  Estimates of population size for hidden and hard-to-reach individuals are of
particular interest to health officials when health problems are concentrated
in such populations. Efforts to derive these estimates are often frustrated by
a range of factors including social stigma or an association with illegal
activities that ordinarily preclude conventional survey strategies. This paper
builds on and extends prior work that proposed a method to meet these
challenges. Here we describe a rigorous formalization of a one-step,
network-based population estimation procedure that can be employed under
conditions of anonymity. The estimation procedure is designed to be implemented
alongside currently accepted strategies for research with hidden populations.
Simulation experiments are described that test the efficacy of the method
across a range of implementation conditions and hidden population sizes. The
results of these experiments show that reliable population estimates can be
derived for hidden, networked population as large as 12,500 and perhaps larger
for one family of random graphs. As such, the method shows potential for
cost-effective implementation health and disease surveillance officials
concerned with hidden populations. Limitations and future work are discussed in
the concluding section.
