# Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combination

arXiv: https://arxiv.org/abs/2502.18960 · HTML: https://mlsanity.com/paper/2502.18960/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables](https://mlsanity.com/paper/1611.09925/) (2016)
- [Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning](https://mlsanity.com/paper/2405.03342/) (2024)
- [Estimating individual treatment effects under unobserved confounding using binary instruments](https://mlsanity.com/paper/2208.08544/) (2022)
- [Long-Term Effect Estimation with Surrogate Representation](https://mlsanity.com/paper/2008.08236/) (2020)
- [Long-term Causal Effects Estimation via Latent Surrogates Representation Learning](https://mlsanity.com/paper/2208.04589/) (2022)
- [Data Integration in Causal Inference](https://mlsanity.com/paper/2110.01106/) (2021)
- [Inferring the Long-Term Causal Effects of Long-Term Treatments from Short-Term Experiments](https://mlsanity.com/paper/2311.08527/) (2023)
- [Identification and estimation of treatment effects on long-term outcomes in clinical trials with external observational data](https://mlsanity.com/paper/2208.10163/) (2022)
- [Policy Learning for Balancing Short-Term and Long-Term Rewards](https://mlsanity.com/paper/2405.03329/) (2024)
- [Double Robustness for Complier Parameters and a Semiparametric Test for Complier Characteristics](https://mlsanity.com/paper/1909.05244/) (2019)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)

## Built on by (most cited first, 2 of 2)

- [Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning](https://mlsanity.com/paper/2505.05192/) (2025)
- [Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects](https://mlsanity.com/paper/2604.00915/) (2026)

## Abstract (arXiv)

Long-term causal inference has drawn increasing attention in many scientific domains. Existing methods mainly focus on estimating average long-term causal effects by combining long-term observational data and short-term experimental data. However, it is still understudied how to robustly and effectively estimate heterogeneous long-term causal effects, significantly limiting practical applications. In this paper, we propose several two-stage style nonparametric estimators for heterogeneous long-term causal effect estimation, including propensity-based, regression-based, and multiple robust estimators. We conduct a comprehensive theoretical analysis of their asymptotic properties under mild assumptions, with the ultimate goal of building a better understanding of the conditions under which some estimators can be expected to perform better. Extensive experiments across several semi-synthetic and real-world datasets validate the theoretical results and demonstrate the effectiveness of the proposed estimators.