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The network scale-up method (NSUM) is a cost-effective approach to estimatingthe size or prevalence of a group of people that is hard to reach through astandard survey. The basic NSUM involves two steps: estimating respondents'degrees by one of various methods (in this paper we focus on the probe groupmethod which uses the number of people a respondent knows in various groups ofknown size), and estimating the prevalence of the hard-to-reach population ofinterest using respondents' estimated degrees and the number of people theyreport knowing in the hard-to-reach group. Each of these two steps involvestaking either an average of ratios or a ratio of averages. Using the ratio ofaverages for each step has so far been the most common approach. However, wepresent theoretical arguments that using the average of ratios at the second,prevalence-estimation step often has lower mean squared error when the randommixing assumption is violated, which seems likely in practice; this estimatorwhich uses the ratio of averages for degree estimates and the average of ratiosfor prevalence was proposed early in NSUM development but has largely beenunexplored and unused. Simulation results using an example network data setalso support these findings. Based on this theoretical and empirical evidence,we suggest that future surveys that use a simple estimator may want to use thismixed estimator, and estimation methods based on this estimator may produce newimprovements.

Comparing the Robustness of Simple Network Scale-Up Method (NSUM) Estimators