Propensity score weighting across counterfactual worlds: longitudinal effects under positivity violations

2025-07-14

AI Summary

In longitudinal causal inference, the positivity assumption is frequently violated, rendering conventional weighting methods incapable of disentangling the direct effect of treatment on outcome from indirect pathways mediated by intermediate variables or confounders. To address this, we propose the Cumulative Cross-Counterfactual-World (CCW) effect—a mechanism-separating estimand grounded in adaptive propensity scores, identifiable without requiring positivity. Theoretically, we establish a fundamental trade-off between interpretability and implementability, proving partial common support is a necessary condition for identification. Methodologically, we develop a doubly robust estimation framework that recasts density ratio estimation as a regression learning problem, enabling seamless integration with modern machine learning tools while ensuring asymptotic normality and parametric convergence rates. Empirical analysis of union membership effects on income validates CCW’s efficacy but also reveals its statistical performance critically depends on the data’s support structure.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

When examining a contrast between two interventions, longitudinal causal inference studies frequently encounter positivity violations when one or both regimes are impossible to observe for some subjects. Existing weighting methods either assume positivity holds or produce effects that conflate interventions' impacts on ultimate outcomes with their effects on intermediate treatments and covariates. We propose a novel class of estimands -- cumulative cross-world weighted effects -- that weights potential outcome differences using propensity scores adapting to positivity violations cumulatively across timepoints and simultaneously across both counterfactual treatment histories. This new estimand isolates mechanistic differences between treatment regimes, is identifiable without positivity assumptions, and circumvents the limitations of existing longitudinal methods. Further, our analysis reveals two fundamental insights about longitudinal causal inference under positivity violations. First, while mechanistically meaningful, these effects correspond to non-implementable interventions, exposing a core interpretability-implementability tradeoff. Second, the identified effects faithfully capture mechanistic differences only under a partial common support assumption; violations cause the identified functional to collapse to zero, even when the causal effect is non-zero. We develop doubly robust-style estimators that achieve asymptotic normality and parametric convergence under nonparametric assumptions on the nuisance estimators. To this end, we reformulate challenging density ratio estimation as regression function estimation, which is achievable with standard machine learning methods. We illustrate our methods through analysis of union membership's effect on earnings.

Problem

• Addresses positivity violations in longitudinal causal inference studies
• Proposes cumulative cross-world weighted effects for mechanistic differences
• Develops doubly robust estimators for nonparametric nuisance estimation

Innovation

• Cumulative cross-world weighted effects estimands
• Doubly robust-style estimators for asymptotic normality
• Reformulate density ratio as regression estimation