Causal Estimation of Exposure Shifts with Neural Networks

TL;DR

This paper introduces TRESNET, a neural-network framework designed to estimate shift-response functions (SRFs), i.e., the causal effect of distribution shifts in a continuous exposure. It advances targeted regularization to SRFs, yielding double-robust and semiparametric-efficient estimates, and extends the method to outcomes from the exponential family (e.g., counts). The approach combines a learned outcome model with a density-ratio head and uses a specialized TR loss to ensure the estimator satisfies the efficient estimating equation, achieving consistent SRF estimates under mild model misspecification. The authors demonstrate strong performance in simulations and apply the method to a high-stakes public-health policy question: the potential mortality impact of lowering PM$_{2.5}$ NAAQS, using data from 68 million Medicare beneficiaries. The results suggest approximately a 4% reduction in elder deaths at a 9 μg/m3 cutoff, highlighting SRFs’ relevance for policy evaluation and the practical utility of SRF-oriented neural estimators in large-scale epidemiological studies.

Abstract

A fundamental task in causal inference is estimating the effect of distribution shift in the treatment variable. We refer to this problem as shift-response function (SRF) estimation. Existing neural network methods for causal inference lack theoretical guarantees and practical implementations for SRF estimation. In this paper, we introduce Targeted Regularization for Exposure Shifts with Neural Networks (TRESNET), a method to estimate SRFs with robustness and efficiency guarantees. Our contributions are twofold. First, we propose a targeted regularization loss for neural networks with theoretical properties that ensure double robustness and asymptotic efficiency specific to SRF estimation. Second, we extend targeted regularization to support loss functions from the exponential family to accommodate non-continuous outcome distributions (e.g., discrete counts). We conduct benchmark experiments demonstrating TRESNET's broad applicability and competitiveness. We then apply our method to a key policy question in public health to estimate the causal effect of revising the US National Ambient Air Quality Standards (NAAQS) for PM 2.5 from 12 $μg/m^3$ to 9 $μg/m^3$. This change has been recently proposed by the US Environmental Protection Agency (EPA). Our goal is to estimate the reduction in deaths that would result from this anticipated revision using data consisting of 68 million individuals across the U.S.

Figures (5)

• Figure 1: Estimated mortality reduction under a cutoff exposure shift lowering the annual $\text{PM}_{2.5}$ in all regions below a given threshold. Uncertainty bands represent the interquartile range from an ensemble of networks. Data source: US Medicare claims from 2000--2016.
• Figure 2: Two examples of exposure shifts with their implied counterfactuals and, for comparison, the implied counterfactuals of an exposure-response function at a given treatment value.
• Figure 3: tresnet architecture using a head for the density ratio model and a head for the outcome model.
• Figure 4: Fraction (%) of observed units remaining above $\text{PM}_{2.5}$ limit as a function of reduction (%) considering different NAAQS (current NAAQS is set at 12 $\mathrm{\upmu g/m^3}$).
• Figure 5: Estimated SRF of the total deaths (%) for different cutoffs.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2
• Proposition 1
• corollary 1
• Proposition 2