A stochastic simulation model to study respondent-driven recruitment

Respondent-driven detection is a chain recruitment method used to sample contact persons of infected persons in order to enhance case finding. It starts with initial individuals, so-called seeds, who are invited for participation. Afterwards, seeds receive a fixed number of coupons to invite individuals with whom they had contact during a specific time period. Recruitees are then asked to do the same, resulting in successive waves of contact persons who are connected in one recruitment tree. However, often the majority of participants fail to invite others, or invitees do not accept an invitation, and recruitment stops after several waves. A mathematical model can help to analyse how various factors influence peer recruitment and to understand under which circumstances sustainable recruitment is possible. We implemented a stochastic simulation model, where parameters were suggested by empirical data from an online survey, to determine the thresholds for obtaining large recruitment trees and the number of waves needed to reach a steady state in the sample composition for individual characteristics. We also examined the relationship between mean and variance of the number of invitations sent out by participants and the probability of obtaining a large recruitment tree. Our main finding is that a situation where participants send out any number of coupons between one and the maximum number is more effective in reaching large recruitment trees, compared to a situation where the majority of participants does not send out any invitations and a smaller group sends out the maximum number of invitations. The presented model is a helpful tool that can assist public health professionals in preparing research and contact tracing using online respondent-driven detection. In particular, it can provide information on the required minimum number of successfully sent invitations to reach large recruitment trees, a certain sample composition or certain number of waves.

受访者驱动检测（Respondent-driven detection）是一种链式招募方法，用于采集感染者接触者样本以提升病例发现效能。该方法以初始招募对象（即所谓的“种子”个体）为起点，受邀参与研究。随后，种子个体将获得固定数量的邀请券，用于邀请其在特定时段内有过接触的人员。后续被招募者也需完成相同操作，由此形成依托单一招募树（recruitment tree）串联的多轮接触者招募队列。但实际场景中，多数参与者往往无法成功邀请他人，或受邀者拒绝邀约，导致招募在数轮波次后便宣告终止。数学模型可用于分析各类因素对同伴招募的影响，并探究可持续招募得以实现的前提条件。本研究构建了随机模拟模型（stochastic simulation model），模型参数基于一项在线调研的实证数据设定，用于确定生成大规模招募树所需的阈值，以及实现样本个体特征构成稳态所需的招募波次数量。本研究还分析了参与者发出邀请数的均值与方差，和生成大规模招募树的概率之间的关联。本研究的核心发现为：相较于“多数参与者未发出任何邀请，仅少数群体发出最大额度邀请券”的场景，“参与者发出1至最大额度之间任意数量的邀请券”的模式，更有助于生成大规模招募树。本研究所提出的模型可作为实用工具，协助公共卫生专业人员开展基于线上受访者驱动检测的研究与接触者追踪工作。具体而言，该模型可提供所需的成功发出邀请的最小数量信息，以实现大规模招募树构建、特定样本构成或特定招募波次的目标。