Estimation of causal dose-response functions under data fusion

TL;DR

This paper introduces a data fusion framework with a Neyman-orthogonal loss for estimating causal dose-response functions, improving accuracy and efficiency by leveraging multiple data sources.

Contribution

It develops a novel orthogonal loss function and stochastic approximation method for data fusion, enhancing estimation of dose-response functions with theoretical guarantees.

Findings

Tighter finite-sample regret bounds with additional data sources

Improved worst-case performance demonstrated through minimax bounds

Simulation results show increased estimation accuracy using data fusion

Abstract

Estimating the causal dose-response function is challenging, particularly when data from a single source are insufficient to estimate responses precisely across all exposure levels. To overcome this limitation, we propose a data fusion framework that leverages multiple data sources that are partially aligned with the target distribution. Specifically, we derive a Neyman-orthogonal loss function tailored for estimating the dose-response function within data fusion settings. To improve computational efficiency, we propose a stochastic approximation that retains orthogonality. We apply kernel ridge regression with this approximation, which provides closed-form estimators. Our theoretical analysis demonstrates that incorporating additional data sources yields tighter finite-sample regret bounds and improved worst-case performance, as confirmed via minimax lower bound comparison. Simulation studies validate the practical advantages of our approach, showing improved estimation accuracy when employing data fusion. This study highlights the potential of data fusion for estimating non-smooth parameters such as causal dose-response functions.