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Estimating the size of stigmatized, hidden, or hard-to-reach populations is a major problem in epidemiology, demography, and public health research. Capture-recapture and multiplier methods are standard tools for inference of hidden population sizes, but they require random sampling of target population members, which is rarely possible. Respondent-driven sampling (RDS) is a survey method for hidden populations that relies on social link tracing. The RDS recruitment process is designed to spread through the social network connecting members of the target population. In this article, we show how to use network data revealed by RDS to estimate hidden population size. The key insight is that the recruitment chain, timing of recruitments, and network degrees of recruited subjects provide information about the number of individuals belonging to the target population who are not yet in the sample. We use a computationally efficient Bayesian method to integrate over the missing edges in the subgraph of recruited individuals. We validate the method using simulated data and apply the technique to estimate the number of people who inject drugs in St. Petersburg, Russia. Supplementary materials for this article are available online.

The network scale-up method enables researchers to estimate the sizes of hidden populations, such as drug injectors and sex workers, using sampled social network data. The basic scale-up estimator offers advantages over other size estimation techniques, but it depends on problematic modeling assumptions. The authors propose a new generalized scale-up estimator that can be used in settings with nonrandom social mixing and imperfect awareness about membership in the hidden population. In addition, the new estimator can be used when data are collected via complex sample designs and from incomplete sampling frames. However, the generalized scale-up estimator also requires data from two samples: one from the frame population and one from the hidden population. In some situations these data from the hidden population can be collected by adding a small number of questions to already planned studies. For other situations, the authors develop interpretable adjustment factors that can be applied to the basic scale-up estimator. The authors conclude with practical recommendations for the design and analysis of future studies.

Respondent-driven sampling (RDS) is a chain-referral method for sampling members of hidden or hard-to-reach populations, such as sex workers, homeless people, or drug users, via their social networks. Most methodological work on RDS has focused on inference of population means under the assumption that subjects' network degree determines their probability of being sampled. Criticism of existing estimators is usually focused on missing data: the underlying network is only partially observed, so it is difficult to determine correct sampling probabilities. In this article, the author shows that data collected in ordinary RDS studies contain information about the structure of the respondents' social network. The author constructs a continuous-time model of RDS recruitment that incorporates the time senes of recruitment events, the pattern of coupon use, and the network degrees of sampled subjects. Together, the observed data and the recruitment model place a well-defined probability distribution on the recruitment-induced subgraph of respondents. The author shows that this distribution can be interpreted as an exponential random graph model and develops a computationally efficient method for estimating the hidden graph. The author validates the method using simulated data and applies the technique to an RDS study of injection drug users in St. Petersburg, Russia.

A population is \"hidden\" when no sampling frame exists and public acknowledgment of membership in the population is potentially threatening. Accessing such populations is difficult because standard probability sampling methods produce low response rates and responses that lack candor. Existing procedures for sampling these populations, including snowball and other chain-referral samples, the key-informant approach, and targeted sampling, introduce well-documented biases into their samples. This paper introduces a new variant of chain-referral sampling, respondent-driven sampling, that employs a dual system of structured incentives to overcome some of the deficiencies of such samples. A theoretic analysis, drawing on both Markov-chain theory and the theory of biased networks, shows that this procedure can reduce the biases generally associated with chain-referral methods. The analysis includes a proof showing that even though sampling begins with an arbitrarily chosen set of initial subjects, as do most chain-referral samples, the composition of the ultimate sample is wholly independent of those initial subjects. The analysis also includes a theoretic specification of the conditions under which the procedure yields unbiased samples. Empirical results, based on surveys of 277 active drug injectors in Connecticut, support these conclusions. Finally, the conclusion discusses how respondent-driven sampling can improve both network sampling and ethnographic 44investigation.

•Estimating the size of hidden populations often relies on difficult to obtain data.•Respondent-driven sampling (RDS) is often used to sample hidden populations.•RDS collects data on recruitment and social network size.•We introduce a method (SS-PSE) to estimate population sizes using RDS data.•SS-PSE reduces the cost and effort of estimating the size of hidden populations. Successive sampling (SS)–population size estimation (PSE) is a technique used to estimate the sizes of hidden populations using data collected in respondent-driven sampling (RDS) surveys. We assess past estimations and use new data from an RDS survey to calculate a new PSE. In 2012, 852 adult women in South Kivu Province, Democratic Republic of Congo, who self-identified as survivors of sexual violence, resulting in a pregnancy, since the start of the war (in 1996) were sampled using RDS. We used imputed visibility, enrollment order, and prior estimates for PSE using SS-PSE in RDS Analyst. Prior estimates varied between Congolese local experts and researchers. We calculated the PSE of women with a sexual violence-related pregnancy in South Kivu using researchers’ priors to be approximately 17,400. SS–PSE is an effective method for estimating the population sizes of hidden populations, useful for providing evidence for services and resource allocation. SS–PSE is beneficial because population sizes can be calculated after conducting the survey and do not rely on separate studies or additional data (as in network scale-up, multiplier, and capture-recapture methods).

Certain social groups are often difficult for researchers to access because of their social or physical location, vulnerability, or otherwise hidden nature. This unique review article based on both the small body of relevant literature and our own experiences as researchers is meant as a guide for those seeking to include hard-to-reach, hidden, and vulnerable populations in research. We make recommendations for research process starting from early stages of study design to dissemination of study results. Topics covered include participant mistrust of the research process; social, psychological, and physical risks to participation; participant resource constraints; and challenges inherent in nonprobability sampling, snowball sampling, and derived rapport. This article offers broadly accessible solutions for qualitative researchers across social science disciplines attempting to research a variety of different populations.

Network sampling emerged as a set of methods for drawing statistically valid samples of hard-to-reach populations. The first form of network sampling, multiplicity sampling, involved asking respondents about events affecting those in their personal networks; it was subsequently applied to studies of homicide, HIV, and other topics, but its usefulness is limited to public events. Link-tracing designs employ a different approach to study hard-to-reach populations, using a set of respondents that expands in waves as each round of respondents recruit their peers. Link-tracing as applied to hidden populations, often described as snowball sampling, was initially considered a form of convenience sampling. This changed with the development of respondent-driven sampling (RDS), a widely used network sampling method in which the link-tracing design is adapted to provide the basis for statistical inference. The literature on RDS is large and rapidly expanding, involving contributions by numerous independent research groups employing data from dozens of different countries. Within this literature, many important research questions remain unresolved, including how best to choose among alternative RDS estimators, how to refine existing estimators to make them less dependent on assumptions that are sometimes counterfactual, and perhaps the greatest unresolved issue, how best to calculate the variability of the estimates.

Respondent-driven sampling is a form of link-tracing network sampling, which is widely used to study hard-to-reach populations, often to estimate population proportions. Previous treatments of this process have used a with-replacement approximation, which we show induces bias in estimates for large sample fractions and differential network connectedness by characteristic of interest. We present a treatment of respondent-driven sampling as a successive sampling process. Unlike existing representations, our approach respects the essential without-replacement feature of the process, while converging to an existing with-replacement representation for small sample fractions, and to the sample mean for a full-population sample. We present a successive-sampling based estimator for population means based on respondent-driven sampling data, and demonstrate its superior performance when the size of the hidden population is known. We present sensitivity analyses for unknown population sizes. In addition, we note that like other existing estimators, our new estimator is subject to bias induced by the selection of the initial sample. Using data collected among three populations in two countries, we illustrate the application of this approach to populations with varying characteristics. We conclude that the successive sampling estimator improves on existing estimators, and can also be used as a diagnostic tool when population size is not known. This article has supplementary material online.

A decline in response rates in traditional household surveys, combined with increased internet coverage and decreased research budgets, has resulted in increased attractiveness of web survey research designs based on purposive and voluntary opt-in sampling strategies. In the study of hidden or stigmatised behaviours, such as cannabis use, web survey methods are increasingly common. However, opt-in web surveys are often heavily criticised due to their lack of sampling frame and unknown representativeness. In this article, we outline the current state of the debate about the relevance of pursuing representativeness, the state of probability sampling methods, and the utility of non-probability, web survey methods especially for accessing hidden or minority populations. Our article has two aims: (1) to present a comprehensive description of the methodology we use at Global Drug Survey (GDS), an annual cross-sectional web survey and (2) to compare the age and sex distributions of cannabis users who voluntarily completed (a) a household survey or (b) a large web-based purposive survey (GDS), across three countries: Australia, the United States, and Switzerland. We find that within each set of country comparisons, the demographic distributions among recent cannabis users are broadly similar, demonstrating that the age and sex distributions of those who volunteer to be surveyed are not vastly different between these non-probability and probability methods. We conclude that opt-in web surveys of hard-to-reach populations are an efficient way of gaining in-depth understanding of stigmatised behaviours and are appropriate, as long as they are not used to estimate drug use prevalence of the general population.

Spreen (1992:41) noted that \"the historical purpose that Coleman had in mind ... of using a snowball design to study social structure changed into a total [sic] different purpose of using some kind of snowball design, namely as an expethent for locating members of a special population.\" [...] the transition from snowball sampling for studying network structure to snowball sampling as a convenience sampling method fit the needs of scholars whose exclusive concern was accessing hidden populations. 2.