  Long-term causal effect estimation is a significant but challenging problem
in many applications. Existing methods rely on ideal assumptions to estimate
long-term average effects, e.g., no unobserved confounders or a binary
treatment,while in numerous real-world applications, these assumptions could be
violated and average effects are unable to provide individual-level
suggestions.In this paper,we address a more general problem of estimating the
long-term heterogeneous dose-response curve (HDRC) while accounting for
unobserved confounders. Specifically, to remove unobserved confounding in
observational data, we introduce an optimal transport weighting framework to
align the observational data to the experimental data with theoretical
guarantees. 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 an HDRC estimator building upon the above
theoretical foundations. Extensive experimental studies conducted on multiple
synthetic and semi-synthetic datasets demonstrate the effectiveness of our
proposed method.
