Estimating causal effects in the presence of spillover among individuals embedded within a social network is often challenging with missing information. The spillover effect is the effect of an intervention if a participant is not exposed to the intervention themselves but is connected to intervention recipients in the network. In network-based studies, outcomes may be missing due to the administrative end of a study or participants being lost to follow-up due to study dropout, also known as censoring. We propose an inverse probability censoring weighted (IPCW) estimator, which is an extension of an IPW estimator for network-based observational studies to settings where the outcome is subject to possible censoring. We demonstrated that the proposed estimator was consistent and asymptotically normal. We also derived a closed-form estimator of the asymptotic variance estimator. We used the IPCW estimator to quantify the spillover effects in a network-based study of a nonrandomized intervention with censoring of the outcome. A simulation study was conducted to evaluate the finite-sample performance of the IPCW estimators. The simulation study demonstrated that the estimator performed well in finite samples when the sample size and number of connected subnetworks (components) were fairly large. We then employed the method to evaluate the spillover effects of community alerts on self-reported HIV risk behavior among people who inject drugs and their contacts in the Transmission Reduction Intervention Project (TRIP), 2013 to 2015, Athens, Greece. Community alerts were protective not only for the person who received the alert from the study but also among others in the network likely through information shared between participants. In this study, we found that the risk of HIV behavior was reduced by increasing the proportion of a participant's immediate contacts exposed to community alerts.

翻译：在社会网络中，当个体之间存在溢出效应时，估计因果效应往往因信息缺失而充满挑战。溢出效应是指参与者本身未接受干预，但与网络中接受干预的个体存在联系时，干预措施产生的影响。在基于网络的研究中，结果可能因研究行政终止、或参与者因退出研究而失访（即删失）而缺失。我们提出一种逆概率删失加权（IPCW）估计量，它是针对基于网络观察性研究的逆概率加权（IPW）估计量的扩展，适用于结果可能存在删失的场景。我们证明该估计量具有一致性和渐近正态性，并推导了渐近方差的闭合形式估计量。我们采用IPCW估计量量化一项非随机化干预中基于网络研究在结果存在删失时的溢出效应。通过模拟研究评估IPCW估计量在有限样本下的性能，结果表明当样本规模和连接子网络（组件）数量足够大时，该估计量表现良好。随后，我们将该方法应用于2013年至2015年在希腊雅典开展的"传播减少干预项目（TRIP）"中，评估社区警报对注射吸毒者及其接触者自报HIV风险行为的溢出效应。社区警报不仅对接收警报的研究参与者具有保护作用，还可能通过参与者之间的信息共享对网络中的其他个体产生保护效应。本研究发现，当参与者直接接触者中暴露于社区警报的比例增加时，HIV风险行为的发生率显著降低。