This work is concerned with the estimation of hard-to-reach population sizes using a single respondent-driven sampling (RDS) survey, a variant of chain-referral sampling that leverages social relationships to reach members of a hidden population. The popularity of RDS as a standard approach for surveying hidden populations brings theoretical and methodological challenges regarding the estimation of population sizes, mainly for public health purposes. This paper proposes a frequentist, model-based framework for estimating the size of a hidden population using a network-based approach. An optimization algorithm is proposed for obtaining the identification region of the target parameter when model assumptions are violated. We characterize the asymptotic behavior of our proposed methodology and assess its finite sample performance under departures from model assumptions.
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 have become standard tools for inference of hidden population sizes, but they require independent 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…
In this paper, a new randomized response technique aimed at protecting respondents' privacy is proposed. It is designed for estimating the population total, or the population mean, of a quantitative characteristic. It provides a~high degree of protection to the interviewed individuals, hence it may be favorably perceived by them and increase their willingness to cooperate. Instead of revealing the true value of the characteristic under investigation, a respondent only states whether the value is greater (or smaller) than a~number which is selected by him/her at random, and is unknown to the in…
Respondent-driven sampling (RDS) is a chain-referral method for sampling members of a hidden or hard-to-reach population such as sex workers, homeless people, or drug users via their social network. 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 paper, we show that data collected…
Respondent-driven sampling is a survey method for hidden or hard-to-reach populations in which sampled individuals recruit others in the study population via their social links. The most popular estimator for for the population mean assumes that individual sampling probabilities are proportional to each subject's reported degree in a social network connecting members of the hidden population. However, it remains unclear under what circumstances these estimators are valid, and what assumptions are formally required to identify population quantities. In this short note we detail nonparametric id…
Objective: Lack of representative data about hidden groups, like men who have sex with men (MSM), hinders an evidence-based response to the HIV epidemics. Respondent-driven sampling (RDS) was developed to overcome sampling challenges in studies of populations like MSM for which sampling frames are absent. Internet-based RDS (webRDS) can potentially circumvent limitations of the original RDS method. We aimed to implement and evaluate webRDS among a hidden population. Methods and Design: This cross-sectional study took place 18 February to 12 April, 2011 among MSM in Vietnam. Inclusion criteria …
Respondent-Driven Sampling (RDS) is an approach to sampling design and inference in hard-to-reach human populations. Typically, a sampling frame is not available, and population members are difficult to identify or recruit from broader sampling frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an appr…
We develop methods for estimating the size of hard-to-reach populations from data collected using network-based questions on standard surveys. Such data arise by asking respondents how many people they know in a specific group (e.g., people named Michael, intravenous drug users). The Network Scale up Method (NSUM) is a tool for producing population size estimates using these indirect measures of respondents' networks. Killworth et al. [Soc. Netw. 20 (1998a) 23-50, Evaluation Review 22 (1998b) 289-308] proposed maximum likelihood estimators of population size for a fixed effects model in which …
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 converg…
Respondent-driven sampling (RDS) is a method of chain referral sampling popular for sampling hidden and/or marginalized populations. As such, even under the ideal sampling assumptions, the performance of RDS is restricted by the underlying social network: if the network is divided into communities that are weakly connected to each other, then RDS is likely to oversample one of these communities. In order to diminish the "referral bottlenecks" between communities, we propose anti-cluster RDS (AC-RDS), an adjustment to the standard RDS implementation. Using a standard model in the RDS literature…
Respondent-driven sampling (RDS) is a popular approach to study marginalized or hard-to-reach populations. It collects samples from a networked population by incentivizing participants to refer their friends into the study. One major challenge in analyzing RDS samples is seed bias. Seed bias refers to the fact that when the social network is divided into multiple communities (or blocks), the RDS sample might not provide a balanced representation of the different communities in the population, and such unbalance is correlated with the initial participant (or the seed). In this case, the distrib…
Respondent-driven sampling (RDS) is a link-tracing procedure for surveying hidden or hard-to-reach populations in which subjects recruit other subjects via their social network. There is significant research interest in detecting clustering or dependence of epidemiological traits in networks, but researchers disagree about whether data from RDS studies can reveal it. Two distinct mechanisms account for dependence in traits of recruiters and recruitees in an RDS study: homophily, the tendency for individuals to share social ties with others exhibiting similar characteristics, and preferential r…
This paper explores bias in the estimation of sampling variance in Respondent Driven Sampling (RDS). Prior methodological work on RDS has focused on its problematic assumptions and the biases and inefficiencies of its estimators of the population mean. Nonetheless, researchers have given only slight attention to the topic of estimating sampling variance in RDS, despite the importance of variance estimation for the construction of confidence intervals and hypothesis tests. In this paper, we show that the estimators of RDS sampling variance rely on a critical assumption that the network is First…
Respondent-driven sampling (RDS) is a commonly used substitute for random sampling when studying hidden populations, such as injecting drug users or men who have sex with men, for which no sampling frame is known. The method is an extension of the snowball sample method and can, given that some assumptions are met, generate unbiased population estimates. One key assumption, not likely to be met, is that the acquaintance network in which the recruitment process takes place is undirected, meaning that all recruiters should have the potential to be recruited by the person they recruit. Here we in…
We proposed new and more efficient estimators for estimating population proportion of respondents belonging to two related sensitive attributes in survey sampling by extending the work of Mangat (1994). Our proposed estimators are more efficient than Lee et al (2013) simple and crossed model estimators as the population proportion of possessing the sensitive attribute increases.
Population size estimates for hidden and hard-to-reach populations are particularly important when members are known to suffer from disproportion health issues or to pose health risks to the larger ambient population in which they are embedded. Efforts to derive size estimates are often frustrated by a range of factors that preclude conventional survey strategies, including social stigma associated with group membership or members' involvement in illegal activities. This paper extends prior research on the problem of network population size estimation, building on established survey/sampling m…
Respondent-driven sampling (RDS) is a link-tracing sampling method that is especially suitable for sampling hidden populations. RDS combines an efficient snowball-type sampling scheme with inferential procedures that yield unbiased population estimates under some assumptions about the sampling procedure and population structure. Several seed individuals are typically used to initiate RDS recruitment. However, standard RDS estimation theory assume that all sampled individuals originate from only one seed. We present an estimator, based on a random walk with teleportation, which accounts for the…
Estimating treatment effects plays a crucial role in causal inference, having many real-world applications like policy analysis and decision making. Nevertheless, estimating treatment effects in the longitudinal setting in the presence of hidden confounders remains an extremely challenging problem. Recently, there is a growing body of work attempting to obtain unbiased ITE estimates from time-dynamic observational data by ignoring the possible existence of hidden confounders. Additionally, many existing works handling hidden confounders are not applicable for continuous-time settings. In this …
Respondent-driven sampling (RDS) is a popular method for sampling hard-to-survey populations that leverages social network connections through peer recruitment. While RDS is most frequently applied to estimate the prevalence of infections and risk behaviors of interest to public health, like HIV/AIDS or condom use, it is rarely used to draw inferences about the structural properties of social networks among such populations because it does not typically collect the necessary data. Drawing on recent advances in computer science, we introduce a set of data collection instruments and RDS estimato…
Respondent-Driven Sampling is a popular technique for sampling hidden populations. This paper models Respondent-Driven Sampling as a Markov process indexed by a tree. Our main results show that the Volz-Heckathorn estimator is asymptotically normal below a critical threshold. The key technical difficulties stem from (i) the dependence between samples and (ii) the tree structure which characterizes the dependence. The theorems allow the growth rate of the tree to exceed one and suggest that this growth rate should not be too large. To illustrate the usefulness of these results beyond their obvi…
We present a new design and inference method for estimating population size of a hidden population best reached through a link-tracing design. The strategy involves the Rao-Blackwell Theorem applied to a sufficient statistic markedly different from the usual one that arises in sampling from a finite population. An empirical application is described. The result demonstrates that the strategy can efficiently incorporate adaptively selected members of the sample into the inference procedure.
A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a wide variety of indirect statistical approaches, under different models for sampling and observation, for estimating the size of a hidden set. Some methods make use of random sampling with known or estimable sampling probabilities, and others make structural assumptions about relationships (e.g. ordering or network information) between the elements that com…
Estimating the individual treatment effect (ITE) from observational data is meaningful and practical in healthcare. Existing work mainly relies on the strong ignorability assumption that no hidden confounders exist, which may lead to bias in estimating causal effects. Some studies consider the hidden confounders are designed for static environment and not easily adaptable to a dynamic setting. In fact, most observational data (e.g., electronic medical records) is naturally dynamic and consists of sequential information. In this paper, we propose Deep Sequential Weighting (DSW) for estimating I…
We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter estimation algorithms are gradient based and cover both offline and online estimation. We demonstrate their performance by estimating the parameters of three intractable models, namely the alpha-stable distribution, g-and-k distribution, and the stochastic volatility model with alpha-stable returns, using both real and synthetic data.
The present paper introduces a new model used to study and analyse the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) epidemic-reported-data from Spain. This is a Hidden Markov Model whose hidden layer is a regeneration process with Poisson immigration, Po-INAR(1), together with a mechanism that allows the estimation of the under-reporting in non-stationary count time series. A novelty of the model is that the expectation of the innovations in the unobserved process is a time-dependent function defined in such a way that information about the spread of an epidemic, as modelled thr…
In multivariate data analysis, it is often important to estimate a graph characterizing dependence among (p) variables. A popular strategy uses the non-zero entries in a (p\times p) covariance or precision matrix, typically requiring restrictive modeling assumptions for accurate graph recovery. To improve model robustness, we instead focus on estimating the {\em backbone} of the dependence graph. We use a spanning tree likelihood, based on a minimalist graphical model that is purposely overly-simplified. Taking a Bayesian approach, we place a prior on the space of trees and quantify uncertaint…
It is difficult to accurately estimate the rates of rape and domestic violence due to the sensitive nature of these crimes. There is evidence that bias in estimating the crime rates from survey data may arise because some women respondents are "gagged" in reporting some types of crimes by the use of a telephone rather than a personal interview, and by the presence of a spouse during the interview. On the other hand, as data on these crimes are collected every year, it would be more efficient in data analysis if we could identify and make use of information from previous data. In this paper we …
Transporting Trial Evidence Under Posterior Drift and Possible Hidden Confounding
Qiuzhen College, Tsinghua University（清华大学邱氏书院）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Beijing Institute of Mathematical Sciences and Applications（北京数学科学与应用研究院）
Estimating the size of hard-to-reach populations is an important problem for many fields. The Network Scale-up Method (NSUM) is a relatively new approach to estimate the size of these hard-to-reach populations by asking respondents the question, "How many X's do you know," where X is the population of interest (e.g. "How many female sex workers do you know?"). The answers to these questions form Aggregated Relational Data (ARD). The NSUM has been used to estimate the size of a variety of subpopulations, including female sex workers, drug users, and even children who have been hospitalized for …
Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sa…
We consider the problem of simultaneous estimation of a sequence of dependent parameters that are generated from a hidden Markov model. Based on observing a noise contaminated vector of observations from such a sequence model, we consider simultaneous estimation of all the parameters irrespective of their hidden states under square error loss. We study the roles of statistical shrinkage for improved estimation of these dependent parameters. Being completely agnostic on the distributional properties of the unknown underlying Hidden Markov model, we develop a novel non-parametric shrinkage algor…
Measles is a significant source of global disease burden and child mortality. Measles vaccination through routine immunization (RI) programs in high-burden settings remains a challenge due to poor health care infrastructure and access. Supplementary immunization activities (SIA) in the form of vaccination campaigns are therefore implemented to prevent measles outbreaks by reducing the size of the susceptible population. The SIA efficacy, defined as the fraction of susceptible population immunized by an SIA, is a critical metric for assessing campaign effectiveness. We propose a discrete-time h…
Accurate power and sample size estimation are crucial to the design and analysis of genetic association studies. When analyzing a binary trait via logistic regression, important covariates such as age and sex are typically included in the model. However, their effects are rarely properly considered in power or sample size computation during study planning. Unlike when analyzing a continuous trait, the power of association testing between a binary trait and a genetic variant depends, explicitly, on covariate effects, even under the assumption of gene-environment independence. Earlier work recog…
