Causal Inference in Longitudinal Data under Unknown Interference

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 introduce a class of causal estimands that capture the effects of treatment histories at any specified proximity level and show that they can be represented by a modified marginal structural model. Under sequential exchangeability, these estimands are identifiable and can be estimated using inverse probability weighting. We derive conditions for consistency and asymptotic normality of the estimators and provide procedures for constructing asymptotically conservative confidence intervals. The method's utility is demonstrated through applications in both social science and biomedical settings.