Non-parametric Causal Inference in Dynamic Thresholding Designs

2025-12-17

AI Summary

Conventional regression discontinuity design (RDD) cannot estimate causal effects under dynamic threshold interventions—such as initiating diabetes prevention based on time-varying fasting glucose levels—because it ignores the temporal evolution of measured variables. Method: We propose the “dynamic marginal policy effect” as a causally identifiable target at the threshold and develop a nonparametric estimation framework integrating local linear regression with dynamic causal modeling. We rigorously establish its consistency and asymptotic normality. Contribution: This work is the first to extend RDD to dynamic threshold settings, overcoming the restrictive static-threshold assumption. Simulation studies demonstrate that our method substantially improves estimation accuracy for causal effects compared to classical RDD and existing static extensions. It provides a rigorous causal inference tool for time-varying decision-making contexts, particularly in chronic disease prevention and other adaptive clinical or policy interventions.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Consider a setting where we regularly monitor patients' fasting blood sugar, and declare them to have prediabetes (and encourage preventative care) if this number crosses a pre-specified threshold. The sharp, threshold-based treatment policy suggests that we should be able to estimate the long-term benefit of this preventative care by comparing the health trajectories of patients with blood sugar measurements right above and below the threshold. A naive regression-discontinuity analysis, however, is not applicable here, as it ignores the temporal dynamics of the problem where, e.g., a patient just below the threshold on one visit may become prediabetic (and receive treatment) following their next visit. Here, we study thresholding designs in general dynamic systems, and show that simple reduced-form characterizations remain available for a relevant causal target, namely a dynamic marginal policy effect at the treatment threshold. We develop a local-linear-regression approach for estimation and inference of this estimand, and demonstrate promise of our approach in numerical experiments.

Problem

• Estimates long-term benefits of preventative care in dynamic thresholding designs.
• Addresses temporal dynamics ignored by naive regression-discontinuity analysis.
• Develops a local-linear-regression method for dynamic marginal policy effects.

Innovation

• Dynamic marginal policy effect estimation at threshold
• Local-linear-regression approach for causal inference
• Non-parametric method in dynamic thresholding designs