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Respondent-Driven Sampling (RDS) is a popular method for surveying hard-to-reach populations, especially in the public health domain. Adjusting for the complex sampling mechanism of the RDS procedure is challenging. We propose a new model for the RDS mechanism motivated by a graph model, which we call the Homophily Configuration Graph. Under this model, we develop a new estimator for population proportions that is robust to seed bias, differential activity, differential recruitment and short recruitment chains. We also connect it to existing RDS theory by showing that, if the sample fraction is small, our estimator limits to the popular Salganik-Heckathorn estimator. We perform simulation studies on both empirically observed networks and networks with known statistical properties, suggesting that this new estimator has less bias than currently recommended estimators. [ABSTRACT FROM AUTHOR]

The study of hard-to-reach populations presents significant challenges. Typically, a sampling frame is not available, and population members are difficult to identify or recruit from broader sampling frames. This is especially true of populations at high risk for HIV/AIDS. Respondent-driven sampling (RDS) is often used in such settings with the primary goal of estimating the prevalence of infection. In such populations, the number of people at risk for infection and the number of people infected are of fundamental importance. This article presents a case-study of the estimation of the size of the hard-to-reach population based on data collected through RDS. We study two populations of female sex workers and men-who-have-sex-with-men in El Salvador. The approach is Bayesian and we consider different forms of prior information, including using the UNAIDS population size guidelines for this region. We show that the method is able to quantify the amount of information on population size available in RDS samples. As separate validation, we compare our results to those estimated by extrapolating from a capture-recapture study of El Salvadorian cities. The results of our case-study are largely comparable to those of the capture-recapture study when they differ from the UNAIDS guidelines. Our method is widely applicable to data from RDS studies and we provide a software package to facilitate this. [ABSTRACT FROM AUTHOR]