Respondent-driven sampling and an unusual epidemic

TL;DR

This paper models respondent-driven sampling (RDS) as a network epidemic process, analyzing how the limited number of recruitment coupons influences sampling dynamics and outbreak probabilities, and compares it to traditional epidemic models.

Contribution

It introduces a novel epidemic model for RDS that accounts for limited contacts, providing analytical insights into recruitment patterns and outbreak likelihoods.

Findings

Coupon number significantly affects RDS recruitment size.

RDS behaves differently from standard epidemic models with unlimited contacts.

The model explains empirical observations of RDS recruitment patterns.

Abstract

Respondent-driven sampling (RDS) is frequently used when sampling hard-to-reach and/or stigmatized communities. RDS utilizes a peer-driven recruitment mechanism where sampled individuals pass on participation coupons to at most $c$ of their acquaintances in the community ($c=3$ being a common choice), who then in turn pass on to their acquaintances if they choose to participate, and so on. This process of distributing coupons is shown to behave like a new Reed-Frost type network epidemic model, in which becoming infected corresponds to receiving a coupon. The difference from existing network epidemic models is that an infected individual can not infect (i.e.\ sample) all of its contacts, but only at most $c$ of them. We calculate $R_0$, the probability of a major "outbreak", and the relative size of a major outbreak in the limit of infinite population size and evaluate their adequacy in finite populations. We study the effect of varying $c$ and compare RDS to the corresponding usual epidemic models, i.e.\ the case of $c=\infty$. Our results suggest that the number of coupons has a large effect on RDS recruitment. Additionally, we use our findings to explain previous empirical observations.