Doubly robust estimation in observational studies with partial interference

Interference occurs when the treatment (or exposure) of one individual affects the outcomes of others. In some settings, it may be reasonable to assume that individuals can be partitioned into clusters such that there is no interference between individuals in different clusters, that is, there is partial interference. In observational studies with partial interference, inverse probability weighted (IPW) estimators have been something else different possible treatment effects. However, the validity of IPW estimators depends on the propensity score being known or correctly modelled. Alternatively, one can estimate the treatment effect using an outcome regression model. In this paper, we propose doubly robust (DR) estimators that utilize both models and are consistent and asymptotically normal if either model, but not necessarily both, is correctly specified. Empirical results are presented to demonstrate the DR property of the proposed estimators and the efficiency gain of DR over IPW estimators when both models are correctly specified. The different estimators are illustrated using data from a study examining the effects of cholera vaccination in Bangladesh.