  Interference occurs when the treatment (or exposure) of one individual
affects the outcomes of others. In some settings it may be reasonable to assume
individuals can be partitioned into clusters such that there is no interference
between individuals in different clusters, i.e., there is partial interference.
In observational studies with partial interference, inverse probability
weighted (IPW) estimators have been proposed of different possible treatment
effects. However, the validity of IPW estimators depends on the propensity
score being known or correctly modeled. Alternatively, one can estimate the
treatment effect using an outcome regression model. In this paper, we propose
doubly robust (DR) estimators which 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, as well as 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.

Methodology