  Assessing population-level effects of vaccines and other infectious disease
prevention measures is important to the field of public health. In infectious
disease studies, one person's treatment may affect another individual's
outcome, i.e., there may be interference between units. For example, use of bed
nets to prevent malaria by one individual may have an indirect or spillover
effect to other individuals living in close proximity. In some settings,
individuals may form groups or clusters where interference only occurs within
groups, i.e., there is partial interference. Inverse probability weighted
estimators have previously been developed for observational studies with
partial interference. Unfortunately, these estimators are not well suited for
studies with large clusters. Therefore, in this paper, the parametric g-formula
is extended to allow for partial interference. G-formula estimators are
proposed of overall effects, spillover effects when treated, and spillover
effects when untreated. The proposed estimators can accommodate large clusters
and do not suffer from the g-null paradox that may occur in the absence of
interference. The large sample properties of the proposed estimators are
derived, and simulation studies are presented demonstrating the finite-sample
performance of the proposed estimators. The Demographic and Health Survey from
the Democratic Republic of the Congo is then analyzed using the proposed
g-formula estimators to assess the overall and spillover effects of bed net use
on malaria.
