Causal Inference in Longitudinal Data under Unknown Interference

TL;DR

This paper presents a flexible framework for causal inference in longitudinal studies with unknown interference, allowing estimation of direct and spillover effects without detailed interference structure knowledge.

Contribution

It introduces a class of causal estimands and estimation methods that work under minimal assumptions about complex, heterogeneous interference structures.

Findings

Estimators are consistent and asymptotically normal under sequential exchangeability.

The framework applies to social science and biomedical data.

Procedures for conservative confidence intervals are provided.

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 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.