RESPONDENT-DRIVEN SAMPLING AND AN UNUSUAL EPIDEMIC

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 < infinity 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.