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

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.