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A new estimation method is presented for network sampling designs, includingRespondent Driven Sampling (RDS) and Snowball (SB) sampling. These types oflink-tracing designs are essential for studies of hidden populations, such aspeople at risk for HIV. The simple idea behind the new method is to run afast-sampling process on the sample network data to estimate the inclusionprobabilities of the actual survey, and incorporate those in unequalprobability estimators of population means and proportions. Improved versionsof the usual RDS and SB designs are also proposed, termed RDS+ and SB+, toobtain information on more of the within-sample links. In simulations using thenetwork from the Colorado Springs study on the heterosexual spread of HIV, thenew estimators produce in most cases lower bias and lower mean square thancurrent methods. For the variables having the largest mean square errors withcurrent estimators, the improvement with the new estimator is dramatic. Theestimates are improved even more with the enhanced design versions. Forestimating the population mean degree, the efficiency gains using he new methodare 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 iscomputationally intricate but is fast and scales up well. The new estimationmethod can be used to re-analyze existing network survey data. For new networksampling studies, it is recommended to use the improved designs as well as thenew estimators.

Simple estimators for network sampling