Causal inference on a population of units connected through a network often presents technical challenges, including how to account for interference. In the presence of local interference, for instance, potential outcomes of a unit depend on its treatment as well as on the treatments of other local units, such as its neighbors according to the network. In observational studies, a further complication is that the typical unconfoundedness assumption must be extended - say, to include the treatment of neighbors, and individual and neighborhood covariates - to guarantee identification and valid inference. Here, we derive analytical expressions for the bias of a naive estimator that wrongly assumes away interference. The bias depends on the level of interference but also on the degree of association between individual and neighborhood treatments. We propose an extended unconfoundedness assumption that accounts for interference, and we develop new covariate-adjustment methods that lead to valid estimates of treatment and interference effects in observational studies on networks. Valid estimation is based on a generalized propensity score that balances individual and neighborhood covariates across units under different levels of individual treatment and of exposure to neighbors' treatment. We illustrate how the proposed approach improves over alternative methods in a simulation study, leveraging Add-Health network and covariate data.
@cite_0: Interference is said to be present when the exposure or treatment received by one individual may affect the outcomes of other individuals. Such interference can arise in settings in which the outcomes of the various individuals come about through social interactions. When interference is present, causal inference is rendered considerably more complex, and the literature on causal inference in the presence of interference has just recently begun to develop. In this article we summarise some of the concepts and results from the existing literature and extend that literature in considering new results for finite sample inference, new inverse probability weighting estimators in the presence of interference and new causal estimands of interest.
On the other hand, work on causal inference for observational network data is still in its infancy. @cite_0 extend these IPW estimators in the presence of general forms of interference on networks. They focus on direct and indirect effects based on Bernoulli allocation strategies similar to those defined by . Although their estimators allows for general forms of interference, their estimator and their asymptotic results are proved under partial interference and clustered data. and then propose a TMLE estimator for similar treatment and spillover effects and prove asymptotic results under IID assumptions. Finally extend this TMLE estimator to allow for dependence due to both contagion and homophily and derive asymptotic results that allow the number of ties per node to increase as the network grows.