  The stable unit treatment value assumption states that the outcome of an
individual is not affected by the treatment statuses of others, however in many
real world applications, treatments can have an effect on many others beyond
the immediately treated. Interference can generically be thought of as mediated
through some network structure. In many empirically relevant situations
however, complete network data (required to adjust for these spillover effects)
are too costly or logistically infeasible to collect. Partially or indirectly
observed network data (e.g., subsamples, aggregated relational data (ARD),
egocentric sampling, or respondent-driven sampling) reduce the logistical and
financial burden of collecting network data, but the statistical properties of
treatment effect adjustments from these design strategies are only beginning to
be explored. In this paper, we present a framework for the estimation and
inference of treatment effect adjustments using partial network data through
the lens of structural causal models. We also illustrate procedures to assign
treatments using only partial network data, with the goal of either minimizing
estimator variance or optimally seeding. We derive single network asymptotic
results applicable to a variety of choices for an underlying graph model. We
validate our approach using simulated experiments on observed graphs with
applications to information diffusion in India and Malawi.
