G-estimation with partial interference

In the study of infectious disease interventions, one individual's treatment may affect another individual's outcome, i.e., there may be interference. In this paper, methods are developed to draw inference about causal effects when interference may be present in observational studies. The special case of partial interference is considered wherein individuals within a cluster may interfere with one another, but they cannot interfere with individuals in other clusters. Existing methods that handle partial interference utilize inverse probability weighting or the g-formula. Some of these methods require correctly specifying parametric models and often do not perform well in the presence of large clusters. In this paper a G-estimation approach is considered instead which is able to handle larger clusters. Singly-robust and doubly-robust G-estimators of overall effects, effects when treated, and effects when untreated are proposed. The large sample properties of the estimators are derived using estimating equation theory. Simulation studies are presented to demonstrate the finite-sample performance of the proposed estimators. The 2013-14 Demographic and Health Survey in the Democratic Republic of the Congo is analyzed to estimate the effects of bed net use on malaria prevalence.