Novel sampling design for respondent-driven sampling

Khabbazian, Mohammad; Hanlon, Bret; Russek, Zoe; Rohe, Karl

doi:10.1214/17-ejs1358

Cited by 14 publications

(13 citation statements)

References 45 publications

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“…In previous research, Verdery et al [2013] and Khabbazian et al [2015] prove this theorem for the special case that T is a chain. The first step to prove Theorem 2.1 is to show that if d(σ, τ ) = t, then by the reversibility of P ,…”

Section: The Variance Under Rdsmentioning

confidence: 85%

A critical threshold for design effects in network sampling

Rohe¹

2019

Ann. Statist.

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Web crawling, snowball sampling, and respondent-driven sampling (RDS) are three types of network sampling techniques used to contact individuals in hard-to-reach populations. This paper studies these procedures as a Markov process on the social network that is indexed by a tree. Each node in this tree corresponds to an observation and each edge in the tree corresponds to a referral. Indexing with a tree (instead of a chain) allows for the sampled units to refer multiple future units into the sample.In survey sampling, the design effect characterizes the additional variance induced by a novel sampling strategy. If the design effect is some value DE, then constructing an estimator from the novel design makes the variance of the estimator DE times greater than it would be under a simple random sample with the same sample size n. Under certain assumptions on the referral tree, the design effect of network sampling has a critical threshold that is a function of the referral rate m and the clustering structure in the social network, represented by the second eigenvalue of the Markov transition matrix, λ2. If m < 1/λ 2 2 , then the design effect is finite (i.e. the standard estimator is √ n-consistent). However, if m > 1/λ 2 2 , then the design effect grows with n (i.e. the standard estimator is no longer √ n-consistent). Past this critical threshold, the standard error of the estimator converges at the slower rate of n log m λ 2 . The Markov model allows for nodes to be resampled; computational results show that the findings hold in without-replacement sampling. To estimate confidence intervals that adapt to the correct level of uncertainty, a novel resampling procedure is proposed. Computational experiments compare this procedure to previous techniques. * Thank you Zoe Russek and Emma Krauska for recording the referral trees used in Figure 2 and helpful comments on this draft. Thank you

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Section: The Variance Under Rdsmentioning

confidence: 85%

A critical threshold for design effects in network sampling

Rohe¹

2019

Ann. Statist.

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“…Under the Markov model where the covariance between samples is known, Theorems 1 and 2 show that the variance of the GLS estimator decays like

. To estimate the covariance between samples, we use the fact that the covariance between adjacent samples can be exactly specified in terms of the spectral properties of the Markov transition matrix ( 5 , 20 – 24 ). These essential spectral properties of the network can be estimated from the observed data under the DC-SBM and the rank-two model.…”

Section: Discussionmentioning

confidence: 99%

Generalized least squares can overcome the critical threshold in respondent-driven sampling

Roch

Rohe

2018

Proc. Natl. Acad. Sci. U.S.A.

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SignificanceRespondent-driven sampling (RDS) is a popular technique to sample marginalized or hard-to-reach populations, where participants can refer multiple contacts into the sample. Using the sampled participants, we wish to estimate properties of the population, often the proportion of individuals that are HIV+. Because contacts often share the same HIV status, adjacent samples are dependent. As a result, RDS can lead to highly variable estimates of HIV prevalence. This paper studies an estimation technique for HIV prevalence that is based upon the classical idea of generalized least squares.

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“…Proof. Proposition 1 in [Khabbazian et al, 2016] says that Cov(ỹ(X p(τ ) ),ỹ(X τ )) = N =2 ỹ, f 2 π λ .…”

Section: Proofs Of Propositions 4 Andmentioning

confidence: 99%

Central limit theorems for network driven sampling

Li¹,

Rohe²

2017

Electron. J. Statist.

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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 obvious use, an example shows that in certain cases the sample average is preferable to inverse probability weighting. We provide a test statistic to distinguish between these two cases.arXiv:1509.04704v2 [stat.ME] 28 Aug 2016 population that is HIV+). Extensive previous statistical research has proposed various estimators of µ which are approximately unbiased based upon various types of models for an RDS sample [Salganik and Heckathorn, 2004, Volz and Heckathorn, 2008, Gile, 2011. We note that in the papers cited above (except [Gile, 2011]), RDS is assumed to sample with replacement. Previous research has also explored the variance of these estimators Salganik, 2009, Rohe, 2015]. This paper studies the asymptotic distribution of statistics related to these estimators.Results on asymptotic distributions for RDS are useful for two obvious reasons. First, they allow us to construct asymptotic confidence intervals for µ. Second, they provide essential tools to test various statistical hypotheses. The only central limit theorem associated considered in the RDS literature studied the case when the tree indexed process reduces to a Markov chain [Goel and Salganik, 2009]; this presumes that each individual refers exactly one person. Previous research suggests that the number of referrals from each individual is fundamental in determining the variance of common estimators [Rohe, 2015]. This paper establishes two central limit theorems in settings which allow for multiple referrals.The main results apply to both the sample average and the Volz-Heckathorn estimator, which is an approximation of the inverse probability weighted estimator (cf Remark 1). Because the inverse probability weighted (IPW) estimator and its extensions are asymptotically unbiased, these estimators are often preferred to the sample average. However, sometimes survey weights are not needed and they only introduce additional variance to the estimator [Bollen et al., 2016]. This issue is particularly salient when sampling weights are highly heterogeneous, as is often the case in RDS. Proposition 3 shows that if the outcomes y i are uncorrelated with the sampling weights, then the sample average is unbiased. Theorem 3 extends this result to RDS to show that the IPW estimator can have a larger variance than the sample average. Taken together, these results imply that the sample average can have a lower mean squared error (MSE) than the IPW estimator. Section 4 introduce...

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Novel sampling design for respondent-driven sampling

Cited by 14 publications

References 45 publications

A critical threshold for design effects in network sampling

A critical threshold for design effects in network sampling

Generalized least squares can overcome the critical threshold in respondent-driven sampling

Central limit theorems for network driven sampling

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