Inference for the Visibility Distribution for Respondent-Driven Sampling

Respondent-Driven Sampling (RDS) is used throughout the world to estimate prevalences and population sizes for hard-to-reach populations. Although RDS is an effective method for enrolling people from key populations (KPs) in studies, it relies on an unknown sampling mechanism and thus each individual’s inclusion probability is unknown. Current estimators rely on a participant’s network size (degree) to compute their visibility and their inclusion probability in the networked population. However, in most RDS studies a participant’s network size is attained via a self-report, and is subject to many types of misreporting and bias. We therefore propose a measurement error model to impute visibility in the context of the sample based on each participant’s self-reported network size, number of recruits, and time to recruit. These imputed visibilities can also be thought of as a way to smooth the degree distribution and bring in outliers, as well as a mechanism to deal with missing and invalid network sizes. They can be used in place of degree in existing RDS estimators. Finally, we demonstrate the performance of inference for the visibility distribution on a population of men who have sex with men (MSM) from Prishtina, Kosovo in 2014.