Brief Report: Respondent-driven Sampling Estimators Under Real and Theoretical Recruitment Conditions of Female Sex Workers in China : Epidemiology

Secondary Logo

Journal Logo

Infectious Disease

Brief Report

Respondent-driven Sampling Estimators Under Real and Theoretical Recruitment Conditions of Female Sex Workers in China

Verdery, Ashton M.a; Merli, M. Giovannab; Moody, Jamesc,d; Smith, Jeffrey A.e; Fisher, Jacob C.f

Author Information
Epidemiology 26(5):p 661-665, September 2015. | DOI: 10.1097/EDE.0000000000000335


Hidden and hard-to-reach populations, such as female sex workers and others at high risk of acquiring sexually transmitted infections (STIs), lack a sampling frame but are of special interest to public health.1 Traditional observation schemes for these populations—from direct observation to clinic-based inquiries to snowball sampling—are nonrepresentative, impeding efforts to understand STI prevalence and transmission. Respondent-driven sampling has become the dominant method for collecting generalizable samples of hidden populations, with more than $150 million in federal funding.2–4 Respondent-driven sampling uses peer referral and a dual incentive structure to recruit a sample, compensating respondents for participating and referring others. Several estimators have been suggested to reduce sampling biases in respondent-driven sampling, but each makes stringent assumptions about recruitment dynamics that may diverge from the real world.5,6 Therefore, applied researchers have little guidance on which estimator to present in manuscripts and reports.

Here, we consider the relative performance of seven estimators under ideal sample recruitment conditions as well as real-world conditions observed in respondent-driven sampling studies of female sex workers in China, a hidden population with socially ordered tiers of sex work,7,8 each related to different levels of STI infection in the backdrop of a growing Chinese STI epidemic.9–11 We examine the following respondent-driven sampling estimators: (1) naive, (2) RDS1-SH,12 (3) RDS1-DS,13 (4) RDS1-DG,14 (5) RDS2-VH,15 (6) RDS2-SS,16 and (7) RDS1-LEN17 (these estimators are discussed in the eAppendix; We anchor our evaluation in empirically grounded simulations,18 which combine novel statistical techniques for network estimation and prediction19,20 with data collected with respondent-driven sampling and a venue-based sampling approach among Chinese female sex workers. We follow up these analyses with an application of each estimator to two empirical samples of female sex workers in China.7,18

Prior Evaluations of Respondent-driven Sampling

Prior empirical assessments of the methodologic validity of respondent-driven sampling have compared it to alternative sampling approaches,21–25 or benchmarked its estimates against known population parameters in nonhidden populations.26–29 Prior studies show that respondent-driven sampling recruits samples more quickly, more cost– effectively, and with more confidentiality than other approaches, but that its estimates “are reasonable but not precise” compared with benchmarks.27 Few comparative studies have examined the validity of respondent-driven sampling assumptions in the field, but recent work has shown that respondents in the real world recruit peers preferentially, violating crucial respondent-driven sampling assumptions.7,30 Other evaluations have simulated respondent-driven sampling-style samples on synthetic or empirical social networks and evaluated robustness to violations of assumptions about social network structure,4,5,31–33 data collection practices,5,16 and recruitment dynamics,6,18 but these studies typically only look at one or two estimators; more extensive comparisons have presented inconclusive findings.6


We focus on a variable of particular relevance to the expanding STI epidemic in China: the proportion of female sex workers in low tiers of sex work, who solicit clients in saunas, massage parlors, or streets, as opposed to high-tier female sex workers who solicit clients in karaoke bars, star hotels, and night clubs.7 Tiers are a distinctive feature of sex work in Asia34 and STI infections and risky behaviors are concentrated among female sex workers in low tiers.11,35,36 The tier-based social stratification of sex work has also been shown to bias recruitment dynamics in respondent-driven sampling, leading to overestimates of the proportion in low tiers.7,18

We first consider how respondent-driven sampling estimators perform under realistic and idealized recruitment conditions using multiple data sources including (1) a population social network generated from data collected in the PLACE-RDS Comparison Study of female sex workers in Liuzhou, China,18,21 and (2) two sets of respondent-driven sampling chains simulated over this network, one that mimics recruitment patterns observed in the PLACE-RDS Comparison Study (“real-world scenario”), the other consistent with respondent-driven sampling assumptions (“ideal-world scenario”). These data sources are drawn from a previous study18 and are discussed in greater detail in the eAppendix ( After examining simulation results, we also draw on empirical respondent-driven sampling data from the PLACE-RDS Comparison Study and the Shanghai Women’s Health Survey in an application section where we explore whether the simulation results generalize to empirical contexts. Respondents in both the PLACE-RDS Comparison Study and the Shanghai Women’s Health Survey provided verbal informed consent before participation. Surveys were administered face-to-face by trained interviewers in Mandarin Chinese or Zhuang. The PLACE-RDS Comparison Study protocol was approved by the Research Ethics Committee of the National Center for STD Control, China and the Institutional Review Boards at the University of North Carolina and Duke University. The Shanghai Women’s Health Survey protocol was approved by the Research Ethics Committee of the University of Wisconsin, Madison and of the Shanghai Institute of Planned Parenthood Research.

We examine both bias (accuracy) and efficiency (precision). Bias is measured as the mean difference between the statistic and parameter across simulated samples; it reflects tendencies toward over- or underestimation of population proportions of female sex workers in low tiers. To measure efficiency, we follow the respondent-driven sampling literature and examine design effects,37,38 which are the ratio of the variance of the sampling distribution of RDS estimates to the sampling variance that would be obtained via simple random sampling. Because a biased estimator with low design effects may be preferable to one that is accurate but inefficient, we also compute the root mean square error, defined as the square root of the sum of sampling variance and squared bias. Statistical analyses were performed using SAS (version 9.3, Cary, NC) and STATA (version 13, StataCorp, College Station, TX); code for the analyses is provided in the supplementary online content.


Performance of Respondent-driven Sampling Estimators in Simulated Samples

Figure 1 focuses on how an estimator commonly presented in the literature, RDS2-VH, performs under real-world versus ideal-world conditions.5,18 Deviations from theoretical ideals in the real-world scenario lead to upward bias in the RDS2-VH estimator and to an overstatement of the fraction of the population in low tiers of sex work. However, estimates from the real-world scenario are less variable than estimates in the ideal-world scenario. Figure 2 shows the performance of all seven respondent-driven sampling estimators under the real-world scenario, where each tends to overstate the fraction of the population in low tiers of sex work. The RDS1-LEN estimator is least sensitive to these tendencies, followed by the Naive mean, which has been reported to perform well in gold-standard evaluations.28

Distributions of estimates of proportion in low tiers of sex work using the RDS2-VH estimator, by seeding and recruitment scenario. The population proportion is computed from the largest connected component of the simulated population network and is shown with a dashed vertical line. Population social network is priorities for local AIDS control efforts survey data source with venue size adjustments and weak geographic distribution of ties assumption (see eAppendix [] for description of population social networks). Distributions are plotted by kernel density estimation.
Distributions of estimates of proportion in low tiers of sex work in the real world recruitment scenario, by estimator. Dashed vertical line The population proportion. Population social network is priorities for local AIDS control efforts survey data source with venue size adjustments and weak geographic distribution of ties assumption (see eAppendix [] for description of population social networks). Recruitment and seeding scenario is matched seeds and matched recruitments.

Table 1 extends these evaluations to both recruitment scenarios and quantifies estimator performance in terms of bias, design effect, and root mean square error. The ideal-world scenario has smaller biases but larger design effects than the real-world scenario. The RDS1-LEN estimator is the least biased and has the lowest design effects under both scenarios. Other estimators show substantial biases or else persistently high design effects, at levels consistent with prior literature,4,33,38 resulting in poor root mean square errors. These conclusions are robust to the underlying population distribution of female sex workers (eAppendix;

Summary Measures of Estimator Performance for Proportion in Lower Tiers, by Scenario

Performance of Respondent-driven Sampling Estimators in Empirical Samples

Table 2 considers estimator performance in two empirical respondent-driven sampling samples of female sex workers in China, one recruited in Liuzhou for the PLACE-RDS Comparison Study in 2010,18 the other recruited in 2007 for the Shanghai Women’s HealthSurvey.7 Both studies gathered unique self-reports of network composition in follow-up interviews administered to recruiting participants when they collected incentives for successful referrals, which we use to provide the first empirical comparison of RDS1-LEN estimates to other RDS estimators.

Estimated Proportions in Low Tiers of Sex Work in Two Datasets, by Estimator

The top portion of Table 2 shows few large differences between estimates obtained in the full sample versus the subset of respondents who were administered network composition questions. The bottom portion of the table presents RDS1-LEN results for three measured network types: (1) invited peers who accepted the invitation, (2) all invited peers, and (3) a respondent’s whole network comprising both invited and uninvited peers. The eAppendix ( provides details on the measurement of these network types. Table 2 yields the following conclusions: the RDS1-LEN estimator generates estimates that suggest a smaller fraction of female sex workers in low tiers than earlier estimators, albeit with a few discrepancies across network types discussed in the eAppendix ( These results are consistent with the simulation results, indicating a smaller proportion of female sex workers in low tiers than that estimated by other estimators when applied to real-world data.


We extended prior evaluations of respondent-driven sampling by comparing seven estimators under realistic sample recruitment scenarios that applied researchers are likely to experience in the field. We find that Lu’s linked ego networks (RDS1-LEN) estimator outperforms all others in simulated samples under both ideal and realistic sample recruitment scenarios, and that these results generalize to two empirical samples of female sex workers. Compared with earlier estimators, the RDS1-LEN estimator generates lower estimates of the proportion of female sex workers in low tiers in empirical settings where respondent-driven sampling recruitment assumptions are known to be violated.7,18 By relying on self-reported personal network information, the RDS1-LEN estimator circumvents preferential recruitment biases, which confound other estimators.

This article makes two contributions to the literature. First, we demonstrate that the RDS1-LEN estimator overcomes the two the most persistent problems plaguing other respondent-driven sampling estimators: bias in the face of realistic preferential recruitment and high design effects. We also demonstrate that it is possible to collect the type of data required by the RDS1-LEN estimator in empirical settings, and we consider three separate approaches to that data collection. We used a strong approach to derive these conclusions, relying on both simulated and empirical data about hidden populations of female sex workers and simulated and comparative approaches to data analysis, which enhances our confidence that the results can generalize, at least to other populations of female sex workers.

An important early paper on respondent-driven sampling estimators considered whether “to ask respondents what percentage of their friends fall into certain groups,”12 but the authors dismissed this approach because respondents may misreport peers’ epidemiologically salient attributes, especially difficult-to-observe characteristics or behaviors, such as STI/HIV status or condom use. The chief limitation of our article is that the RDS1-LEN estimator cannot readily be extended to estimate such unobservable characteristics, which are of considerable interest to public health practitioners. However, RDS1-LEN’s outperformance of earlier estimators suggests that further attention to its development is warranted, especially gaining accurate self-reports about respondents’ personal network composition. We have highlighted measures of three different personal network types in this article, showing that they produce consistent estimates, but more work is needed to develop protocols for accurate personal network data collection in respondent-driven sampling.7,18 By comparing multiple respondent-driven sampling estimators, this article will aid applied researchers in identifying which respondent-driven sampling estimator(s) should be presented in manuscripts and policy reports on the basis of their robustness to real-world sampling conditions.


1. Heckathorn DD. Respondent-driven sampling: a new approach to the study of hidden populations. Soc Probl. 1997;44:174–199
2. White RG, Lansky A, Goel S, et al. Respondent driven sampling—where we are and where should we be going? Sex Transm Infect. 2012;88:397–399
3. Malekinejad M, Johnston LG, Kendall C, Kerr LRFS, Rifkin MR, Rutherford GW. Using Respondent-Driven Sampling Methodology for HIV Biological and Behavioral Surveillance in International Settings: A Systematic Review. AIDS Behav. 2008;12:105–130
4. Verdery AM, Mouw T, Bauldry S, Mucha PJ Network Structure and Biased Variance Estimation in Respondent Driven Sampling.. 2013 Available at: Accessed September 25, 2013
5. Gile KJ, Handcock MS. Respondent-driven sampling: an assessment of current methodology. Sociol Methodol. 2010;40:285–327
6. Tomas A, Gile KJ. The effect of differential recruitment, non-response and non-recruitment on estimators for respondent-driven sampling. Electron J Stat. 2011;5:899–934
7. Yamanis TJ, Merli MG, Neely WW, et al. An empirical analysis of the impact of recruitment patterns on RDS estimates among a socially ordered population of female sex workers in China. Sociol Methods Res. 2013
8. Huang Y, Henderson GE, Pan S, Cohen MS. HIV/AIDS risk among brothel-based female sex workers in China: assessing the terms, content, and knowledge of sex work. Sex Transm Dis. 2004;31:695–700
9. Chen XS, Peeling RW, Yin YP, Mabey DC. The epidemic of sexually transmitted infections in China: implications for control and future perspectives. BMC Med. 2011;9:111
10. Tucker JD, Cohen MS. China’s syphilis epidemic: epidemiology, proximate determinants of spread, and control responses. Curr Opin Infect Dis. 2011;24:50–55
11. Chen X-S, Wang Q-Q, Yin Y-P, et al. Prevalence of syphilis infection in different tiers of female sex workers in China: implications for surveillance and interventions. BMC Infect Dis. 2012;12:84
12. Salganik MJ, Heckathorn DD. Sampling and estimation in hidden populations using respondent-driven sampling. Sociol Methodol. 2004;34:193–240
13. Heckathorn DD. Respondent-driven sampling II: deriving valid population estimates from chain-referral samples of hidden populations. Soc Probl. 2002;49:11–34
14. Heckathorn DD. Extensions of respondent-driven sampling: analyzing continuous variables and controlling for differential recruitment. Sociol Methodol. 2007;37:151–207
15. Volz E, Heckathorn DD. Probability based estimation theory for respondent driven sampling. J Off Stat. 2008;24:79
16. Gile KJ. Improved inference for respondent-driven sampling data with application to HIV prevalence estimation. J Am Stat Assoc. 2011;106:135–146
17. Lu X. Linked Ego networks: improving estimate reliability and validity with respondent-driven sampling. Soc Netw. 2013;35:669–685
18. Merli MG, Moody J, Smith J, Li J, Weir S, Chen X. Challenges to recruiting population representative samples of female sex workers in China using respondent driven sampling. Soc Sci Med. 2015
19. Smith JA. Macrostructure from microstructure generating whole systems from Ego networks. Sociol Methodol. 2012;42:155–205
20. Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M. ergm: a package to fit, simulate and diagnose exponential-family models for networks. J Stat Softw. 2008;24:nihpa54860
21. Weir SS, Merli MG, Li J, et al. A comparison of respondent-driven and venue-based sampling of female sex workers in Liuzhou, China. Sex Transm Infect. 2012;88(Suppl 2):i95–i101
22. Burt RD, Hagan H, Sabin K, Thiede H. Evaluating respondent-driven sampling in a major metropolitan area: comparing injection drug users in the 2005 Seattle Area National HIV Behavioral Surveillance System Survey with participants in the RAVEN and Kiwi studies. Ann Epidemiol. 2010;20:159–167
23. Kendall C, Kerr LRFS, Gondim RC, et al. An empirical comparison of respondent-driven sampling, time location sampling, and snowball sampling for behavioral surveillance in men who have sex with men, Fortaleza, Brazil. AIDS Behav. 2008;12:97–104
24. Platt L, Wall M, Rhodes T, et al. Methods to recruit hard-to-reach groups: comparing two chain referral sampling methods of recruiting injecting drug users across nine studies in Russia and Estonia. J Urban Health. 2006;83:39–53
25. Ma X, Zhang Q, He X, et al. Trends in prevalence of HIV, syphilis, hepatitis C, hepatitis B, and sexual risk behavior among men who have sex with men. Results of 3 consecutive respondent-driven sampling surveys in Beijing, 2004 through 2006. J Acquir Immune Defic Syndr 1999. 2007;45:581–587
26. Wejnert C. An empirical test of respondent-driven sampling: point estimates, variance, degree measures, and out-of-equilibrium data. Sociol Methodol. 2009;39:73–116
27. Wejnert C, Heckathorn DD. Web-based network sampling efficiency and efficacy of respondent-driven sampling for online research. Sociol Methods Res. 2008;37:105–134
28. McCreesh N, Frost SDW, Seeley J, et al. Evaluation of respondent-driven sampling. Epidemiol Camb Mass. 2012;23:138–147
29. McCreesh N, Copas A, Seeley J, et al. Respondent driven sampling: determinants of recruitment and a method to improve point estimation. PLoS One. 2013;8:e78402
30. Iguchi MY, Ober AJ, Berry SH, et al. Simultaneous recruitment of drug users and men who have sex with men in the United States and Russia using respondent-driven sampling: sampling methods and implications. J Urban Health Bull N Y Acad Med. 2009;86(Suppl 1):5–31
31. Goel S, Salganik MJ. Respondent-driven sampling as Markov chain Monte Carlo. Stat Med. 2009;28:2202–2229
32. Lu X, Bengtsson L, Britton T, et al. The sensitivity of respondent-driven sampling. J R Stat Soc Ser A Stat Soc. 2012;175:191–216
33. Mouw T, Verdery AM. Network sampling with memory A proposal for more efficient sampling from social networks. Sociol Methodol. 2012;42:206–256
34. Lim LL The Sex Sector: The Economic and Social Bases of Prostitution in Southeast Asia. 1998 Geneva: International Labour Organization
35. Wang Q, Yang P, Gong XD, et al. Syphilis prevalence and high risk behaviors among female sex workers in different settings. Chin J AIDS STDs. 2009;15:398–400
36. Wang L, Ding ZW, Ding GW, et al. Data analysis of national HIV comprehensive surveillance sites among female sex workers from 2004 to 2008. Zhonghua Yu Fang Yi Xue Za Zhi. 2009;43:1009–1015
37. Salganik MJ. Variance estimation, design effects, and sample size calculations for respondent-driven sampling. J Urban Health. 2006;83:98–112
38. Goel S, Salganik MJ. Assessing respondent-driven sampling. Proc Natl Acad Sci USA. 2010;107:6743–6747

Supplemental Digital Content

Copyright © 2015 Wolters Kluwer Health, Inc. All rights reserved.