One-step Estimation of Networked Population Size: Respondent-Driven Capture-Recapture with Anonymity

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 methodologies commonly used with hard-to-reach groups. Three novel one-step, network-based population size estimators are presented, to be used in the context of uniform random sampling, respondent-driven sampling, and when networks exhibit significant clustering effects. Provably sufficient conditions for the consistency of these estimators (in large configuration networks) are given. Simulation experiments across a wide range of synthetic network topologies validate the performance of the estimators, which are seen to perform well on a real-world location-based social networking data set with significant clustering. Finally, the proposed schemes are extended to allow them to be used in settings where participant anonymity is required. Systematic experiments show favorable tradeoffs between anonymity guarantees and estimator performance. Taken together, we demonstrate that reasonable population estimates can be derived from anonymous respondent driven samples of 250-750 individuals, within ambient populations of 5,000-40,000. The method thus represents a novel and cost-effective means for health planners and those agencies concerned with health and disease surveillance to estimate the size of hidden populations. Limitations and future work are discussed in the concluding section

Migration to the US among rural Puerto Ricans who inject drugs: influential factors, sources of support, and challenges for harm reduction interventions

Background: While PWID of Puerto Rican origin have been migrating to the US for decades, the range of factors influencing their migration to the US and the resources they draw on to do so are not well understood. This is particularly true for rural Puerto Rican PWID, and the present study is the first empirical research to document migration patterns among this population. The specificities of their migration raise important challenges that need to be documented in order to implement more effective harm reduction policies at home (Puerto Rico) and abroad (US). Methods: This paper draws from data obtained employing a modified NHBS survey which was administered to (N =296) PWID in four rural municipalities of Puerto Rico with participants 18 years or older. The primary dependent variables for this paper are the number of times a person has lived in the continental US, and if they are planning on moving to the continental US in the future. Results: Findings suggest that 65% of the sample reported ever lived in the US and that 49% are planning on moving in the future. The number of times living in the US is associated with higher education and older age, but not with self-reported positive HIV or HCV statuses. Planning to move to the US is associated with knowing PWID who have moved or plan to move, negatively associated with age, and is not associated with HIV or HCV status. Around one-third of those that lived in the US reported having some sort of support, with the majority receiving support from family sources. No participant received help to enter HIV/HCV treatment. Conclusions: A multi-region approach to prevention is required to make a dent in curbing HIV/HCV transmission in this population. Understanding PWID migration patterns, risk behaviors, and health care needs in the US is now more important than ever as natural disasters prompted by human-made climate change will only increase in the future, raising demands not only for service providers but also harm reduction policies to cope with an increasing influx of “climate refugees” as PWID move across national borders

Predictors of Police Reporting Among Hispanic Immigrant Victims of Violence

The purpose of this study was to examine predictors of police reporting among Hispanic immigrant victims of violence. A sample of 127 Hispanic immigrants was generated through a chain-referral procedure in the city of Hempstead, New York. Participants were asked about their most recent victimization experiences, and detailed information was collected on up to three incidents. The analyses were based on a total of 214 separate victimization incidents, one third of which were reported to the police. Logistic regression analyses indicated that serious injury, multiple-victim incidents, and perceptions of discrimination increase the odds of a police report. Moreover, incidents involving a Black primary assailant were less likely to be reported to the police than incidents involving an assailant perceived to be of Hispanic origin. Supplementary analyses suggested that this latter relationship may be contingent upon the type of crime and the victim’s relationship with the assailant. At the policy level, these findings call into question assumptions about very recent immigrants being too socially isolated and distrustful of law enforcement to sustain robust reporting levels, as well as pointing to encouraging possibilities for productive engagement between police and Hispanic immigrant populations

Improving the Network Scale-Up Estimator: Incorporating Means of Sums, Recursive Back Estimation, and Sampling Weights

Researchers interested in studying populations that are difficult to reach through traditional survey methods can now draw on a range of methods to access these populations. Yet many of these methods are more expensive and difficult to implement than studies using conventional sampling frames and trusted sampling methods. The network scale-up method (NSUM) provides a middle ground for researchers who wish to estimate the size of a hidden population, but lack the resources to conduct a more specialized hidden population study. Through this method it is possible to generate population estimates for a wide variety of groups that are perhaps unwilling to self-identify as such (for example, users of illegal drugs or other stigmatized populations) via traditional survey tools such as telephone or mail surveys—by asking a representative sample to estimate the number of people they know who are members of such a “hidden” subpopulation. The original estimator is formulated to minimize the weight a single scaling variable can exert upon the estimates. We argue that this introduces hidden and difficult to predict biases, and instead propose a series of methodological advances on the traditional scale-up estimation procedure, including a new estimator. Additionally, we formalize the incorporation of sample weights into the network scale-up estimation process, and propose a recursive process of back estimation “trimming” to identify and remove poorly performing predictors from the estimation process. To demonstrate these suggestions we use data from a network scale-up mail survey conducted in Nebraska during 2014. We find that using the new estimator and recursive trimming process provides more accurate estimates, especially when used in conjunction with sampling weights

Attractor-Based Obstructions to Growth in Homogeneous Cyclic Boolean Automata

We consider a synchronous Boolean organism consisting of N cells arranged in a circle, where each cell initially takes on an independently chosen Boolean value. During the lifetime of the organism, each cell updates its own value by responding to the presence (or absence) of diversity amongst its two neighbours’ values. We show that if all cells eventually take a value of 0 (irrespective of their initial values) then the organism necessarily has a cell count that is a power of 2. In addition, the converse is also proved: if the number of cells in the organism is a proper power of 2, then no matter what the initial values of the cells are, eventually all cells take on a value of 0 and then cease to change further. We argue that such an absence of structure in the dynamical properties of the organism implies a lack of adaptiveness, and so is evolutionarily disadvantageous. It follows that as the organism doubles in size (say from m to 2m) it will necessarily encounter an intermediate size that is a proper power of 2, and suffers from low adaptiveness. Finally we show, through computational experiments, that one way an organism can grow to more than twice its size and still avoid passing through intermediate sizes that lack structural dynamics, is for the organism to depart from assumptions of homogeneity at the cellular level

Attractor-Based Obstructions to Growth in Homogeneous Cyclic Boolean Automata

We consider a synchronous Boolean organism consisting of N cells arranged in a circle, where each cell initially takes on an independently chosen Boolean value. During the lifetime of the organism, each cell updates its own value by responding to the presence (or absence) of diversity amongst its two neighbours’ values. We show that if all cells eventually take a value of 0 (irrespective of their initial values) then the organism necessarily has a cell count that is a power of 2. In addition, the converse is also proved: if the number of cells in the organism is a proper power of 2, then no matter what the initial values of the cells are, eventually all cells take on a value of 0 and then cease to change further. We argue that such an absence of structure in the dynamical properties of the organism implies a lack of adaptiveness, and so is evolutionarily disadvantageous. It follows that as the organism doubles in size (say from m to 2m) it will necessarily encounter an intermediate size that is a proper power of 2, and suffers from low adaptiveness. Finally we show, through computational experiments, that one way an organism can grow to more than twice its size and still avoid passing through intermediate sizes that lack structural dynamics, is for the organism to depart from assumptions of homogeneity at the cellular level

Improving the Network Scale-Up Estimator: Incorporating Means of Sums, Recursive Back Estimation, and Sampling Weights

Researchers interested in studying populations that are difficult to reach through traditional survey methods can now draw on a range of methods to access these populations. Yet many of these methods are more expensive and difficult to implement than studies using conventional sampling frames and trusted sampling methods. The network scale-up method (NSUM) provides a middle ground for researchers who wish to estimate the size of a hidden population, but lack the resources to conduct a more specialized hidden population study. Through this method it is possible to generate population estimates for a wide variety of groups that are perhaps unwilling to self-identify as such (for example, users of illegal drugs or other stigmatized populations) via traditional survey tools such as telephone or mail surveys—by asking a representative sample to estimate the number of people they know who are members of such a “hidden” subpopulation. The original estimator is formulated to minimize the weight a single scaling variable can exert upon the estimates. We argue that this introduces hidden and difficult to predict biases, and instead propose a series of methodological advances on the traditional scale-up estimation procedure, including a new estimator. Additionally, we formalize the incorporation of sample weights into the network scale-up estimation process, and propose a recursive process of back estimation “trimming” to identify and remove poorly performing predictors from the estimation process. To demonstrate these suggestions we use data from a network scale-up mail survey conducted in Nebraska during 2014. We find that using the new estimator and recursive trimming process provides more accurate estimates, especially when used in conjunction with sampling weights

A method for assessing the success and failure of community-level interventions in the presence of network diffusion, social reinforcement, and related social effects

Prevention and intervention work done within community settings often face unique analytic challenges for rigorous evaluations. Since community prevention work (often geographically isolated) cannot be controlled in the same way other prevention programs and these communities have an increased level of interpersonal interactions, rigorous evaluations are needed. Even when the `gold standard' randomized control trials are implemented within community intervention work, the threats to internal validity can be called into question given informal social spread of information in closed network settings. A new prevention evaluation method is presented here to disentangle the social influences assumed to influence prevention effects within communities. We formally introduce the method and it's utility for a suicide prevention program implemented in several Alaska Native villages. The results show promise to explore eight sociological measures of intervention effects in the face of social diffusion, social reinforcement, and direct treatment. Policy and research implication are discussed.Comment: 18 pages, 5 figure

One-step estimation of networked population size: Respondent-driven capture-recapture with anonymity

Size estimation is particularly important for populations whose members experience disproportionate health issues or pose elevated health risks to the ambient social structures in which they are embedded. Efforts to derive size estimates are often frustrated when the population is hidden or hard-to-reach in ways that preclude conventional survey strategies, as is the case when social stigma is associated with group membership or when group members are involved in illegal activities. This paper extends prior research on the problem of network population size estimation, building on established survey/sampling methodologies commonly used with hard-to-reach groups. Three novel one-step, network-based population size estimators are presented, for use in the context of uniform random sampling, respondent-driven sampling, and when networks exhibit significant clustering effects. We give provably sufficient conditions for the consistency of these estimators in large configuration networks. Simulation experiments across a wide range of synthetic network topologies validate the performance of the estimators, which also perform well on a real-world location based social networking data set with significant clustering. Finally, the proposed schemes are extended to allow them to be used in settings where participant anonymity is required. Systematic experiments show favorable trade-offs between anonymity guarantees and estimator performance. Taken together, we demonstrate that reasonable population size estimates are derived from anonymous respondent driven samples of 250-750 individuals, within ambient populations of 5,000-40,000. The method thus represents a novel and cost-effective means for health planners and those agencies concerned with health and disease surveillance to estimate the size of hidden populations. We discuss limitations and future work in the concluding section