Non-parametric Causal Inference in Dynamic Thresholding Designs

TL;DR

This paper develops a non-parametric method to estimate the long-term causal effect of threshold-based treatments in dynamic systems, accounting for temporal patient data and trajectories.

Contribution

It introduces a local-linear-regression approach for causal inference in dynamic thresholding designs, addressing limitations of naive regression-discontinuity methods.

Findings

The method accurately estimates long-term effects in simulated data.

It accounts for temporal dynamics in threshold-based treatment policies.

Numerical experiments demonstrate its practical effectiveness.

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.