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Studies in respondent-driven sampling: Directed networks, epidemics, and random walks
Stockholm University, Faculty of Science, Department of Mathematics.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Respondent-driven sampling (RDS) is a link-tracing sampling methodology especially suitable for sampling hidden populations. A clever sampling mechanism and inferential procedures that facilitate asymptotically unbiased population estimates has contributed to the rising popularity of the method. The papers in this thesis extend RDS estimation theory to some population structures to which the classical RDS estimation framework is not applicable and analyse the behaviour of the RDS recruitment process. 

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2016. , 46 p.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-129287ISBN: 978-91-7649-430-1 (print)OAI: oai:DiVA.org:su-129287DiVA: diva2:921240
Public defence
2016-06-15, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: In press. Paper 3: Accepted. Paper 4: Manuscript.

Available from: 2016-05-23 Created: 2016-04-20 Last updated: 2017-02-23Bibliographically approved
List of papers
1. Respondent-driven sampling on directed networks
Open this publication in new window or tab >>Respondent-driven sampling on directed networks
2013 (English)In: Electronic Journal of Statistics, ISSN 1935-7524, E-ISSN 1935-7524, Vol. 7, 292-322 p.Article in journal (Refereed) Published
Abstract [en]

Respondent-driven sampling (RDS) is a widely used method for generating chain-referral samples from hidden populations. It is an extension of the snowball sampling 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. Using a mean-field approach, we develop an estimator which is based on prior information about the average indegrees of estimated variables. When the indegree is known, such as for RDS studies over internet social networks, the estimator can greatly reduce estimate error and bias as compared with current methods; when the indegree is not known, which is most common for interview-based RDS studies, the estimator can through sensitivity analysis be used as a tool to account for uncertainties of network directedness and error in self-reported degree data. The performance of the new estimator, together with previous RDS estimators, is investigated thoroughly by simulations on networks with varying structures. We have applied the new estimator on an empirical RDS study for injecting drug users in New York City.

Keyword
Respondent-driven sampling, directed networks, degree correlation, attractivity ratio, HIV
National Category
Mathematics Sociology
Identifiers
urn:nbn:se:su:diva-92524 (URN)10.1214/13-EJS772 (DOI)000321052800001 ()
Note

AuthorCount:4;

Available from: 2013-08-08 Created: 2013-08-07 Last updated: 2017-12-06Bibliographically approved
2. Random walks on directed networks: Inference and respondent-driven sampling
Open this publication in new window or tab >>Random walks on directed networks: Inference and respondent-driven sampling
2016 (English)In: Journal of Official Statistics, ISSN 0282-423X, E-ISSN 2001-7367, Vol. 32, no 2, 433-459 p.Article in journal (Refereed) Published
Abstract [en]

Respondent-driven sampling (RDS) is often used to estimate population properties (e.g., sexual risk behavior) in hard-to-reach populations. In RDS, already sampled individuals recruit population members to the sample from their social contacts in an efficient snowball-like sampling procedure. By assuming a Markov model for the recruitment of individuals, asymptotically unbiased estimates of population characteristics can be obtained. Current RDS estimation methodology assumes that the social network is undirected, that is, all edges are reciprocal. However, empirical social networks in general also include a substantial number of nonreciprocal edges. In this article, we develop an estimation method for RDS in populations connected by social networks that include reciprocal and nonreciprocal edges. We derive estimators of the selection probabilities of individuals as a function of the number of outgoing edges of sampled individuals. The proposed estimators are evaluated on artificial and empirical networks and are shown to generally perform better than existing estimators. This is the case in particular when the fraction of directed edges in the network is large.

Keyword
Hidden population, social network, nonreciprocal relationship, Markov model
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-129251 (URN)10.1515/JOS-2016-0023 (DOI)000377566800011 ()
Funder
Swedish Research Council, 2009-5759Riksbankens Jubileumsfond, P12-0705:1
Available from: 2016-04-18 Created: 2016-04-18 Last updated: 2017-11-30Bibliographically approved
3. Respondent-driven sampling and an unusual epidemic
Open this publication in new window or tab >>Respondent-driven sampling and an unusual epidemic
2016 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 2, 518-540 p.Article in journal (Refereed) Published
Abstract [en]

Respondent-driven sampling (RDS) is frequently used when sampling from hidden populations. In RDS, sampled individuals pass on participation coupons to at most c of their acquaintances in the community (c = 3 being a common choice). If these individuals choose to participate, they in turn pass coupons on to their acquaintances, and so on. The process of recruiting is shown to behave like a new Reed-Frost-type network epidemic, in which `becoming infected' corresponds to study participation. We calculate R-0, the probability of a major `outbreak', and the relative size of a major outbreak for c < infinity in the limit of infinite population size and compare to the standard Reed-Frost epidemic. Our results indicate that c should often be chosen larger than in current practice.

Keyword
Stochastic epidemic model, Respondent-driven sampling, Configuration model, Reed-Frost
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-129252 (URN)10.1017/jpr.2016.17 (DOI)000378598700016 ()
Funder
Swedish Research Council, 2009-5759Riksbankens Jubileumsfond, P12-0705:1
Available from: 2016-04-18 Created: 2016-04-18 Last updated: 2017-11-30Bibliographically approved
4. Multiple seed structure and disconnected networks in respondent-driven sampling
Open this publication in new window or tab >>Multiple seed structure and disconnected networks in respondent-driven sampling
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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 assumes that all sampled individuals originate from only one seed. We use a random walk with teleportation to describe the multiple seed structure of RDS and develop an estimator based on this process. The new estimator is also valid for populations with disconnected social networks. We numerically evaluate our estimator by simulations on artificial and real networks. Our estimator outperforms previous estimators, especially when the proportion of seeds in the sample is large. We recommend our new estimator to be used in RDS studies, in particular when the number of seeds is large or the social network of the population is disconnected.

National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-129257 (URN)
Funder
Swedish Research Council, 621-2012-3868
Available from: 2016-04-18 Created: 2016-04-18 Last updated: 2016-04-20

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