Identification of Homophily and Preferential Recruitment in Respondent-Driven Sampling

Respondent-driven sampling (RDS) is a link-tracing procedure used in epidemiologic research on hidden or hard-to-reach populations in which subjects recruit others via their social networks. Estimates from RDS studies may have poor statistical properties due to statistical dependence in sampled subjects' traits. Two distinct mechanisms account for dependence in an RDS study: homophily, the tendency for individuals to share social ties with others exhibiting similar characteristics, and preferential recruitment, in which recruiters do not recruit uniformly at random from their network alters. The different effects of network homophily and preferential recruitment in RDS studies have been a source of confusion and controversy in methodological and empirical research in epidemiology. In this work, we gave formal definitions of homophily and preferential recruitment and showed that neither is identified in typical RDS studies. We derived nonparametric identification regions for homophily and preferential recruitment and showed that these parameters were not identified unless the network took a degenerate form. The results indicated that claims of homophily or recruitment bias measured from empirical RDS studies may not be credible. We applied our identification results to a study involving both a network census and RDS on a population of injection drug users in Hartford, Connecticut (2012-2013).