A Correlated Network Scale-up Model: Finding the Connection Between Subpopulations.

Aggregated relational data (ARD), formed from "How many X's do you know?" questions, is a powerful tool for learning important network characteristics with incomplete network data. Compared to traditional survey methods, ARD is attractive as it does not require a sample from the target population and does not ask respondents to self-reveal their own status. This is helpful for studying hard-to-reach populations like female sex workers who may be hesitant to reveal their status. From December 2008 to February 2009, the Kiev International Institute of Sociology (KIIS) collected ARD from 10,866 respondents to estimate the size of HIV-related groups in Ukraine. To analyze this data, we propose a new ARD model which incorporates respondent and group covariates in a regression framework and includes a bias term that is correlated between groups. We also introduce a new scaling procedure utilizing the correlation structure to further reduce biases. The resulting size estimates of those most-at-risk of HIV infection can improve the HIV response efficiency in Ukraine. Additionally, the proposed model allows us to better understand two network features without the full network data: 1. What characteristics affect who respondents know, and 2. How is knowing someone from one group related to knowing people from other groups. These features can allow researchers to better recruit marginalized individuals into the prevention and treatment programs. Our proposed model and several existing NSUM models are implemented in the networkscaleup R package.

Mapping the number of female sex workers in countries across sub-Saharan Africa.

Female sex workers (FSW) are affected by individual, network, and structural risks, making them vulnerable to poor health and well-being. HIV prevention strategies and local community-based programs can rely on estimates of the number of FSW to plan and implement differentiated HIV prevention and treatment services. However, there are limited systematic assessments of the number of FSW in countries across sub-Saharan Africa to facilitate the identification of prevention and treatment gaps. Here we provide estimated population sizes of FSW and the corresponding uncertainties for almost all sub-national areas in sub-Saharan Africa. We first performed a literature review of FSW size estimates and then developed a Bayesian hierarchical model to synthesize these size estimates, resolving competing size estimates in the same area and producing estimates in areas without any data. We estimated that there are 2.5 million (95% uncertainty interval 1.9 to 3.1) FSW aged 15 to 49 in sub-Saharan Africa. This represents a proportion as percent of all women of childbearing age of 1.1% (95% uncertainty interval 0.8 to 1.3%). The analyses further revealed substantial differences between the proportions of FSW among adult females at the sub-national level and studied the relationship between these heterogeneities and many predictors. Ultimately, achieving the vision of no new HIV infections by 2030 necessitates dramatic improvements in our delivery of evidence-based services for sex workers across sub-Saharan Africa.

Modeling the Marked Presence-only Data: A Case Study of Estimating the Female Sex Worker Size in Malawi.

Certain subpopulations like female sex workers (FSW), men who have sex with men (MSM), and people who inject drugs (PWID) often have higher prevalence of HIV/AIDS and are difficult to map directly due to stigma, discrimination, and criminalization. Fine-scale mapping of those populations contributes to the progress towards reducing the inequalities and ending the AIDS epidemic. In 2016 and 2017, the PLACE surveys were conducted at 3,290 venues in 20 out of the total 28 districts in Malawi to estimate the FSW sizes. These venues represent a presence-only data set where, instead of knowing both where people live and do not live (presence-absence data), only information about visited locations is available. In this study, we develop a Bayesian model for presence-only data and utilize the PLACE data to estimate the FSW size and uncertainty interval at a 1.5 × 1.5-km resolution for all of Malawi. The estimates can also be aggregated to any desirable level (city/district/region) for implementing targeted HIV prevention and treatment programs in FSW communities, which have been successful in lowering the incidence of HIV and other sexually transmitted infections.

Thirty Years of The Network Scale-up Method.

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 choking. Within the Network Scale-up methodology, there are a multitude of estimators for the size of the hidden population, including direct estimators, maximum likelihood estimators, and Bayesian estimators. In this article, we first provide an in-depth analysis of ARD properties and the techniques to collect the data. Then, we comprehensively review different estimation methods in terms of the assumptions behind each model, the relationships between the estimators, and the practical considerations of implementing the methods. We apply many of the models discussed in the review to one canonical data set and compare their performance and unique features, presented in the supplementary materials. Finally, we provide a summary of the dominant methods and an extensive list of the applications, and discuss the open problems and potential research directions in this area.