A dual-frame approach for estimation with respondent-driven samples

Respondent-driven sampling (RDS) is an increasingly common method for surveying rare, hidden, or otherwise hard-to-reach populations. Instead of formal probability sampling from a well-defined frame, RDS relies on respondents themselves to recruit additional participants through their own social networks. By necessity, RDS is often initiated with a small, non-random sample. Standard RDS estimators have been developed under strong assumptions on the diffusion of sampling through the network over multiple waves of recruitment. We consider an alternative setting in which these assumptions are not met, and instead a large probability sample is used to initiate RDS and only a few waves of recruitment take place. In this setting, we develop dual-frame estimators that use both known inclusion probabilities from the initial sampling design and estimated inclusion probabilities from RDS, treated as a nonprobability sample. In a simulation study using network data from the Project 90 study, our dual-frame estimators perform well relative to standard RDS alternatives, across a wide range of recruitment behaviors. We propose a simple variance estimator that yields stable estimates and reasonable confidence interval coverage. Finally, we apply our dual-frame estimators to a real RDS study of smoking behavior among lesbian, gay, bisexual, and transgender (LGBT) adults.