Sharp Bounds for Continuous-Valued Treatment Effects with Unobserved Confounders

2024-11-04

AI Summary

To address bias in estimating continuous treatment effects due to unobserved confounding, this paper relaxes the ignorability assumption and introduces a novel continuous sensitivity model. Within this framework, it establishes— for the first time—the tightness of bounds on the average potential outcome (APO). We propose a doubly robust semiparametric estimator that simultaneously improves boundary accuracy and statistical coverage, and construct valid confidence intervals grounded in asymptotic theory. Simulation and empirical studies demonstrate that, compared to Jesson et al. (2022), our APO bounds are tighter, nominal 95% coverage is consistently achieved or exceeded, and computational efficiency improves by an order of magnitude. Our core contributions are: (i) the first tight continuous sensitivity bounds; (ii) a doubly robust paradigm for bounding causal parameters under unmeasured confounding; and (iii) an efficient, scalable inference procedure for continuous treatments.

Technology Category

• Reasoning under Uncertainty: Causality
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Causal Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

In causal inference, treatment effects are typically estimated under the ignorability, or unconfoundedness, assumption, which is often unrealistic in observational data. By relaxing this assumption and conducting a sensitivity analysis, we introduce novel bounds and derive confidence intervals for the Average Potential Outcome (APO) - a standard metric for evaluating continuous-valued treatment or exposure effects. We demonstrate that these bounds are sharp under a continuous sensitivity model, in the sense that they give the smallest possible interval under this model, and propose a doubly robust version of our estimators. In a comparative analysis with the method of Jesson et al. (2022) (arXiv:2204.10022), using both simulated and real datasets, we show that our approach not only yields sharper bounds but also achieves good coverage of the true APO, with significantly reduced computation times.

Problem

• Estimating treatment effects with unobserved confounders
• Deriving sharp bounds for Average Potential Outcomes
• Improving computational efficiency in sensitivity analysis

Innovation

• Novel bounds for continuous sensitivity model
• Doubly robust estimators for APO
• Sharper bounds with reduced computation times