Respondent-driven sampling (RDS) is a widely used method for generating chain-referral samples from hidden populations. It is an extension of the snowball sampling method and can, given that some assumptions are met, generate unbiased population estimates. One key assumption, not likely to be met, is that the acquaintance network in which the recruitment process takes place is undirected, meaning that all recruiters should have the potential to be recruited by the person they recruit. Using a mean-field approach, we develop an estimator which is based on prior information about the average indegrees of estimated variables. When the indegree is known, such as for RDS studies over internet social networks, the estimator can greatly reduce estimate error and bias as compared with current methods; when the indegree is not known, which is most common for interview-based RDS studies, the estimator can through sensitivity analysis be used as a tool to account for uncertainties of network directedness and error in self-reported degree data. The performance of the new estimator, together with previous RDS estimators, is investigated thoroughly by simulations on networks with varying structures. We have applied the new estimator on an empirical RDS study for injecting drug users in New York City.
"Respondent-driven sampling on directed networks." Electron. J. Statist. 7 292 - 322, 2013. https://doi.org/10.1214/13-EJS772