Sensitivity analysis for incremental effects, with application to a study of victimization&offending

2026-01-25

AI Summary

This study addresses the challenge of conducting sensitivity analysis for unmeasured confounding under incremental propensity score interventions, a setting where existing methods fall short. The authors develop the first analytical framework based on Rosenbaum’s sensitivity model, deriving sharp bounds for incremental causal effects at a single time point and proposing an estimator that is both doubly robust and asymptotically normal. They further extend this framework to longitudinal data with time-varying treatments, examining identifiability and estimation under marginal sensitivity models. Theoretical results show that the derived effect bounds can be either tighter or wider than those from traditional potential outcomes approaches. Empirical validation using the Add Health dataset demonstrates the robustness of estimated effects of victimization on subsequent criminal behavior across varying levels of unmeasured confounding.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Sensitivity analysis for unmeasured confounding under incremental propensity score interventions remains relatively underdeveloped. Incremental interventions define stochastic treatment regimes by multiplying the odds of treatment, offering a flexible framework for causal effect estimation. To study incremental effects when there are unobserved confounders, we adopt Rosenbaum's sensitivity model in single time point settings, and propose a doubly robust estimator for the resulting effect bounds. The bound estimators are asymptotically normal under mild conditions on nuisance function estimation. We show that incremental effect bounds can be narrower or wider than those for mean potential outcomes, and that the bounds must lie between the expected minimum and maximum of the conditional bounds on E(Y^0|X) and E(Y^1|X). For time-varying treatments, we consider the marginal sensitivity model. Although sharp bounds for incremental effects are identifiable from longitudinal data under this model, practical estimators have not yet been established; we discuss this challenge and provide partial results toward implementation. Finally, we apply our methods to study the effect of victimization on subsequent offending using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health), illustrating the robustness of our findings in an empirical setting.

Problem

• sensitivity analysis
• unmeasured confounding
• incremental effects
• causal inference
• propensity score

Innovation

• incremental propensity score
• sensitivity analysis
• unmeasured confounding
• doubly robust estimation
• causal inference