  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, the use of
bed nets to prevent malaria by one individual may have an indirect effect on
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 for overall
effects, effects when treated, and 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 assuming no unmeasured
confounders and that the partial interference takes a particular form (referred
to as `weak stratified interference'). 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 effects of bed
net use on malaria.
