Gaussian Processes for Observational Dose-Response Inference

TL;DR

This paper introduces a Gaussian process-based method for estimating dose-response functions in observational studies, effectively handling uncertainty and confounding, and demonstrating improved accuracy and robustness over existing methods.

Contribution

It adapts Gaussian processes for dose-response inference, incorporating propensity score uncertainty and establishing theoretical foundations for the kernel used, with demonstrated robustness and improved estimation.

Findings

Improved dose-response estimation accuracy.

Enhanced robustness to model misspecification.

Reduced sensitivity to confounding effects.

Abstract

We adapt Gaussian processes for estimating the average dose-response function in observational settings, introducing a powerful complement to treatment effect estimation for understanding heterogeneous effects. We incorporate samples from a Gaussian process posterior for the propensity score into a Gaussian process response model using Girard's approach to integrating over uncertainty in training data. We show Girard's method admits a positive-definite kernel, and provide theoretical justification by identifying it with an inner product of kernel mean embeddings. We demonstrate double robustness of our approach under a misspecified response function or propensity score. We characterize and mitigate regularization-induced confounding in Gaussian process response models. We show improvement over other methods for average dose-response function estimation in terms of coverage of the dose-response function and estimation bias, with less sensitivity to misspecification across experiments.