Doubly Robust Inference on Causal Derivative Effects for Continuous Treatments

2025-01-12

AI Summary

This paper addresses causal inference under continuous treatment, focusing on nonparametric estimation of the derivative function of the dose–response curve—i.e., the marginal treatment effect—to overcome the limitation of conventional methods that only target the mean response and neglect critical slope information. We propose the first doubly robust framework for causal derivative estimation: under the positivity assumption, we construct a kernel-smoothed doubly robust estimator; when positivity fails, we develop bias-corrected inverse-probability-weighted (IPW) and doubly robust estimators, and establish the nonparametric efficiency bound. Our estimators achieve the standard nonparametric convergence rate and are asymptotically normal. Simulation studies and empirical analysis of a job training program demonstrate both statistical efficiency and model robustness.

Technology Category

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

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Statistical methods for causal inference with continuous treatments mainly focus on estimating the mean potential outcome function, commonly known as the dose-response curve. However, it is often not the dose-response curve but its derivative function that signals the treatment effect. In this paper, we investigate nonparametric inference on the derivative of the dose-response curve with and without the positivity condition. Under the positivity and other regularity conditions, we propose a doubly robust (DR) inference method for estimating the derivative of the dose-response curve using kernel smoothing. When the positivity condition is violated, we demonstrate the inconsistency of conventional inverse probability weighting (IPW) and DR estimators, and introduce novel bias-corrected IPW and DR estimators. In all settings, our DR estimator achieves asymptotic normality at the standard nonparametric rate of convergence with nonparametric efficiency guarantees. Additionally, our approach reveals an interesting connection to nonparametric support and level set estimation problems. Finally, we demonstrate the applicability of our proposed estimators through simulations and a case study of evaluating a job training program.

Problem

• Estimating derivative of dose-response curve for continuous treatments
• Addressing inconsistency in IPW and DR estimators without positivity
• Proposing bias-corrected estimators with asymptotic normality guarantees

Innovation

• Doubly robust inference for derivative effects
• Bias-corrected IPW and DR estimators
• Kernel smoothing with nonparametric efficiency