The Network Labeling Optimization for Hidden Population Size Estimation : A Case Solution for the Bangladesh Kidney Sellers Problem

Estimating the prevalence of hidden population is a challenging but important task for policymakers. Without knowing the precise scale of the problem, it is difficult to design a sharp remedy. Existing tools such as facility-based sentinel surveillance, snowball sampling, respondent-driven sampling, and network scale-up methods are prone to respondents' misinformation, false responses, and sample misrepresentation. Therefore, this paper proposes a novel analytical framework to overcome such weaknesses and derive better estimates. Specifically, our optimization-based mathematical model employs the Integer Programming (IP) and Social Network Analysis (SNA) to directly remove double-counting from the survey of more accessible subjects of the general public. To validate the model, the study implemented a survey on kidney trafficking in the kidney selling hotspot of Bangladesh. Reflecting the survey responses of 400 residents in a Ward of one Union in Kalai Upazila, we simulated an Exponential Random Graph Models (ERGMs) driven network. Although the model validation using the simulated network showed some signs of over-representation, a secondary validation using other data showed that the model estimates are fairly accurate