Longitudinal weighted and trimmed treatment effects with flip interventions

2025-06-10

AI Summary

This paper addresses the long-standing challenge of positivity violations—specifically, non-baseline-period propensity score overlap—in longitudinal causal inference. We propose a novel weighting and truncation framework grounded in randomized “flip interventions,” the first extension of flip interventions to longitudinal settings. This approach endows the weighted average treatment effect with a clear policy interpretation and ensures identifiability of causal effects under arbitrary non-baseline positivity violations—overcoming a key limitation of conventional methods that cannot weight non-baseline covariates. Integrating efficient influence-function-driven multiple robustness and sequential double robustness, smoothed propensity score modeling, and asymptotic theory, our estimator achieves √n-consistency and asymptotic normality. Empirical analysis demonstrates its effectiveness and robustness in evaluating the income effects of union membership.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements

Abstract

Weighting and trimming are popular methods for addressing positivity violations in causal inference. While well-studied with single-timepoint data, standard methods do not easily generalize to address non-baseline positivity violations in longitudinal data, and remain vulnerable to such violations. In this paper, we extend weighting and trimming to longitudinal data via stochastic ``flip'' interventions, which maintain the treatment status of subjects who would have received the target treatment, and flip others' treatment to the target with probability equal to their weight (e.g., overlap weight, trimming indicator). We first show, in single-timepoint data, that flip interventions yield a large class of weighted average treatment effects, ascribing a novel policy interpretation to these popular weighted estimands. With longitudinal data, we then show that flip interventions provide interpretable weighting or trimming on non-baseline covariates and, crucially, yield effects that are identifiable under arbitrary positivity violations. Moreover, we demonstrate that flip interventions are policy-relevant since they could be implemented in practice. By contrast, we show that alternative approaches for weighting on non-baseline covariates fail to achieve this property. We derive flexible and efficient estimators based on efficient influence functions when the weight is a smooth function of the propensity score. Namely, we construct multiply robust-style and sequentially doubly robust-style estimators that achieve root-n consistency and asymptotic normality under nonparametric conditions. Finally, we demonstrate our methods through an analysis of the effect of union membership on earnings.

Problem

• Extend weighting and trimming to longitudinal data via flip interventions
• Address non-baseline positivity violations in causal inference
• Provide interpretable and policy-relevant treatment effects under violations

Innovation

• Extends weighting and trimming to longitudinal data
• Uses stochastic flip interventions for treatment effects
• Develops robust estimators via influence functions