Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights

TL;DR

This paper proposes a novel method for estimating long-term heterogeneous dose-response curves in observational data by using optimal transport weights to address unobserved confounders and provide generalization guarantees.

Contribution

It introduces an optimal transport weighting framework to align observational data with experimental data and establishes a generalization bound for counterfactual prediction in long-term effects.

Findings

Effective in removing unobserved confounders

Accurate prediction of heterogeneous long-term effects

Validated on synthetic and semi-synthetic datasets

Abstract

Long-term treatment effect estimation is a significant but challenging problem in many applications. Existing methods rely on ideal assumptions, such as no unobserved confounders or binary treatment, to estimate long-term average treatment effects. However, in numerous real-world applications, these assumptions could be violated, and average treatment effects are insufficient for personalized decision-making. In this paper, we address a more general problem of estimating long-term Heterogeneous Dose-Response Curve (HDRC) while accounting for unobserved confounders and continuous treatment. Specifically, to remove the unobserved confounders in the long-term observational data, we introduce an optimal transport weighting framework to align the long-term observational data to an auxiliary short-term experimental data. Furthermore, to accurately predict the heterogeneous effects of continuous treatment, we establish a generalization bound on counterfactual prediction error by leveraging the reweighted distribution induced by optimal transport. Finally, we develop a long-term HDRC estimator building upon the above theoretical foundations. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our approach.