Efficient Treatment Effect Estimation in Observational Studies under Heterogeneous Partial Interference

In many observational studies in social science and medicine, individuals are connected in ways that affect the adoption and efficacy of interventions. One individual's treatment and attributes may affect another individual's treatment and outcome. In particular, this violates the commonly made stable unit treatment value assumption (SUTVA). Interference is often heterogeneous, and an individual's outcome is not only affected by how many, but also which, neighbors or connections are treated. In this paper, we propose a flexible framework for heterogeneous partial interference that partitions units into subsets based on observables. We allow interactions to be heterogeneous across subsets, but homogeneous for individuals within a subset. In this framework, we propose a class of estimators for heterogeneous direct and spillover effects from observational data that are shown to be doubly robust, asymptotically normal, and semiparametric efficient. In addition, we discuss a bias-variance tradeoff between robustness to heterogeneous interference and estimation efficiency. We further propose consistent matching-based variance estimators and hypothesis tests to determine the appropriate specification of interference structure. We apply our methods to the Add Health data and find that regular alcohol consumption exhibits negative effects on academic performance, but the magnitude of effect varies by gender and friends' alcohol consumption.