  In most real-world systems units are interconnected and can be represented as
networks consisting of nodes and edges. For instance, in social systems
individuals can have social ties, family or financial relationships. In
settings where some units are exposed to a treatment and its effect spills over
connected units, estimating both the direct effect of the treatment and
spillover effects presents several challenges. First, assumptions on the way
and the extent to which spillover effects occur along the observed network are
required. Second, in observational studies, where the treatment assignment is
not under the control of the investigator, confounding and homophily are
potential threats to the identification and estimation of causal effects on
networks. Here, we make two structural assumptions: i) neighborhood
interference, which assumes interference operates only through a function of
the immediate neighbors' treatments ii) unconfoundedness of the individual and
neighborhood treatment, which rules out the presence of unmeasured confounding
variables, including those driving homophily. Under these assumptions we
develop a new covariate-adjustment estimator for treatment and spillover
effects in observational studies on networks. Estimation is based on a
generalized propensity score that balances individual and neighborhood
covariates across units under different levels of individual treatment and of
exposure to neighbors' treatment. Adjustment for propensity score is performed
using a penalized spline regression. Inference capitalizes on a three-step
Bayesian procedure which allows to take into account the uncertainty in the
propensity score estimation and avoiding model feedback. Finally, correlation
of interacting units is taken into account using a community detection
algorithm and incorporating random effects in the outcome model.
