Probability Based Estimation Theory for Respondent Driven Sampling

Abstract

Many populations of interest present special challenges for traditional survey methodology when it is difficult or impossible to obtain a traditional sampling frame. In the case of such hidden populations at risk of HIV/AIDS, many researchers have resorted to chain-referral sampling. Recent progress on the theory of chain-referral sampling has led to Respondent Driven Sampling (RDS), a rigorous chain-referral method which allows unbiased estimation of the target population. In this article we present new probability-theoretic methods for making estimates from RDS data. The new estimators offer improved simplicity, analytical tractability, and allow the estimation of continuous variables. An analytical variance estimator is proposed in the case of estimating categorical variables. The properties of the estimator and the associated variance estimator are explored in a simulation study, and compared to alternative RDS estimators using data from a study of New York City jazz musicians. The new estimator gives results consistent with alternative RDS estimators in the study of jazz musicians, and demonstrates greater precision than alternative estimators in the simulation study.