Estimation of heterogeneous long-term treatment effects (HLTEs) is relevant for personalized decision-making in marketing, economics, and medicine, where short-term observational datasets are often combined with long-term observational datasets. However, HLTE estimation is challenging due to limited overlap in treatment assignments or in long-term outcomes for certain subpopulations, which can lead to unstable HLTE estimates with large finite-sample variance. To address this challenge, we introduce the LT-O-learners (Long-Term Orthogonal Learners), a set of novel orthogonal learners for HLTE estimation in the canonical HLTE setting with surrogacy. The key idea of our LT-O-learners is to retarget the loss via custom overlap weights that downweight low-overlap samples. We show that the retargeted loss recovers the true HLTE pointwise and satisfies Neyman-orthogonality. We further prove two key theoretical results: (i) The nuisance error enters the error bound only through higher-order terms, which means our learners are robust to nuisance estimation error. (ii) Under a linear function class, the retargeting effectively controls the asymptotic variance of the HLTE estimator via the overlap weights in low-overlap regimes. We conduct experiments on synthetic and real-world datasets to confirm the theoretical properties of our LT-O-learners, particularly robustness in low-overlap regimes. To our knowledge, ours are the first orthogonal learners for HLTE estimation robust to low overlap in long-term settings.
Figures & tables
Figure 1: Our HLTE setting: The yellow and green box illustrate our two-sample setting. D1 and D2 share covariates X and surrogates S . The surrogate index (i.e. ED2[Y∣S,X] ), learned in the long-term dataset, is used as a proxy for long-term outcomes in the short-term dataset. The left plot shows the two overlap issues.
Meta-learner
Analogy in standard HTE
Neyman orthogonal
Robust to low treatment overlap
Robust to low outcome overlap
LT-T-learner
T-learner [ 38 ]
✗
✗
✗
LT-RA-learner
RA-learner [ 15 ]
✗
✗
✗
LT-IPW-learner
IPW-learner [ 15 ]
✗
✗
✗
LT-O-DR-learner ( ours , ω≡1 )
DR-learner [ 37 ]
✓
✗
✗
LT-O-TO-learner ( ours , ω=π2(1−π)2 )
R-learner [ 42 ]
✓
✓
✗
LT-O-LO-learner ( ours , ω=ρ )
–
✓
✗
✓
Table 1: Overview of meta-learners for HLTE estimation. Our LT-O-learners are the only approaches that are both Neyman-orthogonal and robust to different types of low-overlap scenarios.
Table 3
Figure 2: Variance of estimator across different overlap scenarios ( γ ): Low overlap leads to a high finite-sample variance of the DR-learner, while our LT-O-learners maintain a low variance.
Figure 3: Heterogeneity on GAIN. Subgroup HLTEs on Q13:36 earnings of the LT-O-DO-learner against the pseudo ground-truth. Our method captures the known heterogeneity across age, education, prior labour status, and ethnicity.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: Causal diagram for the canonical surrogacy setting. The short-term experimental dataset D1 observes (X,A,S) while Y is unobserved (dashed node); the long-term observational dataset D2 observes (X,S,Y) with treatment A absent. The dotted arrow A→Y marked with × indicates that the surrogacy assumption rules out a direct effect of A on Y given (S,X) .
Setting
Paper
Short-term D1
Long-term D2
Identification through
Target
Benefits
X
A
S
X
A
S
Y
Neyman orthogonality
Robustness to low overlap
Latent unconfoundedness
Chen and Ritzwoller [9] (latent unconf.)
✓
✓
✓
✓
✓
✓
✓
Latent unconfoundedness
ALTE
✓
✗
Yang et al. [61]
✓
✓
✓
✓
✓
✓
✓
Latent unconfoundedness
HLTE (dose-response)
✗
✗
Equi- confounding
Ghassami et al. [24]
✓
✓
✓
✓
✓
✓
✓
Additive equi-conf. †
ALTE, ATT
✓
✗
Chen et al. [10]
✓
✓
✓
✓
✓
✓
✓
CAECB
HLTE
✓
✗
Proximal
Imbens et al. [32]
✓
✓
✓
✓
✓
✓
✓
Outcome + selection bridge functions
ALTE
✓
✗
Appendix
Table 4: Comparison of settings for long-term causal effect estimation. Methods are grouped by their high-level identification setting. ✓/ ✓ indicates that a variable is observed; for the treatment columns, ✓ denotes binary/categorical treatment and ✓ denotes continuous treatment. ✗ indicates that the variable is not observed. ✓ / ✗ in the Benefits columns indicate whether each method satisfies the corresponding property.
Figure 5: Benefit of Neyman-orthogonality: ( Left ) PEHE vs. sample size. The orthogonal LT-O-DO-learner outperforms the weighted (but non-orthogonal) DR/RA-learner. ( Right ) Mean squared error (MSE) of the nuisance estimation. Taken together, high errors in the nuisance functions at small sample sizes drive the instability of non-orthogonal baselines.
Figure 6: PEHE stratified by overlap on Dt+o : The boxplot shows the 0%, 25%, 50%, 75%, and 100% quantiles, as well as the mean (marker) of the square root pseudo-PEHE within each overlap stratum. The plots show that our LT-O-learners (LT-O-DO-learner, LT-O-TO-learner, LT-O-LO-learner) remain accurate even in low-overlap strata, despite the sample retargeting.
Figure 7: PEHE stratified by overlap on Dt : The boxplot shows the 0%, 25%, 50%, 75%, and 100% quantiles, as well as the mean (marker) of the square root pseudo-PEHE within each overlap stratum. The plots show that our LT-O-learners (LT-O-DO-learner, LT-O-TO-learner) remain accurate even in low-overlap strata, despite the sample retargeting.
Figure 8: PEHE stratified by overlap on Do : The boxplot shows the 0%, 25%, 50%, 75%, and 100% quantiles, as well as the mean (marker) of the square root pseudo-PEHE within each overlap stratum. The plots show that our LT-O-LO-learner remains accurate even in low-overlap strata, despite the sample retargeting.
Figure 9: PEHE stratified by overlap on D∗ : The boxplot shows the 0%, 25%, 50%, 75%, and 100% quantiles, as well as the mean (marker) of the square root pseudo-PEHE within each overlap stratum. The plots show that our LT-O-learners (LT-O-DO-learner, LT-O-TO-learner, LT-O-LO-learner) remain accurate even in low-overlap strata, despite the sample retargeting.
Figure 10: Surrogacy violation sensitivity analysis on GAIN: The left (right) figure shows the mean (variance) of pseudo-PEHE of the LT-T-learner, LT-O-DR-learner, and LT-O-DO-learner across different surrogate dimensions T . The surrogacy violation is more severe at lower T , which leads to higher pseudo-PEHE for all methods. However, our LT-O-DO-learner remains more robust than the baselines across all T .
Estimating heterogeneous survival treatment effects (HSTEs) from time-to-event data under time-varying treatments is important in fields such as medicine (e.g., to decide which sequence of treatments is better in terms of survival probability). However, this task is challenging because treatment decisions, patient characteristics, and censoring probability often evolve together, requiring sequential adjustment for both treatments and censoring. Existing survival learners mostly consider a single baseline treatment assignment, while longitudinal treatment-effect learners typically assume uncensored outcomes. In this paper, we introduce a novel doubly robust learner for heterogeneous survival treatment effects under time-varying treatments and history-dependent censoring. Our framework separates the intervention window from the survival horizon, with treatment prescribed for a finite period, after which care follows its natural course. We further establish the favorable theoretical properties of Neyman-orthogonality, rate double robustness and quasi-oracle efficiency. The framework accommodates flexible machine learning models for nuisance estimation and treatment-effect regression. We evaluate our learners through several numerical experiments, demonstrating their effectiveness.
Tomàs Garriga, Munib Mesinovic, Luke De Bretton-Gordon +3
Novartis · Barcelona Supercomputing Center · Universitat Politècnica de Catalunya +1
We study the problem of selecting the best heterogeneous treatment effect (HTE) estimator from a collection of candidates in settings where the treatment effect is fundamentally unobserved. We cast estimator selection as a multiple testing problem and introduce a ground-truth-free procedure based on a cross-fitted, exponentially weighted test statistic. A key component of our method is a two-way sample splitting scheme that decouples nuisance estimation from weight learning and ensures the stability required for valid inference. Leveraging a stability-based central limit theorem, we establish asymptotic familywise error rate control under mild regularity conditions. Empirically, our procedure provides reliable error control while substantially reducing false selections compared with commonly used methods across ACIC 2016, IHDP, and Twins benchmarks, demonstrating that our method is feasible and powerful even without ground-truth treatment effects.
Jiayi Guo, Zijun Gao
Peking University · Marshall School of Business, University of Southern California
Estimating heterogeneous treatment effects (HTEs) from right-censored survival data is critical in high-stakes applications such as precision medicine and individualized policy-making. Yet, the survival analysis setting poses unique challenges for HTE estimation due to censoring, unobserved counterfactuals, and complex identification assumptions. Despite recent advances, from Causal Survival Forests to survival meta-learners and outcome imputation approaches, evaluation practices remain fragmented and inconsistent. We introduce SurvHTE-Bench, the first comprehensive benchmark for HTE estimation with censored outcomes. The benchmark spans (i) a modular suite of synthetic datasets with known ground truth, systematically varying causal assumptions and survival dynamics, (ii) semi-synthetic datasets that pair real-world covariates with simulated treatments and outcomes, and (iii) real-world datasets from a twin study (with known ground truth) and from an HIV clinical trial. Across synthetic, semi-synthetic, and real-world settings, we provide the first rigorous comparison of survival HTE methods under diverse conditions and realistic assumption violations. SurvHTE-Bench establishes a foundation for fair, reproducible, and extensible evaluation of causal survival methods. The data and code of our benchmark are available at: https://github.com/Shahriarnz14/SurvHTE-Bench .
Shahriar Noroozizadeh, Xiaobin Shen, Jeremy C. Weiss +1
Machine Learning Department & Heinz College, Carnegie Mellon University · Heinz College, Carnegie Mellon University · National Library of Medicine, National Institutes of Health