Respondent-driven sampling and an unusual epidemic

Abstract

Respondent-driven sampling (RDS) is frequently used when sampling from hidden populations. In RDS, sampled individuals pass on participation coupons to at most $c$ of their acquaintances in the community ($c=3$ being a common choice). If these individuals choose to participate, they in turn pass coupons on to their acquaintances, and so on. The process of recruiting is shown to behave like a new Reed–Frost-type network epidemic, in which `becoming infected' corresponds to study participation. We calculate $R_0$, the probability of a major `outbreak', and the relative size of a major outbreak for $c\lt\infty$ in the limit of infinite population size and compare to the standard Reed–Frost epidemic. Our results indicate that $c$ should often be chosen larger than in current practice.