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Sampling from networks: respondent-driven sampling

  • Mamadou Yauck ORCID logo EMAIL logo , Erica E.M. Moodie ORCID logo , Herak Apelian , Marc-Messier Peet , Gilles Lambert , Daniel Grace , Nathan J. Lachowsky , Trevor A. Hart and Joseph Cox
From the journal Epidemiologic Methods



Respondent-Driven Sampling (RDS) is a variant of link-tracing, a sampling technique for surveying hard-to-reach communities that takes advantage of community members' social networks to reach potential participants. While the RDS sampling mechanism and associated methods of adjusting for the sampling at the analysis stage are well-documented in the statistical sciences literature, methodological focus has largely been restricted to estimation of population means and proportions, while giving little to no consideration to the estimation of population network parameters. As a network-based sampling method, RDS is faced with the fundamental problem of sampling from population networks where features such as homophily (the tendency for individuals with similar traits to share social ties) and differential activity (the ratio of the average number of connections by attribute) are sensitive to the choice of a sampling method.


Many simple approaches exist to generate simulated RDS data, with specific levels of network features (mainly homophily and differential activity), where the focus is on estimating means and proportions (Gile 2011; Gile et al. 2015; Spiller et al. 2018). However, recent findings on the inconsistency of estimators of network features such as homophily in partially observed networks (Crawford et al. 2017; Shalizi and Rinaldo 2013) raise the question of whether those target features can be recovered using the observed RDS data alone – as recovering information about these features is critical if we wish to condition upon them. In this paper, we conduct a simulation study to assess the accuracy of existing RDS simulation methods, in terms of their abilities to generate RDS samples with the desired levels of two network parameters: homophily and differential activity.


The results show that (1) homophily cannot be consistently estimated from simulated RDS samples and (2) differential activity estimators are more precise when groups, defined by traits, are equally active and equally represented in the population. We use this approach to mimic features of the Engage Study, an RDS sample of gay, bisexual and other men who have sex with men in Montréal, Canada.


In this paper, we highlight that it is possible, in some cases, to simulate population networks by mimicking the characteristics of real-world RDS data while retaining accuracy and precision for target network features in the samples.

Corresponding author: Mamadou Yauck, Department of Epidemiology, Biostatistics & Occupational Health, McGill University, Montréal, QC, Canada, E-mail:

Funding source: Natural Sciences and Engineering Research Council (NSERC) of Canada

Award Identifier / Grant number: RGPIN-2019-04230


The authors would like to thank the Engage study participants, office staff, and community engagement committee members, as well as our community partner agencies REZO, ACCM and Maison Plein Coeur. The authors also wish to acknowledge the support of David M. Moore, Nathan J. Lachowsky and Jody Jollimore and their contributions to the work presented here. Engage/Momentum II is funded by the Canadian Institutes for Health Research (CIHR, TE2-138299), the CIHR Canadian HIV/AIDS Trails Network (CTN300), the Canadian Foundation for AIDS Research (CANFAR, Engage), the Ontario HIV Treatment Network (OHTN, 1051), the Public Health Agency of Canada (Ref: 4500370314), Canadian Blood Services (MSM2017LP-OD), and the Ministère de la Santé et des Services sociaux (MSSS) du Québec. Erica E. M. Moodie acknowledges a chercheur boursier senior career award from the Fonds de recherche du Québec – Santé.

  1. Research funding: MY is funded by a Postdoctoral Fellowship jointly sponsored by the Statistical and Applied Mathematical Sciences Institute (SAMSI) and the Canadian Statistical Sciences Institute (CANSSI). The methodological developments in this manuscript are supported by a Discovery Grant to EEMM from the Canadian Natural Sciences and Research Council (NSERC), grant #RGPIN-2019-04230.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: Authors state no conflict of interest.

  4. Informed consent: Not applicable.

  5. Ethical approval: Not applicable.


Table 4:

Characteristics of the Engage population network and RDS sample.

Parameter Estimated value 95% CI
Population network
Population size 40,400
Mean degree 16.63
Prevalence, %
 Condomless anal sex in the past six months 57.9 [52.7, 63.0]
 Currently in a relationship 43.9 [38.8, 49.0]
 HIV positive 12.7 [9.3, 16.0]
RDS sample
Number of seeds 27
Number of recruits
 0 651
 1 236
 2 117
 3 81
 4 49
 5 27
 6 18
Sample size 1,179
Table 5:

(Pearson) correlation matrix of three nodal covariates for the Engage RDS sample. Unweighted and weighted correlations are displayed, with weighted correlations in parenthesis.

1. CAS 2. CIR 3. HIV+
1. Condomless anal sex (CAS) 1 0.104*** (0.115***) 0.023 (0.018)
2. Currently in a relationship (CIR) 1 0.046 (0.002)
3. HIV positive (HIV+) 1
  1. ***p-Value <0.001.


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Received: 2020-08-20
Accepted: 2020-12-29
Published Online: 2021-01-20

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