  A new estimation method is presented for network sampling designs, including
Respondent Driven Sampling (RDS) and Snowball (SB) sampling. These types of
link-tracing designs are essential for studies of hidden populations, such as
people at risk for HIV. The simple idea behind the new method is to run a
fast-sampling process on the sample network data to estimate the inclusion
probabilities of the actual survey, and incorporate those in unequal
probability estimators of population means and proportions. Improved versions
of the usual RDS and SB designs are also proposed, termed RDS+ and SB+, to
obtain information on more of the within-sample links. In simulations using the
network from the Colorado Springs study on the heterosexual spread of HIV, the
new estimators produce in most cases lower bias and lower mean square than
current methods. For the variables having the largest mean square errors with
current estimators, the improvement with the new estimator is dramatic. The
estimates are improved even more with the enhanced design versions. For
estimating the population mean degree, the efficiency gains using he new method
are 29 for RDS, 54 for RDS+, 26 for SB and 80 for SB+. This means for example,
with the ordinary RDS design, the mean square error with the new estimator,
same data, is 1/29 that of currently used estimators. The new method is
computationally intricate but is fast and scales up well. The new estimation
method can be used to re-analyze existing network survey data. For new network
sampling studies, it is recommended to use the improved designs as well as the
new estimators.
