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.
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.
@cite_0
2036443429
Recently, there has been increasing interest in making causal inference when interference is possible. In the presence of interference, treatment may have several types of effects. In this article, we consider inference about such effects when the population consists of groups of individuals where interference is possible within groups but not between groups. A two-stage randomization design is assumed where in the first stage groups are randomized to different treatment allocation strategies and in the second stage individuals are randomized to treatment or control conditional on the strategy assigned to their group in the first stage. For this design, the asymptotic distributions of estimators of the causal effects are derived when either the number of individuals per group or the number of groups grows large. Under certain homogeneity assumptions, the asymptotic distributions provide justification for Wald-type confidence intervals (CIs) and tests. Empirical results demonstrate that the Wald CIs have good coverage in finite samples and are narrower than CIs based on either the Chebyshev or Hoeffding inequalities provided the number of groups is not too small. The methods are illustrated by two examples which consider the effects of cholera vaccination and an intervention to encourage voting.