  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.
