Causal Inference in Longitudinal Data under Unknown Interference

Abstract: In longitudinal studies where units are embedded in space or a social network, interference may arise, meaning that a unit's outcome can depend on treatment histories of others. The presence of interference poses significant challenges for causal inference, particularly when the interference structure -- how a unit's outcome responds to others' influences -- is complex, heterogeneous, and unknown to researchers. This paper develops a general framework for identifying and estimating both direct and spillover effects of treatment histories under minimal assumptions about the interference structure. We define a class of policy-relevant causal estimands and show that they can be represented by a modified marginal structural model (MSM). Under the standard assumption of sequential exchangeability, these estimands are identifiable and can be estimated using inverse probability weighting (IPW). We derive conditions for consistency and asymptotic normality of the estimators and provide procedures for constructing Wald-type confidence intervals with valid coverage in large samples. The method's utility is demonstrated through applications in both social science and biomedical settings.