Hidden Population Size Estimation From Respondent-Driven Sampling: A Network Approach

ABSTRACT

Estimating the size of stigmatized, hidden, or hard-to-reach populations is a major problem in epidemiology, demography, and public health research. Capture–recapture and multiplier methods are standard tools for inference of hidden population sizes, but they require random sampling of target population members, which is rarely possible. Respondent-driven sampling (RDS) is a survey method for hidden populations that relies on social link tracing. The RDS recruitment process is designed to spread through the social network connecting members of the target population. In this article, we show how to use network data revealed by RDS to estimate hidden population size. The key insight is that the recruitment chain, timing of recruitments, and network degrees of recruited subjects provide information about the number of individuals belonging to the target population who are not yet in the sample. We use a computationally efficient Bayesian method to integrate over the missing edges in the subgraph of recruited individuals. We validate the method using simulated data and apply the technique to estimate the number of people who inject drugs in St. Petersburg, Russia. Supplementary materials for this article are available online.

KEYWORDS:

• Hidden population
• Injection drug use
• Network inference
• Population size

Supplementary Materials

The supplementary materials contain a derivation of the posterior distribution of the population size, conditions for existence of posterior moments, a description of the Monte Carlo algorithm, simulation results under mis-specification of the graph model, an approximation for prior elicitation, and the results of the SS-Size method on the St. Petersburg dataset.

Acknowledgments

The authors are grateful to Leonid Chindelevitch, Mark Handcock, Edward H. Kaplan, Li Zeng, and three anonymous reviewers for helpful comments.

Additional information

Funding

FWC was supported by NIH grants NICHD/BD2K DP2OD022614, NIH/NCATS KL2TR000140, NIMH P30MH062294, the Center for Interdisciplinary Research on AIDS, and the Yale Center for Clinical Investigation. The RDS data presented in the application are from the “Influences on HIV Prevalence and Service Access among IDUs in Russia and Estonia” study, funded by NIH/NIDA grant 1R01DA029888 to Robert Heimer and Anneli Uusküla (Co-PIs). The authors acknowledge the Yale University Biomedical High Performance Computing Center for computing support, funded by NIH grants RR19895 and RR029676-01.