Causal inference with misspecified interference structure

Interference occurs when the potential outcomes of a unit depend on the treatments assigned to other units. That is frequently the case in many domains, such as in the social sciences and infectious disease epidemiology. Often, the interference structure is represented by a network, which is typically assumed to be given and accurate. However, correctly specifying the network can be challenging, as edges can be censored, the structure can change over time, and contamination between clusters may exist. Building on the exposure mapping framework, we derive the bias arising from estimating causal effects under a misspecified interference structure. To address this problem, we propose a novel estimator that uses multiple networks simultaneously and is unbiased if one of the networks correctly represents the interference structure, thus providing robustness to the network specification. Additionally, we propose a sensitivity analysis that quantifies the impact of a postulated misspecification mechanism on the causal estimates. Through simulation studies, we illustrate the bias from assuming an incorrect network and show the bias-variance tradeoff of our proposed network-misspecification-robust estimator. We demonstrate the utility of our methods in two real examples.