064.
   PubMed Web of Science ®Google Scholar
• World Health Organization (2005), “Russian Federation: Summary Country Profile for HIV/AIDS Treatment Scale-Up,” available at http://www.who.int/hiv/HIVCP_RUS.pdf
   Google Scholar
• ——— (2014), “Consolidated Guidelines on HIV Prevention, Diagnosis, Treatment and Care for Key Population,” available at http://who.int/hiv/pub/guidelines/keypopulations/en/
   Google Scholar
• Zheng, T., Salganik, M. J., and Gelman, A. (2006), “How Many People Do You Know in Prison? Using Overdispersion in Count Data to Estimate Social Structure in Networks,” Journal of the American Statistical Association, 101, 409–423.
   Web of Science ®Google Scholar