September 2022 A Bayesian hierarchical model for combining multiple data sources in population size estimation
Jacob Parsons, Xiaoyue Niu, Le Bao
Author Affiliations +
Ann. Appl. Stat. 16(3): 1550-1562 (September 2022). DOI: 10.1214/21-AOAS1556


To combat the HIV/AIDS pandemic effectively, targeted interventions among certain key populations play a critical role. Examples of such key populations include sex workers, people who inject drugs, and men who have sex with men. While having accurate estimates for the size of these key populations is important, any attempt to directly contact or count members of these populations is difficult. As a result, indirect methods are used to produce size estimates. Multiple approaches for estimating the size of such populations have been suggested but often give conflicting results. It is, therefore, necessary to have a principled way to combine and reconcile these estimates. To this end, we present a Bayesian hierarchical model for estimating the size of key populations that combines multiple estimates from different sources of information. The proposed model makes use of multiple years of data and explicitly models the systematic error in the data sources used. We use the model to estimate the size of people who inject drugs in Ukraine. We evaluate the appropriateness of the model and compare the contribution of each data source to the final estimates.

Funding Statement

This work was supported by the National Institute of Allergy and Infectious Diseases of the National Institutes of Health under award number R01AI136664.


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Jacob Parsons. Xiaoyue Niu. Le Bao. "A Bayesian hierarchical model for combining multiple data sources in population size estimation." Ann. Appl. Stat. 16 (3) 1550 - 1562, September 2022.


Received: 1 June 2020; Revised: 1 July 2021; Published: September 2022
First available in Project Euclid: 19 July 2022

MathSciNet: MR4455891
zbMATH: 1498.62030
Digital Object Identifier: 10.1214/21-AOAS1556

Keywords: HIV/AIDS epidemic , key affected population , multiplier method , network scale-up , people who inject drugs

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 3 • September 2022
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