Estimating Hidden Population Size using Respondent-Driven Sampling Data
  Respondent-Driven Sampling (RDS) is an approach to sampling design and inference in hard-to-reach human populations. Typically, a sampling frame is not available, and population members are difficult to identify or recruit from broader sampling frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an approach to estimating the size of a target population based on data collected through RDS.   The proposed approach uses a successive sampling approximation to RDS to leverage information in the ordered sequence of observed personal network sizes. The inference uses the Bayesian framework, allowing for the incorporation of prior knowledge. A flexible class of priors for the population size is proposed that aids elicitation. An extensive simulation study provides insight into the performance of the method for estimating population size under a broad range of conditions. A further study shows the approach also improves estimation of aggregate characteristics. A particular choice of the prior produces interval estimates with good frequentist properties. Finally, the method demonstrates sensible results when used to estimate the numbers of sub-populations most at risk for HIV in two cities in El Salvador. 
Mark S. Handcock and Krista J. Gile and Corinne M. Mar
stat.ME stat.AP stat.CO