  Respondent-Driven Sampling is a method to sample hard-to-reach human
populations by link-tracing over their social networks. Beginning with a
convenience sample, each person sampled is given a small number of uniquely
identified coupons to distribute to other members of the target population,
making them eligible for enrollment in the study. This can be an effective
means to collect large diverse samples from many populations.
  Inference from such data requires specialized techniques for two reasons.
Unlike in standard sampling designs, the sampling process is both partially
beyond the control of the researcher, and partially implicitly defined.
Therefore, it is not generally possible to directly compute the sampling
weights necessary for traditional design-based inference. Any likelihood-based
inference requires the modeling of the complex sampling process often beginning
with a convenience sample. We introduce a model-assisted approach, resulting in
a design-based estimator leveraging a working model for the structure of the
population over which sampling is conducted.
  We demonstrate that the new estimator has improved performance compared to
existing estimators and is able to adjust for the bias induced by the selection
of the initial sample. We present sensitivity analyses for unknown population
sizes and the misspecification of the working network model. We develop a
bootstrap procedure to compute measures of uncertainty. We apply the method to
the estimation of HIV prevalence in a population of injecting drug users (IDU)
in the Ukraine, and show how it can be extended to include application-specific
information.
