  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 have become standard tools for
inference of hidden population sizes, but they require independent 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 paper, 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.
