SurvHTE-Bench: A Benchmark for Heterogeneous Treatment Effect Estimation in Survival Analysis
Authors: Shahriar Noroozizadeh
Xiaobin Shen
Jeremy Weiss
George H. Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Causal Inference
Survival Analysis
Treatment Effect
Datasets and Benchmarks
CATE
Primary area: datasets and benchmarks
TL;DR: We present SurvHTE-Bench, a comprehensive causal inference benchmark to evaluate methods that estimate heterogeneous treatment effects from censored survival data, enabling rigorous, fair, and reproducible comparison across diverse causal scenarios.

Abstract: 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.

Published as a conference paper at ICLR 2026
SURVHTE-BENCH: A BENCHMARK FOR HETEROGENEOUS TREATMENT EFFECT ESTIMATION IN SURVIVAL ANALYSIS
Shahriar Noroozizadeh"
Xiaobín Shen'
Machine Learning Department & Heinz College Cameeiie Mellon University snoroozi@cs. edu
Heinz College
Carnegie Mellon University
xiaobins@andrew. cmu. edu
Jeremy C. Weiss
George H. Chen
National Library of Medicine National Institutes of Health jeremy. weiss@nih. gov
Heinz College
Carnegie Mellon University
georgechen@cmu.com
ABSTRACT
Estimating heterogeneous treatment effects (HTEs) from right-censored survival data is critical in high-stakes applications such as precision medicine and individ- ualized policy-making Yet, the survival analysis setting poses unique challenges for HTE estimation due censoring. unobserved counterfactuals, and complex identification assumptions. Despite recent advances, from Causal Survival Forests survival meta-learners and outcome imputation approaches, evaluation prac- tices remain fragmented and inconsistent. We introduce SURVHTE-BENTE 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 HIV clinical trial. Across synthetic, semi-synthetic, and real- world settings, we provide the first rigorous comparison of survival HTE meth- ods under diverse conditions and realistic assumption violations. SURVHTE- BENCH establishes foundation for fair, reproducible, and extensible evaluation of causal survival methods. The data and code of benchmark available at: /ttps:///iithub. com www.om///aaaaaaaaaaaaaaaaaaaa
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INTRODUCTION
In many causal inference applications where we aim to quantify how well a treatment works, estimat- ing heterogeneous treatment effects (HTEs) could be more useful than only estimating population- level average treatment effects (ATEs), building on the intuition that the same treatment can vary in effectiveness when given to different individuals. In survival analysis with right-censored out- comes (common in clinical trials and electronic health records), estimating HTFFs can be especially challenging. In addition the standard difficulties of causal inference (unobserved counterfactuals, confounding), the analyst must account for censoring, where the event of interest is only observed for subset of subjects. These features complicate identification and estimation, yet they are central in high-stakes applications such as precision medicine and individualized policy-making (Zhu & Chapfuwa al., 202 Curth al. 2021a).
Gallego 2020
Recent years have seen growing set of causal survival methods (Chapfuwa et al. 2021 Curth al. 2021a Cui et al. 2023 Bo al. 2024 Noroozizadeh et al.) [025] Xu et al. [024]] Meir al.)
2025 J. Despite methodological advancement, no standardized benchmark exists, limiting repro-
ducibility and fair comparisons. Most studies rely on bespoke simulations or limited real datasets with unknown ground truth, with differing levels of censoring, survival distributions, and causal
'These authors contributed equally this work and are listed alphabetically.

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Published as a conference paper at ICLR 2026
assumptions. As result, comparisons not standardized, the robustness of different proposed methods is unclear, and progress is difficult to measure.
While there is growing benchmarking literature for treatment heterogeneity in fully ob- served outcomes (c.g., Crabbé et al. (2022): Shimoni et al. (2018): Kapkię et al. (2024)) and recent benchmarks for survival ATE estimation (e.g., Voinot et al. (2025)) to our knowledge, there is not yet any benchmark for survival HTE estimation under ceght-cn This missing piece motivates our focus on heterogeneous effects in censored time-to-event data.
We introduce SURYHTE-BENCEE the first comprehensive benchmark for HTE estimation in right- censored survival data. Our contributions
follows:
Method unification: We categorize existing survival HTE methods (and natural extensions of such existing methods that technically have not previously been published) into three broad fami- lies: outcome imputation methods, direct-survival causal methods, and survival meta-learners. We provide modular implementation of 53 methods among these families. This is the first systematic framework that unifies survival HTE methods, facilitating reproducibility and extensibility. Synthetic benchmark design: We present a curated suite of 40 synthetic datasets spanning eight causal configurations (with different combinations of randomization, unobserved confounding, overlap violation, informative censoring) crossed with five survival scenarios (with different sur- vival and censoring distributions), yielding controlled settings with known mround-truth HTEs under realistic assumption violations.
Semi-synthetic and real data: We also include 10 semi-synthetic datasets adapted from existing literature (real covariates with simulated treatments and outcomes) that aim to be more realistic compared to purely synthetic datasets while still having ground truth on HTEs. We further include 2 widely studied real datasets: the Twins dataset that has known ground truth (Almond et al. 2005) (i.e., per twin, one has the treatment and the other does not, so that we observe both counterfactual outcomes), and the HIV clinical trial dataset without known ground truth (Hammer et al. 1996).
Comprehensive evaluation: We compare representative estimators across all settings. Our re- sults show that no single method dominates: performance depends on causal assumptions, cen- soring, and survival dynamics. Notably, S- and matching-learners among survival meta-learners demonstrate robustness under severe violations and high censoring.
While prior work has explored subsets these design choices (e.g.. Cui et al. (023); Meir et al. 2025 ) SURVHTE-BENCE is the first to systematically evaluate survival HTE methods under sumption violations, diverse survival models, and across symthetic, semi syniheytthetic, and real data. We focus on binary treatments and static covariates with right-censored outcomes, sic setting lacks a standardized benchmark. More complex extensions (time-varying treatments, longitudinal covariates, and instrumental variables) are beyond our present scope.
this ba-
2 BACKGROUND AND RELATED WORK
We briefly review the problem setup, identification assumptions, existing evaluation practices, and the three families of survival HTE estimators.
Problem setup. For each unit (data point) i, we observe covariates X, E X' a binary treatment W. E {0. 1), and an observed, possibly censored event time 7, = min(T,, C2) with event indicator 5. ((T S Ca). where 8, is I if the event of interest happened (in which case T. is the event time) or 0 the outcome is censored (in which case T; is the censoring time). Using the standard potential outcomes framework, T: (w)) denotes the potential event time under treatment w E {0, 1} with T; = (W,). We assume that the tuple (X,, W,, T, (0), (1(1), C+) is i.i.d. across different i.
We aim to estimate the conditional average treatment effect (CATE) with respect to a transformation of the event time (-))
7(x) : E[y[((((())) - (TT) = =]]
where v(-) encodes the survival estimand of interest, and the expectation is taken over the ran- domness of the two potential outcomes. For example, if we want the survival estimand to be the restricted mean survival time (RMST) up to a user-specified time horizon > O, then we would set v(t) minft, h). Other choices for estimands are also possible (c.g., median survival time, survival probability at a fixed time). In this paper, we focus on RMST. which is interpretable, robust under censoring, and widely adopted (Shen et al. 2018 Curth al. 2021a Cui al. 2023), while
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noting that our benchmark design allows extensions to other estimands, and we include example results for survival probabilities in Appendix G.4
Identification assumptions, Identification of (xx) relies on the following assumptions (Cui et al.
2023) (and in our benchmark, we examine settings where these assumptions do not hold);
(A1) Consistency: T, (W)) almost surely.
(A2) Ignorability: (T;(0),T(11)
Wi X;-
(A3) Positivity: Tee S <P(W, = X x) I 1 Te for some T/e >> O.
(A4) Ignorable censoring: T; CL X,, W,
(A5) Censoring positivity: For horizon h, IPC; < N|,,, W.) 1 TJ for some no
unmeasured prognostic factors break ignorability, treatment guidelines un- dermine positivity, and drop-out linked to prognosis induces informative censoring. A central goal of SURVHTE BENCH is to measure how estimators behave under such violations.
Violations are common:
Existing evaluation practice. Because only one potential outcome observed per unit, validation typically relies on author suthor-specific simulations. Prior studies vary assumptions in narrow ways: e.g., censoring up to 30% (Bo et al.] 2024) or heavy censoring but assuming ignorability (Meir et al.) 2025). Consequently, results are not comparable across papers, and estimator robustness under si- multaneous assumption violations remains unclear. To date, no public benchmark exists with known individual- level ground truth with varying levels of assumption violations and survival distributions.
Overview of existing survival HTE estimators. We group existing methods into three families:
Outcome imputation methods (Xu et al., 2024 Meir et al. 2025): Replace censored times with imputed survival times (e.g., IPCW-based reweighting introduced in Qi al. (2023)) Then ap- ply standard CATE estimators such as Causal Forests (Athey et al. 2019). Double-ML (Cher- nozhukov al. 22118) meta-lcarners including S(ingle)-, T(wo)-, X(cross) ((obbl)))(obuss)>>>
learners (Athey & Imbens 2015 Künzel et al. [019 Kennedy/ (2023)]
Direct-survival CATE methods: Extend causal inference directly to time-to-event outcomes, c.g., targeted learning (Van der Laan & Rose 2011]. tree-based estimators (Zhang et al. (017))
Bayesian approaches (Henderson al. 2020), SurvITE (Curth et al., (021a),, or Causal Survival
Forests (Cui et al., (202)).
Survival meta-learners (Xu et al. 2023 Bo et al. 2024: Noroozizadeh et al. 2025): Adapt S(ingle), T(wo)-, or matching-leaman leanners to survival outcomes by using survival models such as Random Survival Forests or deep survival models.
While these approaches appear in disparate lines of work, use the taxonomy above as an or- ganizing lens for our benchmark. In particular, we implement 53 representative methods spanning the three families and estimands. We note that several emerging directions fall outside this taxonomy (e.g., generative causal margin modeling (Yang al.) 2025) and synthetic-controll
unified, modular framework to enable consistent evaluation across datasets
methods (Curth al. 2024 Han & Shah 2025)), whose systematic integration we leave for future work.
Additionally, while our benchmark focuses on static treatments under selection on observables, re- lated work addresses HTEs in alternative settings. This includes instrumental variable approaches for survival (Tchetgen et al. 2015). dynamic treatment regimes (Rudolph et al. 2022]: Bates et al.)
2022 Rudolph et al.) 2023 Cho et al. (023), and Bayesian machine learning approaches (Chen 2024). Additionally, Targeted Maximum Likelihood Estimation- based methods (Stitelman &
ct al.
van der Laan 2010 Stitelman et al., 2011) offer robust estimation for survival parameters, though primarily for average or subgroup effects rather than continuous CATE functions.
SURVHTE-BENCH
SURVHTE-BRE BENCH probes how survival CATE estimators behave when assumptions (AI)-(A5) hold and when they are either mildly or severely violated. As real data with ground -tuth CATES are scarce. the bulk of our benchmark relies on synthetic datasets. We also include gemi-synthee data (real covariates with simulated treatments and outcomes) and two real-world datasets. As already stated in Section 2 in this paper we focus on the case where the target estimand is RMST up to user-specified time horizon h (other estimands are possible, such as survival probability at predefined
'Standard CATE estimators do not handle censoring. By imputing censored times with survival times as preprocessing step, we make appear if there censoring, standard CATE estimators can he applied.
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times, Appendix G.4.2 Access to all of the datasets, except for those requiring credentialed
approval, is provided at: https::: hattps://hugiingface wtt..//attattttttoooooo///ttr..a
Synthetic data. We construct mod- ular suite of 40 synthetic datasets that systematically vary across two orthogonal axes: (1) causal configuration: treatment mechanism, positivity, confounding, cen- soring mechanism; (2) survival scenario: event-time distribution and censoring rate, Crossing 8 causal configurations with 5 sur- vival scenarios yields datasets, each with binary, time-fixed treat- ment, five independently sampled covari- ates, each distributed Uniform(O, 1), and up to 50,000 units. For each unit i, we gen- erate both (0) and (1), ensuring that ground-truun truth CATES are always known.
Causal configurations of synthetic datasets. RCT randomized controlled trial: OBS = observa- tional study; 50(5) = 50%(5%) treatment rate; CPS= correctly specified propensity score (ignorability sat- isfied); UConf unobserved confounding (ignorabil- ity violated); NoPos lack positivity; InfC = in- formative censoring (ignorable censoring violated). held, X= not held.
Table 1:
40 synthetic
Causal Coufigs.
RCT Ignorability
Positivity
Ignorable Censoring
RCT-58 RCT-5
/
OBS-UConf OBS-NePos
x
x
/
/
The 8 causal configurations (Table include randomized controlled trials (RCT-50, RCT-5) and observational stud- ies with correctly specified propensity scores (i.e., these are known during training) with all confounders observed in estimation (OBS-CPS), unobserved confounding (OBS-UConf), or lack of positivity (OBS-NoPos). Each observational setting has variants with suffix "-InfC", where ignorable censoring is replaced by informative censoring, where censoring times depend stochas- tically on event times. These violations reflect common real-world challenges: unmeasured risk factors in treatment decisions (violating ignorability), treatment imbalance observational studies (violating positivity), and dropout mechanisms correlated with health outcomes (violating ignorable censoring). We do not model interference (consistency violations) or censoring-positivig violations, which require specialized designs beyond scope. Additional variations, such as informative censoring with the censoring time driven by unobserved factors, are included in the Appendix to illustrate the extensibility of our modular setup.
CBS-CPS-InfC
V
X
CBS-UConf InfC
/ x
3BS-NoPos-InfC
X
X
x
The 5 survival scenarios (Table 2 include Cox proportional hazards (low censoring), acceler- ated failure time (AFT) models (low and high censoring), and Poisson hazards (medium and high censoring). These distributions cover pro- portional hazards (Cox) and pon-propottional hazards (AFT)) Poisson), with censoring levels ranging from under 30% to over 70%. This va- riety reflects practical challenges like high cen- soring common in EHR cohorts, accelerated pro- cesses in oncology, and discrete hazard approx- imations in epidemiology. Within each survival scenario, coefficients are tuned so that event times are comparable across different causal configu-
Table Survival scenarios of synthetic datasets. "Low" <30%, "Med" 30-70%, "High" > >70% censoring. AFT accelerated failure time.
Survival Survival Time Censoring Scenario
Distribution
Rate
Low
AFT
Poisson
Med
AFT
High
Poisson
High
rations. Full generation formulas and summary statistics (e.g., censoring rate, treatment rate, ATE) for each dataset in Appendix A
Evaluation metrics. Per dataset, averaged over 10 random splits, we report:
CATE root mean square error (RMSE): / (f(x)
ATE bias: 1 Σ +(,,) A, where A the ATE from the population and can be approxi- mated using the average CATE from a very large sample (i.e., from 50,000 simulated samples). Auxiliary imputation accuracy: mean absolute error (MAE) between imputed and true event times. Auxiliary regression/survival fit: MAE for regression- learners, AUC for propensity score models, and the time-dependent C-index (Antolini et al. 2005) for survival models.
2The AFT noise distribution we (that is additive in log survival time) is Gaussian that the resulting model does satisfy the proportional hazards assumption (which would require the noise to be Gumbel).
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Survival CATE methods implemented. We evaluate the three broad families of survival CATE methods (53 variants total;; see Appendix forr the full list, Appendix D for methodological details):
Outcome imputation methods: meta-learners (S-, T-, X- X--DR-Lcamersy paired with base regression learners (lasso, random forest, XGBoost), plus Double-ML and Causal Forest, each combined with the three imputations (Pseudo-obs, Margin, and IPCW-T (Qi et al. for details). In total, we implement 42 variants.
2023), see Appendix B
Direct-survival CATE methods: We include SurvITE (Curth et al. 2021 and Causal Survival
Forests (Cui et al., (023).
Survival meta-learners: S-, T-, and matching-learners paired with survival learners (Random Sur- vival Forests (Ishwaran et al. 2008), DeepSurv (Katzman et al. 2018), and DeepHit (Lee et al.,
20T8)), for total of 3 x
variants.
Note that some implemented methods are straightforward extensions of existing ideas despite not having been previously published. For example, (Qi et al.) 2023) suggested ways of replacing cen- soring times with imputed survival times for the purposes of model evaluation, but their imputation strategies naturally can be coupled with standard CATE learners to obtain survival CATR estima- tors. Similarly, pairing meta-learners with different base learners (e.g., lasso regression, XGBoost, or DeepSurv) yields natural yet previously unpublished variants.
Semi-synthetic data. We include 10 semi-synthetic datasets, pairing real covariates (ACTG HIV trial, MIMIC-IV ICU records) with simulated treatments and outcomes, covering moderate to ex- treme censoring regimes, covariate-dependent treatment assignment, and both linear and non-linear (iteractionnbasedl event-time and censoring mechanisms. These datasets preserve realistic feature distributions while retaining ground-truie CATEs. Details are in Section 4.2
Real data. Finally, incorporate two real datasets, with ground truth (for which we can the same evaluation metrics as with synthetic data) and one without ground truth but with a low censoring rate (for which we compare how models perform on the original dataset on the dataset with artificially introduced censoring). These provide opportunities to evaluate how methods behave under real covariate and outcome structures. Details are in Section
4
BENCHMARKING RESULTS
We now present benchmark results across synthetic, semi-synthetic, and real data, spanning con- trolled violations of causal assumptions to realistic covariate structures.
4.1 SYNTHETIC EXPERIMENT RESULTS AND ANALYSES
We begin with synthetic datasets, where we evaluate 53 estimator variants across the 40 synthetic datasets (Section 3). systematically spanning varying causal configurations and survival scenarios. This controlled setting enables us probe estimator robustness under systematic violations of iden- tification assumptions. Our analyses aim to address four questions: (Q1) Which estimators perform best overall in terms of CATE RMSE and ATE bias? (Q2) How do violations of causal assumptions (ignorability, positivity, ignorable censoring) affect performance? (Q3) How does the censoring rate influence estimation quality? (Q4) How do component choices (imputation algorithms and base leamers) affect final CATE accuracy?
Evaluation protocol. For each synthetic dataset, we conduct experiments with random selection of 5,000, 2.500, and 2,500 points for training, validation, and testing samples, repeated over 10 random splits. The validation set is used for selecting the best variant within each method family, while test sets are reserved strictly for evaluation. Additional convergence analyses with varying training set sizes are in Appendix F7 Across all experiments, the horizon parameter l is set to the maximum observed time in each dataset, which is common practice that allows for consistent estimation of the RMST over the entire observed period. Further experimental details, including hyperparameters, in Appendix E
We present results using the following visualizations:
Borda count rankings. To provide clear summary across the diverse experimental settings, we adopt the Borda count method, which ranks methods by CATE RMSE in each dataset (lower is better) and then averages the ranks across datasets. This approach yields a single, interpretable score that reflects overall relative performance while accounting for variability across scenarios.
Similar strategies have been used in other benchmarking studies (e.g.. Han et al. 2022) to enable
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Figure 2: CATE RMSE in Scenario C across 10 experimental repeats.
transparent comparisons across heterogeneous tasks. We report rankings two levels: (i) indi- vidual estimator variants (53 total; Figure top), and (ii) aggregated method families, where the best variant per family is selected validation data (11 total; Figure [] bottom). The latter mim- ics a practical deployment setting where practitioners would tune and select the strongest model within family. More granular rankings stratified by survival scenario (Figure 6 and by causal configuration (Figure 7 are provided in Appendix [F33
CATE RMSE. We report absolute CATE RMSE across 10 repeats, grouped by survival scenario, with one panel per of eight causal configurations. In the main paper, show Scenario as illustrative example (Figure 2); results for the other scenarios are deferred to Appendix F.4
ATE bias. We report ATE bias results, computed analogously to CATE RMSE, in Appendix While the focus of this benchmark is on CATE estimation, these serve as a complementary check.
F.5
Win-rate analyses. Complementing the Borda rankings, we also report win-rates that quantify how often each method family attains Top-1, Top-3, and Top-5 performance according to CATE RMSE and ATE bias across all synthetic experiments Appendix F Overall win-rates aggre- gated over all survival scenarios and causal configurations are summarized in Table 15 while scenario-specific and configuration-specifii win-rates are reported in Tables [7 and 18 These summaries highlight not only which methods perform well on average, but also which ones most consistently appear among the top performers under varying censoring regimes and patterns of -ussal-sssumption violations.
Additionally, in appendix(F.6) we report a series of auxiliary evaluations of key components, includ- ing imputation error (Appendix 1 for imputation-basee methods and regression model accuracy (Appendix (F6.2) or survival model performance (Appendix [F.63)) for meta-learners. These results establish how component-level performance relates downstream CATE estimation.
Key findings. Overall, performance is strongly context-dependent. For example, in low-censoring randomized settings, outcome imputation methods such X-Learner and Double-ML. excel. As censoring intensifies or when assumptions are violated, survival meta-learners and Causal Survival Forests gain clear advantage. Within method families, the choice of imputation algorithm or survival base model critically determines outcomes. Appendix [mpendix[F]urrdee further supports this pattern quan- titatively through Top-k frequency summaries of CATE RMSE and ATE Bias (Tables [8]. high- lighting methods that consistently rank at the top rather than merely performing well on average. We summarize detailed findings below.

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Overall performance (Q1). Figure D (top) presents Borda count rankings of the top- 10 performing methods out of the 53 total configurations evaluated (full ranking in Appendix [ The highest-performet estimators are sur- vival mneta-leamers built on DeepSurv, with --Leamerr-Srriiyy (average rank 5.17 across 53 methods) and Matching- Survival (5.42) leading, followed by Double-MI. with Margin imputation (6.65). Among outcome imputation approaches, Margin appears most fre- quently among the top performers, though Pseudo-obs and IPCW-T are also represented.
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Figure 1: (top) Borda count rankings of the top 10 estima- tor variants (out of 53 total), based on CATE RMSE across 40 datasets and averaged over 10 repeats (lower is better). (bottom) Family-level rankings, where for each dataset the best method variant within each method family chosen using validation performance and then ranked on the held- out test set. Black bands connect methods without statis- tically significant differences (Wilcoxon signed-rant test, correctee a = 0.05). Shaded regions indicate the standard error of the rank across datasets.
At the method family level (Figure 2 for Scenario C and Figure | (bottom)
across all causal configurations and sur-
vival scenarios), we see how each approach performs when optimally configured. At this level, S-Learner-Suriivl (average rank 3.30 across 11 method families) and Batching-Survive (3.48) maintain their advantage, followed by Double-ML (3.98) and Causal Survival Forests (5.10).
Violations of causal assumptions (Q2). Performance shifts substantially depending on assump- tion violations (Figure 77). In randomized balanced trials (RCT-50), outcome imputation methods dominate, with Double-ML (3.60) and Causal Forest (5.60) showing performance comparable to high-ranking survival meta-learners. However, under imbalanced treatment (RCT-5), Double-MI. remains strong (1 18)), while (:Learmer-Surrival--we
relies on fitting base models on treated drips-drops to last place (9.00), alongside SurvITE, due to sparsity of treated samples.
Under ignorability violation (OBS-UConf, Figure 7d). Double-ML and X-Learner are the main com- petitive imputation methods, whereas survival meta-learners retain relatively stable performance. Examining ATE bias (Figures [3 17t), we that across all scenarios, survival meta-learners and Causal Survival Forests methods maintain relatively consistent bias levels despite ignorability viola- tions, whereas meta-learners exhibit slightly increased bias at times. This stability is also reflected in aggregated win-rate summaries for OBS-UConf, where survival-aware families most consistently appear among the Top-k for both CATE RMSE and ATE Bias (Appendix F3 Table (8).
Under positivity violation (OBS-NoPos, Figure Te). we see the more sophisticated outcome impu- tation approaches like Double-ML and X-Learner maintain strong performance and outperform survival meta-learners. However, when positivity violations occur alongside other violations (Fig- ure 7h. survival meta-learners regain their advantage, demonstrating their robustness to multiple simultaneous violations. This behavior is also reflected in the win-rate summaries, which show a similar shift in Top-k coverage across configurations (Appendix F3 Table T8). Additionally, Causal Survival Forests sees large drop in its ranking when faced with only positivity violation, suggesting its limited robustness to regions of covariate space with deterministic treatment assignment.
Under informative censoring (InfC, Figure 20 2h survival meta-learners and Causal Survival For- est continue to outperform outcome imputation approaches. However, all methods show degraded performance compared to their ignorable censoring counterparts, with substantially higher CATE RMSE variability, indicating the increased difficulty of estimation under dependent censoring.
Impact of censoring rate (Q3). For the impact of censoring rate and survival time distribution (Figure (). in low-censoring Scenarios A and B, Double-ML leads the rankings, but as censoring increases through Scenarios C to E, survival meta-learners and Causal Survival Forests progressively move to the top. By Scenario D (high censoring), LeLenner-Surviiee (1.6) and Matching-Survinn Survival (2.4) dramatically outperform all other approaches. This pattern suggests that direct survival mod- eling provides increasing advantages as censoring rates rise, likely due to better handling of the uncertainty in heavily censored data compared to outcome imputation approaches. The same mono-

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tonic shift toward survival-aware methods with increasing censoring is visible in their Top-k win-rate coverage across scenarios (Appendix F.2).
we show ATE bias across different datasets. We observe apparent di- vergence of the estimated ATE from the true ATE in Scenario D and slightly in Scenario E (Figure [6 17 where the censoring rate is very high. Especially when the true underlying event time follows an AFT distribution (Scenario D), almost all estimators failed under all different causal configurations, suggesting the challenging task of treatment effect estimation under a high censoring rate.
Separately, in Appendix F.5
Component effects on CATE estimation (Q4). Auxiliary evaluations in Appendix F.6 demonstrrate that both imputation accuracy and base learner performance influence downstream CATE estima- tion. Among outcome imputation methods, Margin consistently achieves the lowest imputation error and degrades the least under heavy censoring (Appendix [F6.1). which translates into Margin- based variants appearing more frequently among the top-ranked estimators (Figure [T). For survival meta-learners, higher concordance indices of DeepSurv across survival scenarios (Appendix (.6.3) explain why DeepSurv-based configurations dominate overall rankings.
4.2 SEMI-SYNTHETIC DATA RESULTS
To bridge the gap between controlled synthetic experiments and methods on semi-synthetic datasets that pair real covariate distributions with simulated treatments and outcomes. This approach addresses a critical limitation of purely synthetic data-the potential lack of representativeness in covariate structureswwing maintaining ground-truth CATES for rig- orous evaluation. These datasets preserve real-world covariate correlations, mixed data types, and high dimensionality while enabling controlled evaluation against known treatment effects.
complexity, we evaluate
Dataset construction. We construct 10 semi-synthetic datasets using covariates from two sources (Table 28 summarizes all datasets).
ACTG semi-synthetic: Based on 23 covariates from the ACTG HIV clinical trial (Hammer et al., 1996). with treatment and event times simulated following Chapfuwa et al. (022)). This dataset exhibits moderate censoring (51%) with realistic treatment imbalance.
MIMIC semi-synthetic: Derived from covariates in the MIMIC-IV ICU database (Johnson ct al. 2023). We construct nine MIMIC-based remi-synthetic variants organized into two comple- mentary subsets: MIMIC-i-o follow Meir et al. (2025) and vary censoring severity from 53% to 88% under ewvariae-indepentee
treatment assignment, covering moderate extreme censoring regimes common in longitudinal EHR studies. MIMIC-ui-ic reuse the same covariates but intro- duce covariate-dependent treatment assignment and non-linear (interaction-based) event-time and censoring mechanisms. Full generative details are provided in Appendix G
Primary estimand and reporting. In the main paper, we focus CATE estimation for RMST evaluated at large horizon (the maximum observed time in each dataset). Table reports RMSE on ACTG and the censoring-severity sweep MIMIC-i-U, which provides compact view of per- formance as censoring increases. Results on the remaining MIMIC variants (MIMIC-vi-ir) under the same RMST estimand, as well as results for additional estimands Morizonn-specifee survival- probability CATES and RMST at shorter horizon), are reported in Appendix G
presents CATE RMSE results across semi-synthetic datasets, showing how realistic covariate structure modulates the core performance patterns observed in synthetic experiments.
Validation and extension of synthetic findings. The semi-synthetic results broadly corroborate the synthetic benchmark: In ACTG, Double-ML. achieves the lowest RMSE (10.65), consistent with the advantage of flexible, doubly robust approaches moderate-dimennioona settings with controlled confounding, Across MIMIC-i-u, methods remain competitive within a narrow band, with survival- oriented approaches (SurvITE and survival meta-lcarners) frequently among the top performers.
Censoring sensitivity and stability. The MIMIC-i-U sweep 153%-88% censoring) reveals that differences in stability can be as important as differences in mean RMSE. For example, S-Learner- Survival remains stable across censoring levels (RMSE range 7.897-7.921), while T-Leamer- Survival exhibits increased variability under extreme censoring (e.g., larger standard deviation at 82% censoring).
Practical implications. In these realistic covariate spaces, RMSE differences are often compressed, making method selection depend on secondary considerations such stability under censoring.
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Table 3: CATE RMSE (mean + std over 10 repeats) on ACTG and MIMIC-i-U semi-synthetic datasets. Best two methods per dataset are bolded.
Method Family
ACTG (51%)
MIMIC-i (88%)
MIMIC-N (82%)
MIMIC-Ri (74%)
MIMIC-io (66%)
MIMIC- (53%)
(censoring rale)
Outcome Imputation Methods
T-L.camnrr
11.257 0.239 7.964 0.046
7.912
0.046
7.915
0.043
7.912 - 0.043
7.908
0.043
S-Learner
11,300 0.221 7,977 0.044 7,968 0.047
7,956 = 7,959
0.046 7,958
0.048
X-Leamer
11.072 0.196 7.964
0.046 7.912
0,046
7.915 0.043
7.912 0.043 7.908
0.043
DR- De-LLemeer
11.334 + 0.225 7.964
= =0.046 7.912 0.047
7.911 = -0.44 7.911 0.043
7.909
0.043
Double-ML.
10.651 0.239 7.954 0.047 7.936
0.045
7,919 0..44 7.917 0.046
7,891
0.050
Causal Forest
11.154 0.175 7.967
7.949
0.044
7.934
0.043
7.931 0.047
7.909
0.044
Direct-Surivall CATE Methods
Causal Survival Forests 11.674 + 0.169 7.963
0.057
7.942
0.039
7.929
0.037
7.911
0.051
7,893
0.042
SurvITE
12.714 0.559 7,931 0.050 7.908
0.065
7.906
0.071
7.907
0.058
7.906 0.066
Survival Meta-Learmers
T-Leamer- Survival
11.428 0.160 8.007 0.075
7.980 0.233
7.911
0.054
7.902
0.042
7.902 0.046
S- S-Leamer-Survie Survival
11.713 + 0.237 7,921 = 0.044 7,912
0.052
7,900
0.045
7,901
0.046
7.897 0.042
Matching Survival
12.523 0.289 7,949 0.043 7.935 0.053
7.920
0.047
7,921
0.046
7.912 0.042
interpretability, and computational cost. Overall, the semi-synthetic evaluation suggests: (i) flexible causal methods such as Double-ML remain strong in dimerteead settings with balanced censoring, (ii) survival-oriented methods like SurvITE and survival meta-leamnrss provide robust performance in highly censored EHR- regimes (MIMIC), and (ii) the choice of method should explicitly consider dataset dimensionality and covariate complexity, not just censoring rates and we provide details on the data generation process, experiment setup,
sample sizes. In Appendix G and additional experiment results on the semi cemi-synthetic.
4.3 BENCHMARKING ON REAL DATA
We also evaluate the three families of survival CATE estimators real-world datasets, with known ground truth and one without,
Twin data. The Twins dataset (Almond lt al. 2005 Curth et al.) 2021a) includes twin births from 1989-1991, where be- ing the heavier twin serves as treatment and time to mortality as the outcome. With known outcomes for both twins, this dataset provides ground truth for CATE evaluation. After replicating the same random treatment assignment strategy and the censoring time assignment following Curth et al. (2021)). the treatment rate and censoring rate for the dataset are 68.1% 1% and 84.8% respectively across 11,400 twin pairs. Since most of the mortality events occur within 30 days, we use = 30 days during estimation. Figure 3 shows that S- and DR-Learners (with imputation) and S-Learner- Survival exhibit lower CATE RMSE (7.2 days). T-Learner-Survivy and Causal Forest with impu- tation exhibit the worst performance, consistent with their overall lower ranking from the bench- marking on our synthetic datasets (Figure []. Surprisingly, Double-ML with imputation exhibits the worst performance on the twin data, which is different from the overall ranking, suggesting poten- tial unique patterns in this dataset. In Appendix H. we also show the result with h = 180 days; the conclusions are similar.
Trieron
E-teanter
Acteamer
DR Jaareer
Beuth M.
Caunat faraet
Caotat
Survine Sorvicai
Teieurne Servival
MITchLoR
Figure 3: CATE RMSE for twin birth data with h = 30 days across 10 experimental runs.
HIV clinical trial. The ACTG 175 dataset (Hammer et al., 1996) compared four antiretroviral treatments in 2,139 HIV-infected patients. Following Meir et al. (2025). we convert time to months with /=30 months (13.7% baseline censoring) and introduce artificial censoring to test robustness (increasing to >90% censoring). More details on data and processing can be found in Appendix H Figure 4 compares CATE estimates between baseline and high-censoring conditions for the ZDV vs. ZDV+ddI comparison (results for other treatment comparisons are in Appendix H). Each point represents an individual patient, with the 45-degree dashed line indicating perfect consistency be- tween conditions. We observe distinct behavioral patterss: Causal Survival Forest (green) produces estimates that cluster tightly around their original values; outcome imputation methods (blue) show

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T Learrsrr
Leorser
L-Learmer
S8: Ti-Leerser
Dosble-Ht
Cousal Forext
07T Dr.
Basting
04T Crt. Dessltre
OCT Dr. 0eseto
OnE Dr. toeti
GTT En. -toiioe
Figure 4: CATE estimation comparison between baseline and high- conditions under ZDV vs. ZdV+ treatments. Each point represents an individual patient, with the dashed diagonal line indicating perfect consistency between baseline CATE estimation and that with the additional censoring injected.
higher variation in baseline estimates but concentrated predictions under high censoring; survival meta-learners (red) display substantial deviations from the 45-degree line, indicating sensitivity to censoring conditions. As ground truth is unknown, cannot determine which approach is more curate, but these patterns reveal fundamental differences in how estimators respond to increased cen- soring. For example, survival meta-learners (the red scatter plots), especially the T- and matching- learners, exhibit instability under increased censoring settings (large variance in y-axis values).
DISCUSSION
SURVHTE-BENT provides the first comprehensive and extensible platform for systematically benchmarking heterogeneous treatment effect estimators under right-censored survival settings. By spanning synthetic, semi-synthetic, and real datasets, the benchmark enables both controlled stress- testing of estimators under systematic assumption violations and validation in realistic clinical-like settings. Our empirical evaluations reveal strengths and weaknesses across estimator families.
While we have attempted to make our benchmark representative of common causal survival setups, various limitations remain. First, the synthetic datasets include numerous scenarios representing common real-world violations; however, they do not encompass all possible complexities, such as RCT settings with informative censoring or varying degrees of severity in assumption violations. The binary nature of violations (either present or absent) may not capture the nuanced contin- uum of partial violations. We recognize that in real-world applications, assumption violations often exist continuum of severity. Future extensions of benchmark could incorporate graded sensitivity analyses, such as varying the magnitude of unmeasured confounding (e.g., via Rosen- baum's 's I') or the degree of overlap violation. This would allow for a more granular "dose-response" analysis to pinpoint the exact thresholds at which specific estimators break down. Second, the choice of the most relevant causal estimand inherently task-specific. While our evaluations cover restricted mean survival time alongside survival probabilities at fixed horizons (Appendix G.4.2), different clinical or policy objectives often dictate the need for alternative measures. Extending the benchmark to natively support wider array of task-specific estimands-such as conditional median survival times or time-varying hazard ratios-would further enrich its scope. Additionally, we limit analysis to static, binary treatments with fixed baseline covariates, excluding scenarios involving vime-varying treatments, instrumental variables, and dynamic covariate structures.
Future work could expand SURVHTE-BENCII in several directions. Incorporating wider variety of direct causal estimation methods, such as g-computation approaches specifically designed for survival outcomes, would provide an more comprehensive evaluation landscape, especially because Causal Survival Forests proved to be competitive but showed vulnerability to certain as- sumption violations like positivity. Exploring more complex data-generating mechanisms that bet- ter mimic the heterogeneity and longitudinal nature of real-world clinical data represents another promising direction. Finally, extending the benchmark to support multi-valued continuous treat- ments would address important practical scenarios encountered in precision medicine and policy optimization.
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ACKNOWLEDGMENTS
This research was supported by the Division of Intramural Research (DIR) of the National Library of Medicine (NLM), National Institutes of Health (NIH). G.H.C. was supported by NSF CAREER award #2047981. S.N. was supported by Carnegie Mellon University TCS Presidential Fellowship, and Natural Sciences and Engineering Research Council of Canada (NSERC) PGS-D award. S.N. was also supported in part by an appointment to the National Library of Medicine Research Partici- pation Program administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and the National Library of Medicine, National Institutes of Health. ORISE is managed by ORAU under DOE contract num- ber DE-SC0014666 All opinions expressed in this paper are the authors' and do not necessarily reflect the policies and views of NIH, NLM, DOE, ORAU/ORISE.
ETHICS STATEMENT
SURVHTE BENCH has significant positive potential for improving personalized medicine and clin- ical decision- making by enabling systematic evaluation of survival analysis methods under realistic assumption violations. By providing standardized benchmarks and practical guidance on when dif- ferent estimators excel or fail, our work could accelerate the development of more reliable causal inference methods for high-stakes healthcare applications, ultimately supporting better patient out- comes through more informed treatment selection.
At the same time, our benchmark carries potential risks if misapplied. Practitioners may misinterpret benchmark results or place undue confidence algorithmic decision-making, which could reduce necessary human oversight in clinical contexts. Moreover, although our study is methodological and does not involve human subjects directly, differences in estimator performance across demo- graphic groups could exacerbate existing healthcare disparities if ignored. We therefore stress that our benchmark should not be used as a substitute for rigorous domain-specific validation, fairness assessment, or clinical trial evidence.
All datasets used in this work are either publicly available synthetic or semi-synthetic datasets, or real-world datasets with proper access provisions (e.g., credentialed approval for MIMIC-IV). No personally identifiable information was used, and all data handling complies with the terms of use of the original sources. We encourage future applications of SURVHTE- E-EECCH to incorporate fairness audits, domain specific validation, and appropriate safeguards to ensure responsible deployment.
REPRODUCIBILITY STATEMENT
We provide complete resources to reproduce our results across synthetic, semi-synthetic, and real- data settings. (1) Synthetic data; The benchmark design and evaluation protocol are described in the main text (Sections 3 and
including the 8 causal configurations and 5 survival scenarios (40 datasets total). Extended generation formulas and per-dataset summaries are in Appendix A imputation procedures in Appendix B the full list of implemented estimators in Appendix C causal method overviews in Appendix D training details and hyperparameter grids in Appendix E and
additional synthetic results/analyses in Appendix F. (2) Semi-symthtic data: Setup, statistics, and full results appear in Appendix G with summary discussion in Section (3) Real data: Processing
details and additional analyses are provided in Appendix H see also Section 4.3
We further study
additional censoring mechanisms in Appendix
Code and instructions. The full codebase used for all experiments is available at httpss://// thub. Nom/Shahriarns B//4////SHHHBBBennne with scripts and READMEs to reproduce all results in the paper.
Datasets. In the same repository as well as at ottp::///uugggnneee..ooooattttt co/datasett//soroozl/
SurvHTE-Benchi] we include: (i) the complete synthetic suite (40 datasets from the x 5 de- sign): (ii) the semi-synthetic datasets, comprising the ACTG (semi-synthetic) dataset; and (iii) real-data materials for Twins and ACTG 175. For the semi-synthetic MIMIC resources, be- cause MIMIC-IV requires credentialed access, we provide code to generate these datasets rather than redistributing raw MIMIC data. The MIMIC-IV dataset itself is hosted on PhysioNet at and is publicly available researchers upon credentialed approval. All other datasets listed above are included in the supplementary package in preprocessed or generated form, together with scripts reproduce all splits and metrics.
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In addition enabling replication of our reported results, we intend SURVHTE- BEREE--BCHHH to as community infrastructure for the evaluation of survival HTE methods. The benchmark is designed to be modular and extensible, allowing researchers incorporate new estimators or datasets while preserving comparability. This ensures not only reproducibility of our experiments but also a lasting resource for the community, providing standardized basis for measuring progress in survival causal inference, a resource that has been missing until now, as well as in related areas of machine learning.
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APPENDIX
In this appendix, we provide detailed descriptions of data generation processes, methodological ex- planations, experimental setups, and results supplementing the main text. We begin by describing the mathematical formulations used to create our synthetic datasets, followed by detailed explanations of imputation methods and causal inference techniques. We then provide comprehensive informa- tion about model training procedures and hyperparameter settings for reproducibility. The appendix concludes with additional experimental results on synthetic, semi-synthetic, and real-world datasets.
We would like to declare the use of Large Language Models (LLMs) in this work. LLMs were used as general-purpon assistive tools. Specifically, they supported parts of the writing process (editing, formatting, and polishing text) without contributing to the core methodology, scientific rigor, or originality of the research. In addition, LLMs were used assist with improving visualiza- tion code for figures, documenting the code, and minor refactoring. No part of the conceptualization, design, or execution of the research relied on LLMs.
Appendix A Additional Details of the Synthetic Datasets. This section provides the mathe- matical formulations for generating covariates, treatment assignments, event times, and censoring times across different scenarios. It describes how the synthetic datasets systematically vary across causal configurations and survival scenarios, including details on covariate generation, treatment assignment mechanisms, event time generation, censoring time generation, and observed data con- struction. This section also includes Kaplan- curves for the synthetic event-time and censoring distributions, illustrating scenario-level variation used throughout the benchmark.
Appendix Bi Imputation Methods Details. This section explains three surrogate imputation strate- gies for estimating true event time in right-censored survival data: Margin Imputation, IPCW-T Imputation, and Pseudo-observation Imputation. It provides mathematical formulations for each method and discusses their respective advantages and limitations.
Appendix C List of CATE Estimators in SURVHTE Benchmark. This section details the 53 different conditional average treatment effect (CATE) estimator variants evaluated in the benchmark, including outcome imputation methods, direct-survival CATE models, and survival meta-learners, with a breakdown of how these variants are constructed.
Appendix D Detailed Overview of Causal Inference Methods This section provides compre- hensive explanations of various causal inference methods, including meta-learners (T-Learner, S- Learner, X-Learner, DR-Learner), Double-ML, Causal Forest, Causal Survival Forests, SurvITE, and Survival Meta-Leamnrs, discussing their implementation in survival contexts.
Appendix E: Model Training Details and Hyperparameters. This section covers the hyperpa- rameter grids, model selection procedures, and computational costs associated with each method class evaluated in the benchmark, providing details on the experimental setup for reproducibility.
Appendix Additional Experimental Results for Synthetic Dataset. This section presents com- prehensive experimental results on synthetic datasets, including full rankings of models, win-rate summaries (Top-1 Top-3 / Top-5) across methods, performance across different survival scenar- ios and causal configurations, detailed CATE RMSE and ATE bias plots, evaluation of auxiliary components, and convergence behavior under varying training set sizes.
Appendix G Semi-Synthetic Datasets. This section includes data setup and detailed analysis of semi-synthetic datasets derived from ACTG 175 and MIMIC-IV, including covariate statistics, censoring rate range, and comprehensive performance results across methods. It also presents results for the survival-probabilie based CATE estimand across multiple horizons, and includes sensitivity analyses of the RMST- based CATE where the evaluation horizon is varied.
Appendix Hi Real-World Datasets. This section provides detailed descriptions of data prepro- cessing and additional experimental results for the Twins dataset and the ACTG 175 HIV clinical trial dataset, including CATE RMSE results with different time horizons and comparisons of CATE estimates between baseline and high-censoring conditions.
Appendix T Informative Censoring via Unobserved Confounding. An additional dataset vio- lating the ignorable censoring assumption via latent confounders. This illustrates extensibility of HURVHTE BENCH to incorporate alternative censoring mechanisms beyond the 8 x 5 design.
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A ADDITIONAL DETAILS OF THE SYNTHETIC DATASETS
Our synthetic datasets systematically vary across two orthogonal dimensions: causal configurations (treatment assignment mechanisms and assumption violations) and survival scenarios (event-time distributions and censoring mechanisms). This section provides the mathematical formulations for generating covariates, treatment assignments, event times, and censoring times across all scenarios. For event time and censoring time distribution, we adapt the generation process from Meir et al. (2025) and make some adjustments, with, for example, different censoring mechanisms under in- formative censoring settings; for treatment assignment in observational study settings, we adapt the propensity score from Cui et al. 2023 For simplicity, we omit the unit index in this section.
A.1 COVARIATE GENERATION
Following Cui et al. 2023); : Meir et al. (2025), for all scenarios, we generate five baseline covariates independently from uniform distributions:
Xm Uniform (0, 1), m = 1,2, 4,5
Additionally, we generate two latent confounders U1, U2 Uniform (0, 1) that are used when testing violations of the ignorability assumption.
A.2 TREATMENT ASSIGNMENT MECHANISMS
The treatment assignment mechanism W varies according the causal configuration:
Randomized controlled trials (RCT-50, RCT-5): Treatment assigned randomly with probability
p:
W ~ Bernoulli(p)
where p = 0.5 for RCT-50 and 0.05 for RCT-5.
Observational studies (OBS-): Treatment assignment depends on covariates through a propensity score mechanism:
e(X) = + Beta (x1;244) (OBS-CPS)
e(X,U) = + Beta B0ta(0.3X, + 0.7U1:2,4)
(OBS-UConf)
if X1 > 0.8
e(X) =
X, < 0.2 (OBS-NoPos)
0.5
otherwise
where Beta(1; a, b) denotes the Beta probability density function with parameters a and b evaluated æ. For all observational configurations, W Bernouli(e(-)).
A.3
EVENT TIME GENERATION
Event times T(w) under treatment E 10 are generated according to five different survival scenarios:
Scenario A (Cox model): Event times follow Cox proportional hazards model with Weibull base- line hazard:
Xr (t = ho(t) cx gTz) Z)
0.5 exp[Xi + (-0.5 X2) W +
where (t) 0.5t 00.5 is the Weibull baseline hazard with shape parameter i = 0.5 and scale pa- rameter λo 1.0, = OU5(U, --U--X3 X2) if unobserved confounding is present, and = otherwise. Event times are generated via inverse transform sampling from the corresponding survival function.
Scenario B (AFT model): Event times follow an Accelerated Failure Time (AFT) model:
log T(w) = 1185 0.8 1(X, 0.5) + 0.7 + 0.2X3
[0.7 - 0.4 1 0.5) 0.4 0.4 W +
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where 17 (0, 1) and is defined in Scenario A.
Scenario C (Poisson model): Event times follow a Poisson distribution:
X(w) = x + X3 + - -03) W + T(w) (oisson(A(w)))
Scenario D (AFT model); Event times follow AFT model with parameters adjusted for higher censoring:
log ((w) 0.3 0.5 (X1 0.5) 0.5% X2 0.2X3
+ +11- (X, < 0.5) 0.8v X2) W + +
Scenario E (Poisson model): Event times follow Poisson distribution with adjusted parameters:
X(w)= = X2 + X3 + 7+ 2 - -0.3) W +
T(w) (oisson(N(w))
A.4 CENSORING TIME GENERATION
Censoring times C' generated differently across scenarios and depend whether informative censoring is present:
Ignorable censoring (non-InfC scenarios):
Scenario A:
C ~ Uniform(0,3)
Scenario B:
(x, hto(t) exp((> Z)
2.06 exp|u1
where = 1.75 - X + + 0.5, < 0.5)
0.3 0.3 W
[ C
with probability 0.6
Scenario
(1 1(x, 0.5)
with probability 0.4
Scenario D:
At = hoc(t) exp(>=')
= 2.0( exp[u]
where // - 0..9 2/ X2 + 2X3 + [1.15 0.5 1(X, < 0.5) - 0.3 W Poisson(3 log(1 exp(2X, Xz)))
Scenario E:
For scenarios and D, (t) 2.0 1.0 is the Weibull baseline hazard for censoring with shape parameter = 2.0 and scale parameter Ào = 1.0. Censoring times are generated via inverse transform sampling from the corresponding survival function.
Informative censoring (-InfC scenarios): When testing violations of ignorable censoring assump- tions, we replace the above mechanisms with:
C Exponential Ao T:)
where Ao 1.0 and 0.1 are bascline parameters that create dependence between censoring and event times.
While in the main benchmark we induce informative censoring by making censoring times depen- dent on event times, this not the only way to violate the ignorable censoring assumption. To demonstrate the extensibility of modular design and for completeness, additionally include in Appendix Ma setting where informative censoring arises through unobserved confounding.
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A.5 OBSERVED DATA CONSTRUCTION
The observed survival data consists of:
î m C)
(observed time)
8 = 1( S C)
(event indicator)
where =
= T(W) represents the factual event time under the observed treatment assignment.
The combination of these five survival scenarios with eight causal configurations yields our com- prehensive benchmark of 40 synthetic datasets, each designed to test estimator performance under specific combinations of survival dynamics and causal assumption violations.
Table Summary of event time and censoring time generation across survival scenarios
Scenario
Event Time Distribution
Censoring Mechanism
Censoring Rate
A
Cox (Weibull baseline, & 0.5)
Uniform 3)
Low (< 30%)
B AFT (Log-normal)
Cox (Weibull baseline, 2.0)
Low (< 30%)
C
Poisson
Piecewise uniform
Medium (30-70%)
D
AFT (Log-normal)
Cox (Weibull bascline, k = 2.0)
High (> 70%)
E
Poisson
Poisson
High (> 70%)
Table 5: Censoring rate of synthetic datasets (50,000 samples). Notice that the censoring rates different from Table 2 Juder informative censoring due to changes in the censoring distribution.
Survival Scenarios
Causal Configurations
B
RCT-50
0.203
0.073
0.392
0.913
0.794
RCT-5
0,200
0.036
0.390
0.881
0.770
OBS-CPS
0.201
0.066
0.393
0.914
0.789
OBS-UConf
0,201
0.073
0.392
0.918
0.795
OBS-NoPos
0.203
0.082
0.393
0.912
0.803
OBS-CPS-InfC
0.116
0.052
0.885
0.366
0.926
OBS-UConf-InfC
0.116
0.054
0.888
0.381
0.929
OBS-NoPos-InfC
0.116
0.058
0.891
0.403
0.932
Table 6: Treatment rate of synthetic datasets (50,000 samples).
Survival Scenarios
Causal Configurations
B
D
RCT-50
0.502
0.502
0.502
0.502
0,502
RCT-5
0.049
0.049
0.049
0.049
0.049
OBS-CPS
0,503
0.503
0.503
0.503
0.503
OBS-UConf
0.539
0.539
0.539
0.539
0.539
0BS-NoPos
0,500
0.500
0.500
0.500
0.500
0BS-CPS-InfC
0.503
0.503
0.503
0.503
0.503
OBS-UConf-InfC
0,539
0.539
0.539
0.539
0.539
InS
0.500
0.500
0.500
0.500
0.500
Remark on parameter calibration. The constants used in our synthetic generators are inherited from and aligned with prior causal-survival simulation setups (Cui et al. 2023 Meir et al., 2025). and are set to span distinct, interpretable regimes that the benchmark aims to cover. In particular, we calibrate (i) censoring severity by shifting the relative scales of event-time and censoring time pro- cesses (e.g., the AFT intercept change between Scenarios B and D increases typical event times and, together with the corresponding censoring model, yields higher censoring in D); (ii) treatment preva- lence and confounding strength by adjusting propensity-score weights that most configurations
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Table 7: Average treatment effect (ATE) of synthetic datasets (50,000 samples).
Survival Scenarios
Causal Configurations
B
D
RCT-50
0.163
0.125
0.750
0.724
0.754
RCT-5
0.163
0.125
0.750
0.724
0.754
OBS-CPS
0.163
0.125
0.750
0.724
0.754
OBS-UConf
0,004
0.132
0.740
0.831
0.740
OBS-NoPos
0.163
0.125
0.750
0.724
0.754
0BS-CPS-InfC
0,163
0.125
0.750
0.724
0.754
OBS-UConf-InfC
0.004
0.132
0.740
0.831
0.740
OBS-NoPos-InfC 0.163
0.125
0.750
0.724
0.754
remain near balanced treatment except where imbalance is intentional (c.g., RCT-5), while allow- ing controlled dependence on observed or latent drivers; and (iii) effect magnitndehheteroeeeiiyy through the coefficients W and W-covariate interactions, which we keep in moderate range for comparability across scenarios. These choices are not unique, and alternative parameterizations could yield valid benchmarks; goal is to provide a principled and reproducible instantiation that cleanly separates survival dynamics from causal causal-assumption stress and produces broad range of survival CATE evaluation settings.
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Event, Control
Event, Treated CODO Censoring. Control COIO Censoring, Treated
Scenario A
Scenario
Scenario C
Scenario D
Scenario
1.00
9.75
peo 29.
ped 502
24d 322
pet 04.
pm3.500
9.25
0.00
1.00
cil 303
.013
pm3.000)
RCT-5
9.50
1.60
CoB 2011
Coll 801
Col 201
Col 414
Del 799
0BS-10 CP-CP
0.75
0.50
0.00
0:0.281
2-3.796
OBS-UConf
0.75
pe0.000
pio 200
pe3.330
0.25-
0.00
1.00
085 08S-NoPos
p-0.500
p-0.550 500
3-0.530
pHo:500
$12.500
0.50
0.25
0BS -----onn-I II 0BS- 08S-CPS-IC
1.00
CRO 110
CHO 201
24d 225
CH0-206
0.50
LH0 228
9.75-
9.50
0.25
0.c0
085 NoPos IC
1.00
9.75
(eb)
ped 393
24d 538
pee 200
345.590
0.25
Time
Kaplan-Meier Meier curves across causal configurations (rows) and survival scenarios (columns). Solid lines show event-time survival under control (blue) and treatment (or- ange); dotted lines show censoring time survival for each arm. Each panel reports the empirical censoring rate e and treatment probability p.
Figure 5: (Synthetic datasets) Kaplan
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B IMPUTATION METHODS DETAILS
2023) to implement three surrogate imputation strategies for estimating the We follow Qi et al.
true event time T' in right-censored survival data. Let Y min(T, C) be the observed time, with censoring indicator 8 1T < C). Let SKM(D) denote the Kaplan-Meier estimate of the survival function using the dataset D, and N the number of subjects. The three methods below are used to impute a surrogate outcome Tj for censored subject observed at time t,
1. Margin imputation: This method assigns a "best guess" value to each censored subject using the nonparametric Kaplan-Meier estimator. This surrogate value, called the margin time, can be interpreted as the conditional expectation of the event time given that the event occurs after the censoring time. For subject censored at time ii, the margin-imputed event time is computed as:
Se, SKM(D)(
T. Mmmarginn
E T: 4] = 4
(14)
where SKM(D) (t) is the Kaplan- Meilar survival estimate derived from the training dataset.
The reliability of this imputation depends on the censoring time. For example, if a subject is censored very early (e.g., at time 0), the margin time is highly uncertain due to the lack of observed data beyond that point. In contrast, if a subject censored near the maximum observed follow-up, the margin time is more likely to be close to the true event time.
2. IPCW-T imputation: This method imputes surrogate event time for censored subjects based on the observed outcomes of subsequent uncensored individuals. Specifically, for a subject censored at time fg, the imputed value is calculated as the average event time of all uncensored subjects with observed times after fy:
En 1st < (,) 116, 11 13
IPCW
(4)
1(t < t,} 116,-11611111 = 1}
This imputes the event time for subject by averaging the observed event times of those uncen- sored subjects who experienced the event after t, The method is motivated by the idea that these subsequent subjects provide empirical evidence about the possible timing of the unobserved event.
However, a limitation of this approach that fails to provide an imputation when there are no uncensored subjects observed after 4,- In such cases, the denominator of the expression becomes zero, and the method is unable to approximate the event time. In Qi et al. (2023). subjects for whom this occurs excluded from evaluation, whereas in our setup we used the original observed time as the imputed time.
3. Pseudo-obseevation imputation: This method imputes the event time using pseudo- observations, which estimate the contribution of each subject an overall unbiased estimator of the event time distribution. Let i be an estimator of the mean event time based on right-censored data, and let ~- denote the same estimator computed with the i-th subject removed from the dataset. Then, the pseudo-observation for subject is defined as:
ppsendo
CPseudo-Obs (t:, D) N 8- (N
(5)
This quantity can be interpreted as the individual contribution of subject to the overall estimate 0. In practice, both i and 0-i can be computed using the mean of the Kaplan-Meier survival curve:
F. (t),
Ôーه = F, (SxM(D)
Once the pseudo-observation. A.seddo are computed for all censored subjects, they are substituted in place of the true event times for evaluation modeling.
Although pseudo-observatiinn are not exact conditional expectations, they can approximate E[T; X,) under certain assumptions. In particular, when censoring independent of covariates and the
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sample size is large, pseudo-obseervatios behave asymptotically like ii.d. draws from the true conditional expectation:
peeudo
x
R [[ X..]
This makes the pseudo-observation method a principled, nonparametric approach for imputing cen- sored survival times, particularly when estimating global quantities like the mean event time.
These imputation strategies enable us to transform the survival outcome into a fully observed target variable, allowing the application of standard regression- methods in causal effect estimation. To ensure meaningful estimates, it is important that each imputed event time for censored subject guaranteed be greater than equal the censoring time-reflecting the fact that the true event must occur after the last time was observed. In our implementation, we manually enforce this constraint by setting the imputed value to the observed censoring time whenever the imputation procedure yields a value less than t.
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C LIST OF CATE ESTIMATORS IN SURVHTE BENCHMARK
As mentioned in Section S in our benchmark, we evaluate three families of survival CATE methods, totaling 53 variants. We list the number of variants for each type of CATE estimator in Table 8
For the outcome imputation methods, we first apply one of three imputation strategies (Pseudo- observation, Margin, IPCW-T) [Qi al., 2023) handle the censored data, transforming the survival problem into standard regression task. After imputation, we use these imputed outcomes with four different meta-learner frameworks (S-, T-, X-, and DR-Leamerrs, each implemented with three different base regression models (I (Lasso Regression, Random Forest, and XGBoost), resulting in x x 3 36 different variants. Additionally, we pair each imputation method with two special- ized causal inference methods: Causal Forest (Athey et al., (019) and Double-ML. (Chernozhukov et al. 2018), which adds x + method variants.
6 more variants, for a total of 42 outcome imputation
For direct-survival CATE models, we include the Causal Survival Forests (CSF) (Cui et al., 2023) and SurvITE (Curth et al. (202Ia). which specifically designed to handle right-censored data without requiring separate imputation steps. SurvITE estimates individual treatment effects directly from right-censored survival data by learning balanced representations and optimizing survival- specific loss.
For survival meta-learners, implement three types of meta-learning frameworks that have been extended to handle censored data directly: S-Leamer, T-Learner, and matching-learner (Norooz- izadeh al. 2025). Each of these frameworks combined with three different base survival models (Random Survival Forests (Ishwaran et al. 2008), DeepSurv (Katzman et al., 2018). and DeepHit (Lee al., 2018) ) that estimate the underlying survival functions, resulting survival meta-lcarner variants.
3
In total, our benchmark evaluates 42 2 2 53 different method configurations across the 40 synthetic datasets and the two real-world datasets described in Section
Table 8: Breakdown of benchmarked survival-CATE estimator variants used in our experiments. Each row corresponds to specific combination of method class, imputation strategy (if applicable), base learner(s), and CATE learner(s). Cells with numbers in parentheses indicate how many variants are contributed by the method(s) listed in that cell. The final column reports the total number of method variants constructed using that combination.
Imputation
Base Learner
CATE Learner (No. options)
Method Class
No. Variants
(No. options)
(No. options)
Lasso Regression, Random Forest, XGBoost (3)
Meta-Learners
Outcome Imputation
Pseudo-obs, Margin, IPCW-T (3)
(S-, X-, DR-) (4)
Method
Causal Forest (1)
Double-MI.
(1)
Causal Survival Forests
Direct-Survival CATE Models
(1)
SurvITE
(1)
Random Survival Forests, Survival Meta-Learners
Survival Meta-Learners
DeepSurv, DeepHit
(S-, T-, Matching-)
(3)
(3)
Total
53
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D DETAILED OVERVIEW OF CAUSAL INFERENCE METHODS
This section provides a comprehensive explanation of the causal inference methods evaluated in our benchmark. We begin with outcome imputation methods that transform censored survival data into standard regression problems, followed by direct-survival CATE models specifically designed for right-censored data, and finally survival meta-learners that adapt standard meta-learner frameworks to handle censoring. For each method, we present the theoretical foundation, algorithmic procedure. and specific implementation considerations in the survival analysis context. Our exposition focuses on highlighting the unique characteristics that make each approach suitable for different survival and causal inference scenarios, with particular attention how these methods handle the challenges posed by censoring and treatment effect heterogeneity.
D.1 OUTCOME IMPUTATION METHODS
Meta-learners represent a flexible framework for estimating conditional average treatment effects (CATESs) by decomposing the causal inference problem into standard supervised learning tasks. The key advantage of meta-learners is that they allow practitioners to leverage any out-of-the-box machine learning algorithm "base learner" while maintaining principled approaches to causal effect estimation. This modularity makes meta-learners particularly attractive in practice, as they can incorporate state-of-the of-the-art ML. methods (e.g., random forests, gradient boosting, neural networks) without requiring specialized causal inference implementations. For detailed explanations on meta- learners, one can refer Künzel et al. 2019); Kennedy (2023). We provide simplified overview below and largely refer to the documentation of the econml package.
T-Learner (Künzel et al., 2019). The T-Learner (Two-Learner) adopts the most straightforward approach by fitting separate outcome models for treated and control groups. Given binary treatment W E {0, features X, and outcome Y, the T-Learner:
1. Splits the data by treatment assignment: (X", Y") for controls and (X1, Y1) for treated units
2. Trains separate outcome models (i.e. predicting the outcome Y using features X):
For control units: pao MY x²)
For treated units: ú1 = M1(YY X!
3. Estimates CATE as:
- PO(x))
where Mn and Mj can be any regression algorithm. The T-Leamer is conceptually simple but can suffer from high variance when treatment groups have different sizes when the outcome models extrapolate poorly to regions with limited overlap.
S-Learner (Künzel et al. 2019). The S-Learne (Single-Learne) takes unified modeling approach by including treatment assignment as an additional feature. The procedure involves:
1. Training single model using all available data:
A M(Y (X,
2. Estimating CATE as:
+(x) p(x 1) ((x,
This approach leverages all available data for training and can be more sample-efficient than the T-Learner. However, it relies heavily on the base learner's ss ability to capture treatment-featur inter- actions, and may perform poorly when these interactions are complex or when the treatment effect is small relative to the baseline outcome.
X-Learner (ünzel et al. 2019). The X-Learner represents a more sophisticated approach that combines ideas from both T-Learner and inverse propensity weighting. The algorithm proceeds in multiple stages:
1. Fit initial outcome models:
Ad Mi xx)
in M2 x2)
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2. Compute imputed treatment effects:
For treated units: D' = y - -xo(X!)
For control units: D -x1(Xx y
3. Model treatment effects:
tg M3(DD x9)
f1 = Ma(D) ~ x
4. Combine estimates using propensity scores:
f(x) -(x)f((x) + (1-g(z))fi(
where g(x) is the estimation for propensity score P(W 1|x x) and typically fitted using logistic regression. The X-Learner is particularly effective when treatment groups have different sizes or when treatment effects are heterogeneous, as it explicitly models treatment effect variation and uses propensity weighting for optimal combination.
DR-L (Kennedy, 2023). The DR-Learner (Doubly Robust Learner) extends the doubly ro- bust framework to meta-learning by combining outcome modeling with propensity score estimation. The approach constructs doubly robust scores that remain consistent either the outcome model or propensity model is correctly specified. It includes the following steps:
1. Fit outcome modeling for each treatment
Ào Mr(Y0 ~ x²)
A M2 ~ )
2. Construct propensity score modeling
- (W ~ X)
3. Construct doubly robust outcomes:
YDR = (x( + (Y -aO(X)) 1(W = =0}
9(X)
PDR (x()) + (Y - (x)) 1(W = 1}
g(X)
4. Final CATE estimation: f(x) y,DR_ - pn
The DR-Leamnr provides theoretical robustness guarantees and often performs well in practice, particularly when either outcome or treatment assignment can be accurately modeled.
Double-ML (Chernozhukov et al., 2018). Double Machine Learning (Double-ML or DML) rep- resents a principled framework for estimating heterogeneous treatment effects when confounders are nigh-dimensional or when their relationships with treatment and outcome cannot be adequately captured by parametric models. The key insight of DML to decompose the causal inference prob- lem into two predictive tasks that can be solved using arbitrary machine learning algorithms while maintaining favorable statistical properties. Specifically, DML assumes the following structural re- lationships:
Y = ((X) W + te with E|e|X, Z| = W f) +1 with X Z =
E
where Y is the outcome, W is the treatment, X are the features of interest for heterogeneity, Z are confounding variables, and ((X) is the conditional average treatment effect we aim to estimate. The method proceeds by first estimating two nuisance functions:
Outcome regression: qX, Z) = E| X. Z
Treatment regression: s(X, 7) = E. Z]
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These nuisance functions can be estimated using any machine learning algorithm capable of regres- sion (for continuous treatments) or classification (for binary treatments). Popular choices include random forests, gradient boosting, neural networks, regularized linear models. After obtaining estimates ② and f. DML constructs residualized outcomes and treatments:
Y = 2)
W = W f(X.2)
The final step estimates ( by regressing Y on W and X
i arg min E. I 8(X) W
Causal Forest (Athey et al., 2019). Causal Forest extends the random forest methodology to di- rectly estimate heterogeneous treatment effects in non-parametric, data-adaptive manner. Unlike meta-learners that rely on global models, Causal Forest estimates treatment effects locally by learn- ing similarity metries in the feature space and weighting observations accordingly. Causal Forest builds upon the same structural assumptions as DML but estimates (xx) locally for each target point x. The method constructs forest where each tree is grown using causal splitting criterion that maximizes treatment effect heterogeneity rather than prediction accuracy. For target point z, the treatment effect estimated by solving:
((x) arg min Σ (x,))) (Y: 0 W,)²
where (X,) represents the similarity between points x and X, as determined by how frequently they fall in the same leaf across the forest, and Y, W are residuals from nuisance function estimates.
Implementation in survival context In our benehmark, meta-learnens Double-ML, and Causal Forest are applicd to survival outcomes through outcome imputation methods. We first apply impu- tation techniques (Pscudo-obs, Margin, or IPCW-T, Appendix B for details) to convert censored survival times into continuous outcomes, then apply the meta-leamers described above with various base regression algorithms (Lasso Regression, Random Forest, XGBoost). This two-stage approach allows leveraging the rich ecosystem of causal inference methods developed for continuous out- comes while handling the complexities of censored data.
D.2 DIRECT-SURVIVAL CATE METHODS
Causal Survival Forests (CSF) (Cui et al. 2023) extends the Causal Forest methodology directly to right-censored survival data by incorporating doubly robust estimating equations from survival analysis. Unlike meta-learnen that require outcome imputation, CSF handles censored observations natively while maintaining the adaptive partitioning advantages of tree-based methods. CSF builds upon the Causal Forest framework of AAhhy et al. (2019) but adapts the splitting criterion and es- timation procedure for survival outcomes. For a detailed explanation of the method, please refer to the original paper by Cui et al. (203). We provide overview of the estimation procedures as follows:
1. Nuisance estimation: Using cross-fitting, estimate nuisance components including:
Propensity scores: ê(x:) P(W = =|X .))
Outcome regression: ri((::) = F(y(T))X = x]
Censoring survival function: (s(2) P(C 2 W w. X X
Conditional expectations: (s)x) L'y(TT)X
where y(T) is transformation applied on the event time T, the same defined in Eq
2. Forest construction: Build a forest where each tree uses causal splitting criterion that max- imizes treatment effect heterogeneity. The splitting rule targets variation in the doubly robust scores rather than prediction accuracy.
3. Local estimation: For a target point .r compute forest weights axx) indicating similarity based on leaf co-occurrence across trees, then estimate the CATE by solving:
Σ (Xx))) A h W, A mn SC Qw) = 0
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where d is the doubly robust score function that adjusts for both treatment assignment and censoring.
SurvITE (Curth et al. 2021a) adapts the representation learning paradigm for counterfactual inference to time-to-event data. Unlike methods that rely on local similarity the covariate space, SurvITE addresses selection bias by learning shared latent representation where the treated and control distributions are balanced, while simultaneously modeling the censoring mechanism. SurvITE builds upon the theoretical bounds of counterfactual regression but incorporates survival- specific loss functions to handle right-censored outcomes without requiring imputation. A brief outline of the method follows:
1. Representation learning: Map covariates X to a latent representation (X) via a deep neural network, subject a discrepancy penalty. The objective is minimize an Integral Probability Metric (IPM) (e.g., Wasserstein distance or MMD) between the treated and control populations in the latent space:
IX = P& = 0)) <
2. Factual loss minimization: Simultaneously train treatment-specific hypothesis heads (h₃ and ho) on top of ((X) using a survival loss function Leurv (discrete-time log-liiklihood) that accounts for censoring:
N Σ
min 0.
(D(z))), (ww,)ar(
wiCrare (hw,
+ a IPM
3. Effect estimation: For a target point z, the CATE is estimated by passing E through the learned representation and computing the difference between the outputs of the treatment and control heads:
+xx) (()))) W Ely(T)) W
where the expectation derived from the predicted survival curves or time-to-event distribu- tions output by h, and ho.
D.3 SURVIVAL META-LEARNHR
T-Leevner-Survival (Bo et al. 2024; Noroozizadeh et al., 2025). The T-Learner can be adapted to right-censored survival data by fitting separate survival models for each treatment group. Let W E (0. 1} denote the treatment indicator, X be the covariate vector, and T the observed survival time with censoring indicator 6, and h the maximum follow-up time.
70,8%) 1. Split data by treatment: Partition the dataset into (X", T 88) for W 0 and (X2,T1,84 for W
2. Train separate survival models: Fit a survival model (e.g., Random Survival Forests, Deep- Sury, DeepHit) to each group:
(o(la) Survival model fitted on T0
3, (ulx) = Survival model fitted on (x xx, ,,
3. Estimate restricted survival time (RMST): Compute RMST for each treatment
(=(x=) S/" So(ula)du,
Pa (x)) ((a)=1) 1/² h (u
4. Estimate CATE: For any estimate treatment effect:
F (z) fig (z) (x)
S- Suavvva-Survvval (Bo et al. 2024 Noroozizadeh et al., 2025). The S-Learner adapts by training a single survival model over all data with treatment covariate.
1. Fit survival model: Train survival model over the full dataset using (X, W) as inputs: S(up,, w) Survival model fiteed (X,W),
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2. Estimate restricted mean survival time (RMST): Compute RMST under both treatment ditions:
p)x,0)= = //" S(ulæ, O)du, pla, 1) = J," (ul 1)du
3. Estimate CATE:
Tg-Learne (z)) = f1( 1) - fa(x, 0)
Matching-Survival (Noroozizadeh et al., 2025). The Matching-Learmn estimates the CATE by imputing the counterfactual Restricted Mean Survival Time (RMST) using matched data points from the opposite treatment group.
1. Estimate factual RMST: Fit a survival model on the full dataset and compute:
jiN, (X.) L/" S(u) Wi)du
2. Find matches: For each individual i, identify K nearest neighbors JR (x) from the opposite treatment group W.).
3. Estimate counterfactual RMST: Average factual RMSTs of matched neighbors:
M 7n-w (Xi)
1
Σ (X,)
K
JEJX(()
4. Estimate CATE: Compute CATE for each unit:
Fautching (X,) (fw, - (ia-ww(X)).. -W
This approach makes minimal modeling assumptions beyond nearest-neighhor similarity and is par- ticularly helpful in settings with low overlap or where global models may be misspecified.
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E MODEL TRAINING DETAILS AND HYPERPARAMETERS ON BENCHMARKING WITH SYNTHETIC DATA
To rigorously evaluate and compare the performance of causal inference models under controlled conditions, we conducted extensive benchmarking on synthetic datasets. Each synthetic dataset consisted of 50,000 samples generated under known data-genee getta-enerattig processes explained in Ap- pendix A For each experimental repeat, we selected a subset of 5,000 samples for training, 2,500 for validation, and 2,500 for testing. using 10 distinct random seeds (experimental repeats) to en- sure robustness. Hyperparameters for each model were tuned on the validation set to minimize the Conditional Average Treatment Effect Root Mean Squared Error (CATE-RMSE). Throughout this paper, final results are always reported the held-out test set using the best-performing configura- tion. Appendix [F7 provides complementary experiments that analyze the convergence behavior of each method under varying training set sizes.
This appendix details the hyperparameter grids used for model selection, the specific survival and outcome models applied within each causal inference framework, and the average computational cost associated with each method class.
E. HYPERPARAMETERS FOR OUTCOME IMPUTATION METHODS
For methods based outcome imputation, employed standard regressors estimate the ditional mean of the survival outcome given covariates and treatment assignment. We considered Lasso regression, Random Forest, and XGBoost base models. Each optimized using cross- validated grid search on the training set. The corresponding hyperparameter grids are listed in Table g
Table 9: Set of hyperparameters for outcome imputation methods
Regressor
Hyperparameter Grid
Lasso
Alpha: {0.001, 0.01, 0.1, 1, 10}
Random Forest
Number of trees: {50. 100)
Maximum depth: (3. 5, None)
XGBoost
Number of trees: {50, 100)
Learning rate: (0.01, 0.13
Maximum depth: (3.
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E.2 HYPERPARAMETERS FOR DIRECT-SURVIVAL CATE METHODS
For direct modeling of survival outcomes, we employed the Causal Survival Forests (CSF), which adapts the Causal Forest framework handle right-censored data. We used the default hyperparam- eters from the original implementation. These are summarized in Table TO
Table 10: Set of hyperparameters for Causal Survival Forests
Parameter
Default Value
Number trees grown Fraction data per tree Variables tried per split Minimum samples in leaf Maximum imbalance of splits Penalty for imbalance at split Account for treatment and censoring in split stability TRUE
2000
0.5
+ (oo[++++01,,
5
0.05
Trees per subsample for confidence intervals
2
For SurvITE, we implemented PyTorch version based on the original architecture and repository. The main configuration is summarized in Table 11.
Table 11: Set of hyperparameters SurvITE.
Parameter
Value
Model width Adim: hamt haim2
16,16,32 (synthetic, ACTG) or {16, 32, 64) (MIMIC, Twin)
Number of shared layers
2
Number of head layers
2
Activation function
ReLU
Dropout rate
0.3
IPM type
Wasserstein
IPM regula laguziizzttonn weight 3
10-3
Smoothing parameter y
Learning rate
10-3
Batch size
256
Maximum epochs
5000
Early stopping
Checked every 100 epochs; stop after 10 non- con-improving checks
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E.3 HYPERPARAMETERS FOR SURVIVAL META-LEARNERS
For survival mettelleamerr--pecifffaallll T-Leaaner-Survival, S-Leamerr-Srrival, and Matching- Learner-Survival-we used three different base survival models: Random Survival Forests (RSF), DeepSurv, and DeepHit. Each of these models was tuned using a predefined hyperparameter grid, listed in Table [2
Table 12: Set of hyperparameters for Survival Meta-Learners
Model
Hyperparameter
Values
Number of estimators
{100, 250, 500) (5. 10. 20}
RSF
Minimum samples split
Minimum samples leaf
(2. 5, 10}
Number nodes per layer
{32, 64, 128, 256} (True, False]
Batch normalization
Dropout rate
(0.0. 0.1, 0.2, 0.3)
Learning rate
(0.001, 0.05)
DeepHit
Batch size Epochs
{128, 256, 512]
(200, 512, 1000)
Alpha
(0.1. 0.2, 0.3, 0.5)
Sigma
{0.05, 0.1, 0.3)
Number nodes per layer
(32, 64, 128, 256) (True, False] (0.0, 0.1, 0.2, 0.3)
Batch normalization
Dropout rate
DeepSurv
Learning rate
(0.001, 0.01, 0.05)
Batch size Epochs
{128, 256, 512) (200, 512, 1000)
Hyperparameters were selected through empirical tuning informed by prior literature. For neural network-based based models (DeepSurv, DeepHit), used early stopping to mitigate overfitting. All experiments were made reproducible by setting random seeds. The best-perforning hyperparame- ter configuration selected using CATE-RMSE on the validation set, and all final results were obtained on the test set using these optimal configurations.
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E.4 COMPUTATION TIME OF SURVIVAL CATE METHODS
We also measured the computational cost of each CATE estimation method in terms of average run- time per dataset and experimental repeat. Each runtime recorded using Python's time.time () and averaged across 40 synthetic datasets and 10 random seeds. Table T3 presents the mean runtime (in seconds) and standard deviation (excluding the time required for imputation). As expected, neu- ral network- weasrrk-based survival models incur substantially higher computational costs than classical or tree-based methods. All experiments were conducted on a machine equipped with an AMD Ryzen 9 5900X CPU, 128GB RAM, and an NVIDIA GeForce RTX 4090 GPU (CUDA version 12.2).
Table 13: Average computation time per dataset per experimental repeat for each causal method. Runtime reported in seconds with standard deviation across runs.
Method Class
Method
Runtime (s)
T-Learner
2.14 1.38
Outcome Imputation Methods: Meta-learners
S-Leamer
1.84 1: 1.22
X-I E--Leamer
2.92 2.42
DR-Leamer
3.34 1.88
Outcome Imputation Methods: Forest MI.-based learners
Double-ML
5.27 0.40
Causal Forest
5.75 0.40
Causal Survival Forests
0.78 =: 0.06
Direct-Survival CATE Methods
SurvITE
43.15 6.85
T-LLcane--Suriival
31.31 + 16.88
Survival Meta- Meta-Leamers
S-Learer-Survive
22.99 + 14.23
Matching-Survival Survival
49.40 1 23.25
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F ADDITIONAL EXPERIMENTAL RESULTS FOR SYNTHETIC DATASET
This section provides comprehensive experimental results on our synthetic datasets, expanding on the key findings presented in the main text. We begin in Appendix F.I with a full Borda rank- ing of all 53 model combinations, summarizing global performance across every causal configura- tion and survival scenario. In Appendix F22 we explore how performance varies across different survival iaparios-illustratingg the impact of censoring patterns and time-to-even distributions on method rankings. Appendix F3 then delves into how violations of causal assumptions (treatment randomization, ignorability, positivity, and censoring mechanisms) reshape the ranking of models for effectiveness of each causal method.
Subsequent sections F44 and F.5 present detailed performance metrics- CATE RMSE and ATE
bias, aspeetively-across all 8 causal configurations and survival scenarios, with box plots cap- turing variability over 10 experiment repetitions. We also evaluate auxiliary components in F6 including imputation methods and base learners (regression, survival, and propensity models), and in Appendix F.7 we examine convergence behavior under varying training set sizes. Together, these detailed results support the robustness, sensitivity, and practical trade-offs of each model family in wide spectrum of data-generating and causal settings.
F.3 we also report a set of win-rate anal- yses that track how often each method family attains Top-1, Top-3, and Top-5 performance on both CATE RMSE and ATE Bias. Overall win-rates across all survival scenarios and causal con- figurations are summarized in Table while Tables T6 17, and T8 provide scenario-specific and causal-con confoluuttnotooonnnnnnoo speciioinsseiiiicii win-rates. These complementary views highlight not only which meth- ods achieve strong average performance, but also which ones most consistently appear among the top performers across varying censoring regimes, survival experimental conditions, and patterns of causal assumption violations.
In addition to average-rank summaries, in Appendix F.T
F.1 FULL RANKING OF MODELS
To compare the overall performance of the methods across all synthetic datasets, we computed Borda ranking based on the average rank of each method's test set CATE RMSE (Table [4]. The ranking procedure aggregates method performance across all combinations of causal configurations and survival scenarios. For each method, we first computed its RMSE on the test subset of the CATE predictions for each (causal configuration, survival scenario) pair. We then ranked all 53 methods (described in Appendix C within each pair and calculated the average rank across these conditions. This average rank represents the method's 's Borda score and serves as a unified summary of its performance robustness in our synthetic data experiments.
In addition to the Borda rankings, we also summarize how often each method family achieves lead- ing performance across all experimental settings by reporting the percentage of times a method appears in the Top-1, Top-3, and Top-5 for both CATE RMSE and ATE Bias. This provides a com- plementary view that focuses on frequency of strong performance rather than average rank, and helps separate methods that occasionally perform well from those that do so consistently across our full set of survival scenarios and causal configurations.
shows that the strongest performance comes from method families that explic- itly incorporate survival structure, particularly the survival meta-learners. Matching-Surviva has the most consistent high-rank presence on CATE RMSE (Top-5: 92.5%), while L-Learner-Survivee achieves the highest Top-3 and Top-5 rates on CATE RMSE (67.5% and 85.0%, respectively) and also performs strongly on ATE Bias (Top-3: 57.5%, Top-5: 77.5%). Across direct-survival CATE methods, Causal Survival Forests remains competitive and relatively stable, with the highest Top-1 rate on CATE RMSE among direct-survive CATE methods (25.0%) and strong ATE Bias cover- age (Top-5: 75.0%). Double-ML performs well primarily on CATE RMSE (Top-3: 52.5%, Top-5: 72.5%) but is less competitive on ATE Bias. In contrast, the classical outcome-imputation meta- learners (T-, S- X-, and DR-Leerners) attain Top-1 positions only rarely and generally have lower TTo-33Topp5 rates than the survival-aware families, highlighting the advantage of accounting for time-to-event structure when estimating heterogeneous treatment effects in our wide range of exper- imental scenarios.
Overall, Table 15
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Table 14: Borda ranking of all methods
Rank Method
Score
Rank Method
Score
(S-Learner- S--Levler-Survivall DeepSurv)
5.18
28 (Causal Forest, Pscudo-Obs)
24.70
2 (Mutching-Survival DeepSurv)
5.43
29 (T-Leurner, Margin, RandomFFores)
26.23
3 (Double-Me ML, Margin)
6.65
30 (S (S-Learner, IPCW-T, RandomForest)
26.50
4 (Causal Forest, Margin)
10.78
31 (SurvITE)
27.28
5 (Double-ML, IPCW-T)
11.78
32 -S-Learner Margin, Lasso)
27.98
6 (Causal Survival Forests)
12.53
33 Learnee, IPCW-T, Lasso)
27.98
7 (Douhle-ML,, Pscudo-Obs)
15.38
34 (S-1 Learner, Pseudo-Obs, I Lasso)
28.18
8 (S-Learner-Survive
RSF)
15.50
35 (T-Learner, IPCW-T, RandomForest)
29.85
9 (Causal Forest, IPCW-T)
15.93
36 (T-Leurerr-Survival. DeepHit)
30.30
10 (X-Learner, Margin, RandomForest)
16.53
37 (T-Learmer-Survival. RSF)
30.83
11 (S-Learner, Margin, XGB)
18.33
38 (S-Lecrner, Pseudo-Obs, XGB)
32.80
(Matching-Survae) Survival,, DeepHit)
18.50
(S-Learner, Pseudo-Obs, RandomForest)
32.85
(DR-Leamer, Margin, Lasso)
18.83
(X-Learner, Margin, XGB) (X-Learner, Pseudo-Obs, RundomForest)
34.00
Learner-Survvall DeepSurv)
19.60
35.33
15 Learner-Survivar DeepHit)
19.78
42 (X- X--Learner IPCW-T, XGB)
35.75
16 (X XX-Learner, Margin, Lasso)
20.53
43 (DR-Leames Margin, RandomForest)
37.45
17 (T-Learner, Margin, Lasso)
20.53
44 (DR-Leamer, IPCW-T, RandomForest)
38.70
18 (DR-L.camer, Pseudo-Ohs, Lasso)
20.93
45 (T-4 .earner, Margin, XGB)
41.18
19 (S-Learner, IPCW-T, XGB)
21.85
46 (T-1 .earner, IPCW-T, XGB)
42.08
20 (X-Learner, IPCW-T, RandomForest)
22.05
47 (T-Learnerr, Pseudo-Ohs. RandomForest)
42.50
21 Suutching-Survival, RSF)
22.35
48 (DR-Leamer, IPCW-T, XGB)
46,63
22 (DR-Leamer, IPCW-T, Lasso)
22.65
49 (DR-Leamer. Margin, XGB)
46.70
23 (X-Learner, Pseudo-Obs, Lasso)
22.85
50 (X-ILearner, Pscudo-Ohs, XGB)
47.35
24 (T-Learner, Pseudo-Obs, Lasso)
22.90
51 (DR-Leamer, Pseudo-Obs, RandomForest)
49.60
25 (S-Learner. Margin, RandomForest)
23.05
52 (T-Learner, Pseudo-Obs. XGB)
50.55
26 (T-Leamer, IPCW-T, Lasso)
24.40
53 (DR-Leamer, Pseudo-Obs, XGB)
52.80
27 (X-Learner, IPCW-T, Lasso)
24.45
Table 15: Win-rate (%) of method families across all experimental configurations. Values denote the percentage of times method appears in the Top-1, Top-3, and Top-5 according to CATE RMSE and ATE Bias.
CATE RMSE
ATE Bias
Method Family
Top-1 Top-3 Top-5
Top-1 Top-3 Top-5
Outcome Imputation Methods
T-Leamer
2.5
12.5
30.0
2.5
15.0
32.5
S-Learner
2.5
2.5
5.0
15.0
25.0
X-Learner
2.5
12.5
35.0
5.0
17.5
40.0
DR-Learner
7.5
22.5
5.0
12.5
30.0
Double-ML
20.0
52.5
72.5
2.5
5,0
17.5
Causal Forest
17.5
42.5
2.5
27.5
Direct-Survival CATE Methods
Causal Survival Forests
25.0
45.0
52.5
17.5
75.0
SurvITE
2.5
5.0
22.5
7.5
22.5
40.0
Survival Meta- Learners
T--earner-Suree Survival
12.5
32.5
42.5
25.0
37.5
62.5
S S-Learner Lecrner-Survival
17.5
67.5
85.0
12.5
57.5
77.5
Matching Survival
12.5
50.0
92.5
17.5
57.5
72.5
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F.2 RANKING OF CAUSAL METHODS FOR DIFFERENT SURVIVAL SCENARIOS
In Figure 66 we present the Borda ranking of all causal model families across five different survival scenarios (A-E). For each scenario, the average rank of each method is computed over 8 distinct causal configurations, allowing us to assess robustness across varying underlying data-generating processes. The horizontal layout of each plot ranks methods from best (left, top to bottom) to worst (right, bottom to top), with rank values annotated next to each method for clarity. The colors of the lines connecting the methods to the horizontal axis represent the specific family of the method (e.g., outcome imputation, direct-survival CATE, survival meta-learners Additionally, thick black horizontal bands connect methods whose difference in ranking is not statistically significant.
These plots illustrate how model performance shifts as censoring rates and survival distributions vary. In Scenario A, which involves minimal censoring. Double-MI. achieves the best overall ranking (1.5), though survival meta- approaches like Secaanerr-Suriive and perform highly, sharing statistical overlap with the top spot. However, as we move toward Scenar- ios C, D, and E-which are characterized by higher censoring direet survival modeling approaches consistently rise to the top. Specifically, S-Leerner-Survival, vival Forests dominate the highest ranks across these later scenarios, although SurvITE does not show a really strong average performance even with more censoring. Conversely, the relative per- formance of Double-ML steadily declines, eventually dropping the bottom half of average ranking (rank 6.9) in Scenario E. This pattern reinforces that survival-specions modeling is better equipped to handle the uncertainty introduced by heavy censoring, outperforming standard outcome imputation strategies in such settings.
Shearner-Surviee also
Matching-SSuviial and Causal Sur-
Pa 2-4
13. BundTT
Cuaal Santiot feet Slaamer
Kioamer
(a) Scenario
(b) Scenario B
11
Ang
Fask
Cand, Cambel ferst
Suammer- 2-2
16 Lo-
Lommen
Sendict
(c) Socnario
(d) Sccnario D
Ang
Lareer Lur
(c) Scenario
Figure 6: Average ranking of each model for each Survival Scenario. Shaded regions indicate the standard error of the rank across datasets.
In addition the global rankings in Figure 6 For each survival scenario (A-E), we compute how often each method family appears in the Top- I, Top-3, and Top-5 positions for CATE RMSE and ATE Bias across the eight causal configurations. This provides complementary view of robustness, highlighting which families consistently occupy the top ranks as we vary the survival time model (Cox, AFT, Poisson) and the censoring rate (low, medium, high; Table
we report scenario-specific win-rates in Table T6
Under low censoring (Scenarios A and B), outcome-imputation approaches can still be competi- tive on CATE RMSE, but the winners are scenario-dependent and survival-aware methods remain highly prevalent in the Top-k sets. In Scenario A (Cox, low censoring). Double-ML dominates CATE RMSE (62.5% T and 100% Top-3/Top-5), while survival meta-leamers also appear frequently in Top-3/Top-5 (c.g., L-Leamerr-Suvinne and Learner-Surviva are both 100% Top-5). ATE Bias more dispersed: S-Learner and DR-Learner each attain 25.0% Top-1, and survival meta-learners
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(S DeeanerSSuriivll and Buuching-Survivall contribute strongly Top-3/Top-5, whereas the direct- survival CATE methods have limited presence. In Scenario (AFT. low censoring), Causal Survival Forests becomes leading family for both metrics (37.5% Top-1 CATE RMSE; 25.0% Top-1 ATE Bias; 75.0% Top-3/Top-5 ATE Bias). At the same time, Causal Forest remains competitive on CATE RMSE (37.5% Top-1), 1), and survival meta-learnrrs retain substantial Top-5 coverage, particu- larly -atching-Survival (87.5% Top-5 CATE RMSE) and --Learner-Suviive (87.5% Top-5 CATE RMSE). Notably, SurvITE does not appear among the Top-k in this scenario.
As censoring increases, survival-specific modeling becomes increasingly important and accounts for larger fraction of the best-performing sets. In Scenario (Poisson, medium censoring), Causal Survival Forests clearly leads on both metrics (62.5% Top-1 CATE RMSE; 37.5% Top-1 ATE Bias; 100% Top-5 ATE Bias), while Matching-Surva Survival and L-Leernnr-SSurivva frequently ap- pear among the best methods (e.g., Matching-Survive is 25.0% Top-1 CATE RMSE and 100% Top-5 CATE RMSE; both Matching-Survinn Survival and -Leaaner-Survival reach 75.0% Top-3 CATE RMSE). Under high censoring, the dominance shifts even more strongly toward survival-aware families, but with different emphases across scenarios. In Scenario D (AFT, high censoring), S- Learner-Survival is the primary winner CATE RMSE (50.0% Top-1 1 and 100% Top-3/Top-5), while Matching-Survinn Bias, the top positions are shared across multiple survival-aware families (Causal Survival Forests, TH-Learner-Surviva,, and B-L.evver-Surrviva each at 25.0% Top-1). In Scenario (Poisson, high censoring), the strongest ATE Bias performance is achieved by T-Learner-Survival (50.0% Top-1 and 87.5% Top-5), with Matching-Survinn and SurvITE following, whereas CATE RMSE Top-1 more distributed Aatching-Surviier 37.5% Top-1; several other methods across both outcome- imputation and direct-survival CATE methods at 12.5%). Overall, across all scenarios, classical gutcome-impptatiin methods are rarely dominant or ranked Top-1 under moderate or high censor- ing, reinforcing the benefit of explicitly modeling time-to-event structure when the censoring rate is high.
achieves perfect Top-3/Top-5 coverage (100% in both cases). For ATE
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Table 16: Win-rate (%) of method families by Survival Scenario. Values denote the percentage of times method appears the Top-1, Top-3, and Top-5 according to CATE RMSE and ATE Bias across the eight causal configurations for each scenario.
Scenario A: Cox, Low Censoring
Scenario B: AFT, Low Censoring
Method Family
CATE RMSE
ATE Blas
Method Family
CATE RMSE
ATE Blas
Top-1
Top-3 Top-5
Top-1 Top-3
Top-5
Top-1
Top-3 Top-5
Top-1 Top-3 Top-5
Outcome Imputation Methods
Outcome Imputation Meshode
T-Leamer
0
0
25.0
25.0
T-Leareer
12.5
0
12.5
25.0
S-Leamer
12.5
X-Leamer
0
0
12.5
0
25.0
62.5
X-Leamer
12.5
12,5
12.5
37.5
DR Leurner
0
0
25.0
25.0
62.5
DR-Leamner
12.5
25.0
0
25.0
37.5
Double-ML
62.5
100.0
100.0
12.5
37.5
Double-ML
12.5
100.9
100.0
12.5
12.5
37.5
Causal Forest
0
37.5
100.0
12.5
12.5
37.5
Causal Forest
37.5
50.0
75.0
0
25.0
62.5
Direct Survival Methods
Direct-Surviaal CATE Methody
Cansal Survival Forests
0
12.5
25.0
Cansal Survival Forests SurvITE
37.5
62.5
87.5
25.0
75.0
75.0
SurvITE
0
25.0
0
Survival Leta-Le
Survival Meto Leamers
T-l Lamer camer--Survval
12.5
87.5
100.0
12.5
25.0
50.0
T-I T-Leamer-Se
camerr-Srvival Survival
12.5
25.0
37,5
62.5
S-Learce-SSuvival
50.0
100.0
S-Learncr-Suriial
12.5
37.5
Survviag-Survvival Survival
0 12.5
75.0
12.5
50.0
50.0
Matching-Sunn Survival
12.5
87.5
12.5
50.0
75.0
Scenario C: Poisson, Medium Censoring
Scenario D: AFT, High Censoring
Family
CATE RMSE
Method Family
CATE
ATE
Top-1
Tup-3 Top-5
Top-1 Top-3 Top-5
Top-1
Top-3 Top-3
Top-1 Top-3 Top-5
Outcome Imputation Methods
Outcome Imputation Methods
T-Learne
25.0
37.5
12.5
25.0
T-Learner
25.0
12.5
12.5
50.0
S-I S.L.ammer
0
0)
0
0)
S-Leammer
0
0
0
12.5
50.0
X-Leamer
25.0
37.5
X-Leamer
37.5
12.5
DR-I carner
0
0
25.0
DR-I earner
0
12.5
37.5
Double-ML
12.5
50,0
62.5
Doubl-MLL
87.5
0
0
12.5
Cansal Forest
Consal Forest
37.5
37.5
Direct Survival CATE Methods
Direct- Survivll CATE Methody
Causal Survival Forests
75.0
87.5
100.0
Survival
50.0
25.0
62.5
SurvITE
0
50.0
25.0
50.0
87.5
SurvITE
12.5
25.0
0
12.5
12.5
Survival Meta-Leemeen
Survival Meta Learnrrs
T-Learner- Survival
12.5
25.0
12.5
25.0
75.0
L.camer-Survieee
37.5
37.5
37.5
25.0
25.0
37.5
Leammer Survival
0
62.5
75.0
0
62.5
100.0
S-Leareer Survival
50.0
100.0
100.0
25.0
75.0
75.0
Matching Survival
25.0
75.0
100.0
25.0
75.0
87.5
Matching Survival
100.0
100.0
12.5
75.0
75.0
Scenario Poisson, High Censoring
CATE RMSE
ATE Bias
Method Family
Top-1
Top-3 Top-5
Top-1 Top-3 Top-5
Outcome Imputation Methody
T-Learer
12.5
37.5
75.0
12.5
37.5
S-Learner
X-Leamer
12,5
37.5
75.0
0
37,5
50.0
DR-Leamer
0
25.0
62.5
12.5
Double-ML.
12.5
12.5
12.5
0
0
Causall Forest
0
0
0
0
0
Dllwet-Suviiod
Cansal Survisal Forests
12,5
37.5
37.5
0.
37,5
87.5
SurvITE
12.5
12.5
37.5
12.5
30.0
75.0
Survival Meto-lzamers
T-Leunce- Survival
12.5
25.0
37.5
50.0
75.0
87.5
S-Learner-S Survival
Survival
50.0
75.0
Matching Survival
37,5
50.0
100.0
25.0
37.5
75.0
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Published as a conference paper at ICLR 2026
F.3 RANKING OF CAUSAL METHODS FOR DIFFERENT CAUSAL CONFIGURATIONS
In Figure 7 we present the Borda ranking of causal model families across eight distinct causal con- figurations, each representing different combinations of assumptions related to treatment assignment (RCT vs. observational), ignorability, positivity, and censoring mechanisms. Within each configura- tion, the average rank of each method is computed over all survival scenarios, allowing us to isolate how assumption violations affect model performance independently of survival data characteristies. The colors of the lines connecting the methods to the horizontal axis represent the specific family of the method (e.g., outcome imputation based, direct-survival CATE, survival meta-learners).
Notably, outcome imputation approaches perform best in randomized settings with unbalanced treat- ment (e.g., RCT-5%, Figure (7). where Double-ML achieves the top rank of 1.80. However, their performance deteriorates as we move to settings with unmeasured confounding (Figure 7d), or more visibly with informative censoring (Figures 7 7g. 7hp. where Double-ML drops the bottom of the top half and X-Learner falls entirely into the lower- wwerrppeforming half of the rankings. In contrast, survival-specife methods of survival meta-learners such as -Leeaner-Suvvival, Matching-Suree and Causal Survival Forests (belonging to the direct-survival CATE family) consistently rise in the rankings under these conditions, particularly when multiple violations occur simultaneously (e.g., Figures
7g 7h), where S-Learner-Survvve and Batching-Survivee take the top two spots. This trend suggests that survival meta-learners and Causal Survival Forests, which directly model the survival process, offer increased robustness to violations of standard causal assumptions, especially in the presence of unmeasured confounding and informative censoring. Another finding is that Causal Survival Forests maintains strong performance across many configurations, consistently ranking in the top half-paariccularly in settings involving informative censoring (e.g.. Figures 7F 7g How- ever, when the positivity assumption is violated while censoring remains ignorable (Figure 7e), its performance declines substantially, dropping to rank of 6.60 in the bottom half of the ranking. This suggests limitations in modeling highly sparse regions of the covariate space with deterministic treatment assignment under certain censoring conditions.
2.45
Loaney
3.20
Cask. Fane:
Gasaat Foratt
(a) RCT: (50%), Ignorability; V. Positivity: V. Ign Jensoonni:: /f
(h) RCT: ((5%), Ignorability: V. Positivity: V. ggn-Censrring: /
10 11
Sieemer Servhee 2.40
8.32 Strtte
5-temmer-aa Sembeet 3.20
2.92
Sclamer
1:00 Geal brmm
Lamer wervit
servinal 3.3 Comal Wrmm
133 Lramer
2.43
(c) RCT. x. Igmorability: V. Positivity: V. Ignorable Censoring:
(d) RCT: X. Ignorability: X. Pusitivity; V. Ignorable Censoring: /
2
18 11
Reg Park
mouemmr Tilemmer
4.22
4.42
5.8.
3.58
Staamer
Cuas) 'orrtt
Surstaa- 2.06 aa
C.t0
2:c8
11.00
5.28
Candi Sertuat heot
3.M
(c) RCT: X, Ignorability: V. Positivity: X. Ignorable Consoring:
RCT: X. Ignorabiliyy v. Positivity: v. Ignorable Consoring: X
18
Reg bank
Kag bank
2.18
5.85. Liwweer
1.18
5.80
Patcking Sersial 2.66
1.5k.
T-saarear
3.60
7.88
cauai Forust
Canel Sevesal Feret 2.18
Dx 1.44
1,48.
Casa) Fores
6.4k. Laareer
(g) RCT: Ignorability: X. Pusitivity: Ignorable Censoring: X
(b) RCT: X. Ignorability: Posiiivity: X, Igmorable Censoring: X
Figure 7: Average ranking of each model for each causal configuration. Shaded regions indicate the standard error of the rank across datasets.
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Published as a conference paper at ICLR 2026
Table 17: Win-rate (%) of method families by Causal Configuration (randomized controlled trial settings). Values denote the percentage of times a method appears in the Top- Top-3, and Top-5 according to CATE RMSE and ATE Bias across the five survival scenarios for each configuration.
50: 50% % treatment rate
RCT-5: 5% treatment rate
Method Family
CATE RMSE
ATE Blas
Method Family
CATE RMSE
ATE Blas
Top-1 Top-3 Top-5
Top-1 Top-3 Top-5
Top-1
Top-3 Top-5
Top-1 Top-3 Top-5
Outcome Imputation Methods
Outcome Imputation Methods
T-Leamer
0
20.0
20.0
60.0
T-Learner
20.0
60.0
0
20.0
60.0
S.Leamer
20.0
S.Leamer
20.0
20.0
20.0
X-Learee
0
0
40.0
20.0
40.0
40.0
X-Learner
0
20.0
60.0
0
20.0
60.0
DR-Leurnrr
0
20.0
40.0
DR-Leamner
20.0
40.0
0
20.0
60.0
Double-ML.
20.0
60.0
80.0
Double-ML.
60.0
80.0
100.0
20.0
20.0
60.0
Causal Forest
20.0
40.0
40.0
0
20.0
Causal Forest
40.0
0
20.0
40.0
Shret-Survival Methoos
Direct-Survinn CATE Methods
Causal Survival Forests
20.0
40.0
40.0
20.0
60.0
60.0
Cansal Survival Forests 40.0
60.0
60.0
20.0
40.0
60.0
SurvITE
0
20.0
20.0
20.0
SurvITE
0
Survival Metu-Leamers
Survival Meta-Leurners
T-Leamer-Suree
20.0
40.0
60.0
20.0
40.0
80.0
T-Leamer-- Survivaal
20.0
20.0
0
0
S-Leamer- Survival
20.0
60.0
100.0
80.0
S-Learner- -Leeaner-Surivall
40.0
60.0
Matching-Suu Survivall
0
60.0
100.0
40.0
80.0
Matching- Survival
40.0
60.0
40.0
80.0
80.0
In addition to the configuration-agnosiic rankings in Figure 7 we report win-rates by causal con- figuration in Tables 17 and [8] For each configuration, we compute how often each method family appears in the Top-1, 3, and Top-5 positions for CATE RMSE and ATE Bias, aggregating over the five survival scenarios. This lets us separate the effect of causal assumptions (randomization, ig- norability, positivity, and censoring) from the influence of the survival time model. The randomized settings (RCT-50, RCT-5) serve as our classical baselines, while the observational settings introduce unmeasured confounding, positivity violations, and informative censoring in controlled way (Ta- ble
In the randomized configurations, CATE RMSE performance is split between outcome-imputation baselines and survival meta-learners, while ATE Bias results tend to favor survival-aware ap- proaches. Under RCT-50, Double-ML, Causal Forest, Causal Survival Forests, T-LearnerSuur Survival,, and S-Leamer-Survive.. all attain 20.0% Top-1 on CATE RMSE, but the strongest Top-k cov- erage comes from the survival meta-learners: S-LevvnerSSrrviall and Matching- SSrvivval reach 100.0% Top-5, and Matching-Survival achieves 60.0% Top-3. For ATE Bias in RCT-50, S-Learner- Survival is the most frequent Top-1 method (40.0%). with Causal Survival Forests and the sur- vival meta-learners (including Matching-Survival and T-Learner-Survine 60.0% 60.0% Top-3 for Causal Survival Forests and S-Learner-Survin Survival, L-Learner-Survival and Matching-Survival) When treatment assignment becomes sparse in RCT-5, Double-ML clearly leads on CATE RMSE (60.0% Top-1 and 100.0% Top-5), with Causal Survival Forests following (40.0% Top-1; 60.0% Top-3/Top-5). However, the ATE Bias rankings are largely driven by survival meta-learning: 3/Top-5, while --Lamner-Survival reaches 60.0% -0pop/5 Notably, SurvITE does not appear among the Top-k in RCT-5 and has only limited presence in RCT-50.
dominating Top-3/Top-5 80.0% Top-5 for T-Learner-
Survival).
Muiching-Surviver achieves 40.0% Top-1 and 80.0% Top-
The observational configurations further highlight how assumption violations shift performance to- ward survival-aware approaches, while revealing clear differences between direct-survival CATE and survival meta-learner families (Table 18). In OBS-CPS (no violations), CATE RMSE Top- is split across direct-survival CATE (Causal Survival Forests at 20.0%) and Survival Meta-Learners (S-Learner-Survival and Matching-Survival at 20.0% each), but the strongest Top-k coverage comes from the Survival Letaneeersser: S-Leevner-Surriial and Matching-Survin and 100.0% 5op-5. For ATE Bias in OBS-CPS. the lead is primarily driven by Survival Meta-Learners S--Lemerr-Survvaa at 40.0% Top-1; 1; Setichinn-Surriieee at 80.0% Top-3 and 100,0% Top-5; T- Learner-Survival at 80.0% Top-5), while the direct-survival CATE method Causal Survival Forests remains highly competitive in the upper ranks (60.0% Top-3 and 80.0% Top-5). Once unmea- sured confounding is introduced (OBS-UConf), outcome imputation methods remain competitive for CATE RMSE (e.g.. Double-ML at 20.0% Top-1 and 80.0% Top-5), but the top positions are shared with
reach 80.0% Top-3
CATE and Survival Miea-LLarner (Causal Survival Forests, SurvITE, and S- Searner-Survival each at 20.0% Top-1). 1). For ATE Bias under OBS-UConf, direct-survival CATE takes the clearest lead at the very top (Causal Survival Forests at 40.0% Top-1), while Survival Meta- Learners provide the strongest Top-3 presence Matching-SSrviver at 60.0% Top-3) and consis-
39

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Published as a conference paper at ICLR 2026
tent Top-5 coverage (e.g., 60.0% Top-5 for T-Leamer-Suuvival, S-Learner-Suriival. and Matching- Survival). Under positivity violations (OBS-NoPos), Outcome imputation dominates CATE RMSE Top-1 (Double-ML at 40.0% and also T-Learner and X-Learner at 20.0% each), whereas the Survival Meta-Learnnrss remain highly competitive --veeeer-Survi at 40.0% Top-1 and 60.0% Top-5; Sutching-Survival 80.0% Top-5). In contrast, ATE Bias in OBS-NoPOR is driven mainly by direct- survival CATE and Survival Meta-Learners: Causal Survival Forests reaches 80.0% Top-3/Top-5, while Matching-Survive attains 40.0% Top-1 coverage.
Informative censoring amplifies these differences and further separates the three method families. In InfC, CATE RMSE Top-1 led by the direct- survival CATE family via Causal Survival Forests (40.0%), while Survival Meta-Learners dominate and Matching-Survive at 80.0% Top-3 and 100.0% Top-5). For ATE Bias OBS-CPS-InfC, Sur- vival Meta-Leernnrrs are the clear winners in the upper ranks (S-Leerner-SSurvival at 100.0% Top- 3/Top-5; - at 40.0% Top-1 and 80.0% Top-5), with direct-survival CATE (Causal Survival Forests) still frequently among the top methods (80.0% Top-5). Under OBS-UConf-InfC, CATE RMSE Top-1 is shared by direct-survival CATE (Causal Survival Forests at 40.0%) and Sur- vival Meta-Learnet, (T-Leaneer-Survival at 40.0%), while Survival
coverage (S-Learner-Suriing
dominate Top- 3/Top-5 Su-Levaee-SSrvival at 100.0% Top-3/Top-5; Matching-Survive at 100.0% Top-5). For ATE Bias in OBS-UConf-InfC, the strongest Top-1 signal comes from Survival Meta-Learners (T- Learner-Survival at 40.0%), while direct-survival CATE shows the most dominant Top-5 presence (Causal Survival Forests 100.0% Top-5). Finally, in -SS-NoPos-InfC, Survival Meta-Learners clearly lead CATE RMSE MMatching-Survivee at 40.0% Top-1 and 100.0% Top-5; S S-Learner- Survival 100.0% Top-3/Top-5). whereas ATE Bias is again primarily driven by Survival Meta- Learners (T-Learner-Shee Survival at 60.0% Top-1 and 100.0% Top-5), with direct-survival CATE re- maining highly competitive in the upper ranks (Causal Survival Forests at 60.0% Top-3 and 80.0% Top-5). Overall, these patterns reinforce that as assumptions are progressively violated, Outcome imputation families can remain competitive for CATE RMSE some regimes (notably OBS-NoPos). but direct-survival CATE and Survival Meta- Learners dominate the upper ranks for ATE Bias, espe- cially under informative censoring and in settings with multiple simultancous violations.
40

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Published as a conference paper at ICLR 2026
Table 18: Win-rate (%) of method families by Causal Configuration (observational study settings).
Values denote the percentage of times method appears in the Top-1, Top-3, and Top-5 according to CATE RMSE and ATE Bias across the five survival scenarios for each configuration.
OBS-CPS
OBS-UConf
Method Family
CATE RMSE
ATE Bias
Method Family
CATE RMSE
ATE Bias
Top-1
Tup-3 Top-5
Top-1 Top-3 Top-5
Top-1
Top-3 Top-5
Top-1 Top-3
Top-5
Outrome Insputation Meshods
Outcome Imputation Merhods
T-Leamer
0
40.0
20.0
T-Learnr
0
20.0
S-1 Leamer
0
0
20.0
S-L.amerr
0
0
40.0
40.0
X-Learner
0
0
20.0
20.0
20.0
X-Leurerr
20,0
40.0
0
0
60.0
DR-Leamer
20.0
20.0
DR-I earner
20.0
20.0
40.0
40.0
Double-ML
20.0
40.0
80.0
0
0
Double-ML
20.0
60.0
80.0
0
0
20.0
Causal Forest
20.0
20.0
40.0
20.0
20.0
Cousal Forest
40.0
0
20.0
Direct Survival CATE Methods
Direct-Surviva CATE Methody
Causal Survival Forcats
20.0
40,0
60.0
60.0
80.0
Causal Survival Forests SurvITE
20.0
40.0
60.0
40.0
60.0
60.0
SurvITE
20.0
60.0
20.0
40.0
Survival Meta-Leammn Leamers
Survival Meta Leamers
T-I Leaeer- Survical
20.0
20.0
20.0
40.0
80.0
T-Leamer Survival
20.0
0
S-Learnr Survival
20.0
80.0
100.0
40.0
60.0
100.0
S-Learner PLeamme--Surviii Survival
20.0
60.0
80.0
0
40.0
60.0
Matching- Survival
Suavvinn-Survival
20.0
80.0
100.0
20.0
80.0
100.0
Matching- Survival
20.0
100.0
20.0
60.0
60.0
OBS-NoPos
OBS OBS-CPS-InCC
Method Family
CATE RMSE
ATE Blas
Method Family
CATE RMSE
ATE Blas
Top-1
3op-3 Top-5
Top-1 Top-3 Top-5
Top-1
Top-3 Top-5
Top-1 Top-3 Top-5
Outcome Imputation Methods
Outcome Imputation Methods
T-Leamer
20.0
40.0
60.0
20.0
40.0
T-Leaner
0
0
S-Learnr
0
40.0
60.0
S-Learner
0
0
0
X-I Leuner
20.0
40.0
80.0
20.0
60.0
X-Leamer
0
0
0
40.0
Leamnr
20.0
20.0
40.0
DR-Leamer
20.0
20.0
Douhle-MI.
40.0
60.0
60.0
20.0
20.0
Double-ML
0
40.0
60.0
0
0
0
Causal Forest
20.0
40.0
20.0
20.0
20.0
Causal Forest
20.0
60.0
0
0
40.0
Direct-Survival CATE Methods
Direct Survival CATE Methods
Cansal Survival Forests
0
40.0
40.0
20.0
80.0
80.0
Cansal Survival Forests SurvITE
40.0
60.0
60.0
20.0
40.0
80.0
SurvITE
20.0
40.0
20.0
20.0
Survival Mett--Laamers
Survival Mete-Leameess
T-Leamer Survival
20.0
20.0
20.0
20.0
20.0
T-1 Lllmmer--Sme Survesll
20.0
20.0
80.0
40.0
60.0
80.0
S-Learnet-Surviee
40.0
40.0
60.0
20.0
80.0
S-Leande S-Learner-Survee
20.0
80.0
100.0
0
100.0
100.0
Matching Survival
0
20.0
80.0
40.0
40.0
40.0
Matching-Suree
20.0
80.0
100.0
0
60.0
80.0
OBS-UConf-InfF
-BS-NoPosIInfC
CATE RMSE
ATE Bias
CATE RMSE
ATE Bias
Method Fumily
Method Family
Top-1 Top-3 Top-5
Top-1 Top-3 Top-5
Top-1
Top.3 Top:5
Top-1 Top-3 Top-5
Outcome Imputation Methods
Outcome Imputation Meshods
T-Leamer
0
20.0
20.0
T-Leamer
20.0
40.0
20.0
20.0
20.0
S-Leamnr
0
20.0
20.0
20.0
S-Leamer
0
0
0
20.0
X-I Lurner
0
0
0
0
20.0
20.0
K-Leamer
0
20.0
40.0
20.0
20.0
20.0
DR-Learner
0
20.0
DR-Learer
40.0
0
Double-MI.
40.0
60.0
20.0
Doable MI.
40.0
60.0
0
0
20.0
Causal Forest
0
0
60.0
20.0
Causal Forest
20.0
0
0
40.0
Direct-Survival CATE Methods
Direct-Sarvivol CATE Methody
Causal Survival Forests
40.0
40.0
60.0
20.0
100.0
Causal Survival Forests 20,0
40.0
40.0
20.0
60.0
80.0
SurvITE
0
40.0
SurvITE
20.0
40.0
Survival Meta-Leamers
Survival Meto-Leamers
T-Leamer Survival
40.0
80.0
80.0
40.0
60.0
80,0
T-Leamer Survival
20.0
40.0
40.0
60.0
80.0
100.0
S-Leamer- Survivll
100.0
100.0
80.0
80.0
S-I. Leaanee-- Survival
100.0
100.0
0
40.0
60.0
Matching Survival
20.0
40.0
100.0
20.0
60.0
80.0
Matching Survival
40.0
60.0
100.0
0
40.0
60.0
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Published as a conference paper at ICLR 2026
F.4 FIGURE RESULTS CATE RMSE
This section presents the complete CATE RMSE results for each family of causal inference meth- ods across various survival analysis scenarios. For each scenario, display performance under 8 distinct causal configurations, each varying in terms of treatment assignment (RCT vs. observa- tional), ignorability, positivity, and censoring assumptions. These results highlight the robustness and sensitivity of different methods under varying degrees of assumption violations.
For each survival scenario and causal configuration, selected the best hyperparameter setting and base model configuration for each causal method family based on validation set performance. The RMSE values shown in the figures reflect the performance of these selected models on the test set. The box plots are from the 10 independent experimental repeats account for random seed variability.
Oecral Drigar
Sonere Serviall
Servial
S-Uagrae
Derral
Soeere Sorvial
Sortial
(a) RCT: (50%) Ignorability; v. Positivity: d. Iga Censoring:
(b) RCT. ((5%), Ignorability v. Positivity: v. Ign Censoring:
Cestal Somus
Sorety eeeiaa
Fiser miiil
V-lereer
Custal
Soretyy Breial
Fiserne meiiaa
forus
(c) RCT. X. Ignorability: V. Positivity: d. Ignorable Censoring:
(d) RCT: X. Ignorability: X. Positivity: V. Ignorable Censuring:
Dersal Torst
Filpor Sertial Derite Servical
S-
Sereet Sereoa
Servpe Serviaa
Fimpon Servial
(e) RCT: x. Ignerability: V. Positivity: X. Ignorable Censoring: /
(1 RCT: x. Iguorability: /. Positivity: V. Ignerable Censoring: X
Te. Sebewar
Senviel
Getra forset
fombyy Bercaal
Seriill
(g) RCT: X. Ignorability: X. Positivity: V. Ignorable Censuring: X
(b) RCT: X. Ignerability: /, Positivity: X. Ignorable Censaring: X
Figure 8: CATE RMSE across different experiments in Scenario A.
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Published as a conference paper at ICLR 2026
Hearter
Serdiel hardea
Heurner
Firaaay Serviel Porzial
(o) RCT: (80%), Ignorability v. Positivity: v, Ign- gen-oonnri
(b) RCT. /184), Ignorability. v. Posiiviity v. Ign-Censoring:
Edtereet
Arrtng horanal
Ectweert
Serdiet
Sereiee
(c) RCT x. Ignorabilitt:: S Posiiviy:: d. Ignorable Censoring:
(d) RCT: x, Ignomaiiityy X. Positivity; S, Ignorable Censoring:
Smatr
Seveial
Surweel
Smate Rt
Nevecal
Sereial
(e) RCT: x, Ignoraiiiity v, Positivity: X. Ignorable Censaring:
(i) RCT x, Ignorability: /. Positivity: V, Ignorable Censuring: X
Laatte
Smart Salree
Survine Serat horinal
Ecewtet
Smart Satroe
Serviel Poreial
( RCT, x. Ignorability: X, Positivity: V, Ignorable Censoring; X
(h) RCT: x. Ignorability: v, Positivity: X, Ignorable Consoring: X
Figure 9: CATE RMSE across different experiments in Scenario B.
S-
Logneer
Corral Tearr
Bon
Serviall
S-
E-
Lognee
Gertal Thon
T Sermral bon Serviaal
(a) RCT: (50%) Igmorability; v. Positivity: /. Ign Censoring:
(b) RCT: ((5%), Ignorability v. Positivity: v. Ign Censoring:
Talerer
1-terar
Viterner
Podia
Censal farinn
5-ierwrr
Cunsal Satvrs
Fieno meiil Fweety aeviill
Perit
(c) RCT. X, Ignorability: V. Positivity:: /. Ignorable Censoring:
(d) RCT: X, Ignorability: X. Positivity: V. Ignorable Censoring:
L-ternar
Lenewer
Soaka
Coarsl Tertie
Edrere veae Sweete Aervent
I-trere
Lenner
Caarcl Torte
Edrare sereee Swertze Aervaet
aervial
(e) RCT: x, Ignorability: V. Positivity: X. Ignorable Censoring:
( RCT x, Ignorability: v. Positivity: V. Ignorable Censoring: X
beeatt Se pervinl
Sor
La
Sg. Lemner
Creat
beratt Ser serviee
(g) RCT: X. Ignerability: X. Positivity: V. Ignorable Ccnsoring: X
(b) RCT: X. Ignorability: v. Positivity: X. Ignerable Censoring: X
Figure 10: CATE RMSE across different experiments in Scenario C.
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L-Lerna
Letneer
Soab d
Cartal Pares
feeite serviet
Ctarr viee
Lesnner
Paret
Serette serviet
Ciarre viae
(o) RCT: ((0%)) Ignorability: v. Positivity: v, Ign- censornnti
(b) RCT. /184), Ignorability: v. Posiiviiy: d. Ign-Censoring:
Lewner
Phrign
Sweete Servical
Frlgpra Servical
Lesnerr
Serete Servical
Pilapre Servical
(c) RCT: x. Ignocability: V. Posstivity: v. Ignorable Censoring: /
(d) RCT. x. Ignorability X. Positivity v. Ignorable Causering: d
Leunerr
Taakle
Serrit Sorvlast
L-gare wlast
Laarmen
Lewner
Seritt Serviest
wlett
(6) RCT: x. Ignorabiityy V. Positivity: X. Ignorable Consoring:
(1 RCT. x. Iguorability: V. Positivity: V. Ignorable Consoring: X
L-Laprar
Lesnect
Toable R
Soeite Sar varl
viae way
T-iarmer L-
Lew
Corral Peate
Seeiite Sor serviel
e RCT, x. Ignorability: X, Positivity: V, Ignorable Censoring; X
(b) RCT, x. Ignorability: v, Positivity: X, Ignorable Consoring: X
Figure 11: CATE RMSE across different experiments in Scenario D.
Leteman
Soala
rtal Fendty Servial
rtal
S-Lerne
Letenes
Fimer Aietel Feestyy Servill
(a) RCT: ((00)) Ignombility: V, Positivity: /, Ign- Censerinn:::
(h) RCT: ((5%), Ignombility: V, Positivity: d. Agn--gnnnne Son-Censoring:
S-iagres
Swerte Survial
Fimgoe Serciel
Lew
Swerty Survice!
F-lgpr Servicel
fwret
(e) RCT. x. Iggorrablitty V. Positivity: V. Ignorable Consoring: V/
(di RCT. x. Iguorability: X. Positivity: v. Agnorable Cousoring:
S-terrat
Lenewar
Soakle
Edtae reat Swettry serviet
L-trorad
Lennas
Swerty serviet
S-rean servial
(e) RCT: x, Ignorability: V. Positivity: X. Ignorable Censoring:
( RCT X. Ignorability: /. Positivity: V, Ignorable Censoring: X
Latneer
Trlegres
S-lagrae
Latener
(g) RCT: X. Ignorability: X. Positivity: V. Ignorable Ccusoring: X
(b) RCT: X. Ignorabiiity: V. Possiiivtyy: X. Ignerable Censoring: X
Figure 12: CATE RMSE across different experiments in Scenario E.
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F.5 FIGURE RESULTS ATE BIAS
This section presents the ATE bias results for each family of causal inference methods across various survival scenarios. As with the CATE RMSE results in Appendix F.4 display performance under distinct causal configurations per scenario, each varying in treatment assignment (RCT vs. observational), ignorability, positivity, and censoring assumptions.
For each survival scenario and causal configuration, the model shown corresponds to the best hy- perparameter setting and base model configuration selected based on CATE RMSE performance on the validation set ATE bias was not used for model selection for consistent results with other sections. The reported ATE bias values are computed on the test set and defined as the difference between the predicted ATE from the test population and the Irue ATE in the full population.
Each box plot represents results from 10 independent experimental repeats account for random seed variability. For meta-learners and double machine learning models, which by design can pro- vide 95% confidence intervals for ATE estimates, we also include these intervals in the plots- adjusted accordingly to center around the ATE bias. These confidence intervals are obtained via 100 bootstrap samples and are notably wider than the variability observed across the 10 experimental repeats. The zero bias line is shown dashed reference line.
Fearter
Dora Foree.
Seret fermeel
Doad Foreet
(n) /(006), Ignorability: Pocitivity: ce-CCesoring:
/655), Ignombilityy Pocitivity: Agn.ggennnnnenn Censoring:
Fieereer
A-cerror
farcet Porae
Sorty Surwael
Fieererr
F-cewrrr
borte Soreval
(c) X. Iggnorability:: Positivity: Ignorable Censoring:
Ignorability: Positivity:
Ignorable Censoring:
Servial
Omall
bering Perees
Igmorabiliy: Positivity: Ignorable Censoring:
Ignorrbblity:: Positivity: Ignorable Censoring:
Cearter
Chass
Sersto Purian
Heurter
Flewterr
Deaa Fores.
Ignorability: X. Positivity: V, Ignorable Censoring:
Ignorability: Positivity: X. Ignorable Censoring:
Figure 13: ATE Bias across different experiments in Scenario A.
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Eiaereee
Laurre
Leeroer
Fuanre vine!
Faree
vine
Flreet
(a) RCT: (50%), Ignorability: Positivity: Igo- Censoring:
(b) RCT: /(5%), Ignorability: v. Positivity: v. Igo- Ce-CCenoring:
Sttermer
Scherroee
Darial Rorer
Berrg Sertval
Tilarra Serwiel
Luarun
Shanal Rorer
Servial
(c) RCT. x. Ignorability: V. Positivity: d. Igmorable Censoring:
(d) RCT: x, Ignorability: X. Positivity; v. Ignorable Consoring:
Lanrter
Guarga Terlet
Lauvoer
Deunge Teceer
Survnn feratrel
(c) RCT: x. Ignorability: V. Positivity: X. Ignorable Consoring:
(1) RCT. x. Iguorability: v. Positivity: V. Ignorable Censoring: X
Scatrep
Guatu Reran
Swrsng Semipal
Jarroe
Seato Reler
Leanrng vinel Sursnn Servyel
viel
( RCT) Ignorability: X. Positivity V. Ignocable Censoring:
RCT. Ignorability: Positivity: X. Ignorable Censoring:
Figure 14: ATE Bias across different experiments in Scenario B.
Aicsmer
Gepua Perist
Causal
Serving Perdeay
Deieeene A.cammr
boakl
Cansal Cepat Perist
RCT: (500%) Ignorability: V. Positivity: up--Censoiing:
RCT: ((5%), Ignorability: V, Positivity: agn-Censoring: /
Astereer
Gonkle
Cupist Periin
Suntyy bertee wirl
Sonkin
Chars Penil
Scntty Weriial
(6) RCT. X. Ignorability: V. Positivity: V. Ignorabli Consoring:
(d) RCT. x, Iggoorability: X. Positivity: Agnorable Consoring:
Aicurwer
Senare Aomriee
Kicurner
to
(e) RCT, x, Ignorability: V. Positivity: X. Ignorable Censoring:
( RCT: x, Ignorability: v. Positivity: V. Ignorable Censoring: X
Assurret Lspperee
Canual Tergt
Suntry furverie aere
Acserter
Canual Porul
Suntry burrect Sere
tervin
RCT: X. Ignorability: X. Positivity: V. Ignorable Censoring: x
RCT: Ignorability: /. Positivity: X. Ignorable Consoring: X
Figure 15: ATE Bias across different experiments in Scenario C.
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Published as a conference paper at ICLR 2026
Leureer
Swrsng Perpeed
Lerrer
Surstt Perpiel
Ferer
vieel
viee
(0) RCT: /50%) Ignorability: Positivity: d Igo- Censoring:
(b) RCT: /(5%), Ignorability: Positivity: v. Igo- CepConnori
Tumes
porviel
Leurnee
Tumms
Servil rial ferviel
(c) RCT. x. Ignorabilitty S, Positivity: d. Ignorable Censoring:
(d) RCT: x, Ignorability: X. Positivity; v, Ignorable Censoring:
Ecsurmet
Smalie
Servile Surarg Poriies
Hommm
Ecaumen
Surety Poreiel
Servict
servell
(c) RCT: x. Ignerabiity: V. Positivity: X. Ignorable Consoring:
(1) RCT. x. Iguorability: v. Positivity: V. Ignorable Consoring: X
Dertet
Swrrg Servivll
E-ceurea
E-berroe
Surete Seviial
Suaps
(g) RCT: X. Ignorability: X, Positivity: V. Ignerable Censoring: X
(b) RCT: x. Ignerability: /. Positivity: X. Ignerable Censoring: X
Figure 16: ATE Bias across different experiments in Scenario D.
Omcal Dorss Pimit
RCT: (50%), Ignorability: Positivity; Igo Censoring:
Ignorability:
Positivity: Ign Censoring:
Suntreer
Gurss
Roable Ca
Durrs
(c) RCT. X. Ignorability: V. Positivity:: /. Ignorable Censoring:
(d) RCT: X. Iggnrraility: X. Positivity: V. Ignorable Censoring:
Canral
Ooual
Suntre buriiel
Carral Prices
Suntre beriial
Fawe Hertial
(e) RCT: X. Ignerability: V. Positivity: X. Ignorable Censoring: /f
( RCT: X. Ignorability: /. Positivity: V. Ignerable Censoring: X
Leamne
Ronble Deisorar
Permi Finet
Cecat
Laaneer
A.samer
Poakle Deisoner
Cecat Parts Firstt
RCT: Ignorability: X. Positivity: /. Ignorable Censaring: X
RCT: Ignorability: /. Positivity: X. Ignorable Censaring: X
Figure 17: ATE Bias across different experiments in Scenario
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F.6 EVALUATION ON AUXILIARY IMPUTATION AND BASE LEARNERS
In this section, we report the performance of auxiliary imputation and base regression or survival learners on the test sets.
F.6.1 IMPUTATION EVALUATION
Table 19 reports the MAE of the three imputation methods (Pseudo-obs, Margin, IPCW-T) across cight causal configurations and five censoring scenarios on the test sets. Recall that Scenarios A and B have low censoring (<30%), Scenario C medium (30-70%), and Scenarios D and E high (>70%), except is switched in -InfC causal configurations, as mentioned Appendix [ We can tell that the imputation method Pseudo-obs is only competitive under minimal censoring and suffers from high variability. Margin imputation provides the best balance of accuracy and robustness, especially as censoring intensifies. IPCW-T imputation improves over Pseudo-obs in most cases, but generally underperforms relative to Margin in medium- and high-censor contexts.
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Table 19: Evaluation on imputation methods across different survival scenarios and causal config- urations. MAE between the imputed and true event times on testing set is reported as mean + std. over 10 experimental repeats. "Total Win" row counts the number of survival configurations x random split combinations (8 x 10 = 80) in which each method achieved the lowest MAE, and is calculated within each scenario. The same rule applies to all the tables below in Appendix F.
Survival Causal Scenario Configuration
Imputation Method
Pseudo-obs
Margin
IPCW-T
RCT-50
0,437-10.021
0.44610.025
0.470:10.027
RCT-5
0.378++0.025
0.387+0.029 0.405+0.003
OBS-CPS
0.448=:0.014
0.459=0.014 0.481=0.015
0BS-UConf
0.423=:0.026
0.520=0.022
0.455=00003
OBS-NoPos
0.411:10.023
0.420:10.023 0.442:10.025
0BS-CPS-InfC
0.390=10.020
0.3741100014 0.388=0.014
OBS-UConf-InfC
0.369:+0.029
0.482:+0.027
0.062
0BS 0BS-NoPos-Infe 0.347:10.023
0.336:10.024
0.34910.026
Total Win
51
21
8
RCT-50
0.0611:0.05
0.05=00003
0.048:10.006
RCT-5
0.02710.003 0.022.10.00%
0.021
OBS-CPS
0.052+00000
0.042+0.004
0.040
OBS-UConf
0.058110.004
0.152+0.007
0.046
OBS-NoPos
0.068=10.008 0.057=0.005
0.055
0BS-CPS-InfC
0.039.10.005
0.037110.005 0.03611.0005
OBS-UConf-InfC
0.040.10.004
0.140.1..055
0.00811.0044
OBS-NoPos-InfC 0.048+00000
0.046+0.008
0.045+0.008
Total Win
77
RCT-50
0.837.10.008 0.83810.000 008
0.841
RCT-5
0.803++0.013 0.804+0.013
0.793+
OBS-CPS
0.829::0.014 0.830+0.004
0.828
0BS-UConf
0.835::0.026 2.701=00.03
0.837+0.0227
OBS-NoPos
0.845:10.014 0.84510.015
0.85510.012
0BS-CPS-InfC
2.786110.079
2.090-10.046 2.85
OBS-UConf-InfC
2.753
2.443+0.002
2.852+0.058
0BS-NoPos- 2.904:10.061
2.19710.004
3.006110.034
Total Win
35
22
RCT-50
3.303:10.333 2.241:10.065
2.624
RCT-5
2.89711..257 1.845:0.059 2.192.10.059
OBS-CPS
3.191+0.449
2.109-0.002 2.20+
0BS-UConf
3.463+0.706
2,361++0,19
2.610+0.073
0BS-NoPos
3.536:10.435
2.40411.004 2.853+0.072
0BS- (8S-CPS-InfC
1.395:10.067
1.28910.064
1.366.10.06 068
OBS-UConf-InFC
1.524110.069
1.73711.054 1.561
OBS-NoPos-InfC 1.689+0.074
1.595+0.069
1.698+0.073
Total Win
68
RCT-50
2.672.10.348 1.59510.019
2.033:1.002
RCT-5
2.238+002218
1.463
1.823+0.023
OBS-CPS
2.446:1.0.62
1.577:10.022
0.992
OBS-UConf
2.531++0.111
2.651+0.054
2.031+0.031
OBS-NoPos
2.669++0.288
1.639+0.021
2.102+0.035
0BS-CPS-InfC
3.324:10.136
2.483-10.05
3.491
08S-UConf-
3,346:t0.147
2.686-10.01
0.006
08S COS-NoPos-INee InfC
3.373:10.101
2.541
10.038
3.648
Total Win
70
10
49

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Published as a conference paper at ICLR 2026
F.6.2 BASE REGRESSION LEARNER EVALUATION
See Table 21 23 for MAE of prediction by the base regression learners for S-, T-, X-, DR- Learners. The MAE Is calculated by comparing a base learner's predicted event times and imputed event times by the imputation method (the latter used as the "ground truth" for the base regression leamerr). Since there are three imputation methods used, we first take the average of MAE across three different imputation methods within each random split, then report the mean and standard deviation of the average MAF across 10 experimental repeats with different random splits.
See Table 24 for the AUC on the evaluation of the predicted propensity score of DR-Leamers.
Table 20: S-Learner MAE
Survival Causal Scenario Configuration
Base Regression Model
Lasso Reg.
Random Forest
XGBoost
RCT-50
0.661=0.012
0.655=0.014
0.671=0.013
RCT-5
0.645=0.011
0.649=0.012
0.667=0.014
OBS-CPS
0.653+0.011
0.646
0.662+0.012
OBS-UConf
0.604=0.009
0.608=0.009
0.620=0.007
08S-NoPos
0.657=0.010
0.654:0.011
0.671=0.013
OBS-CPS-InFC
0.727+0.018
0.730+0.021
0.752+0.023
0BS-UConf-InfC
0.675=0.019
0.693=0.023
0.713=0.023
OBS-NoPos-
0.724=:00144
0.732=0.018
0.755++0.02
Total Win
44
36
RCT-50
0.33-10008
0.3151 0.011
0.33410.015
RCT-5
0.278+0.0066
0.277+0.006
0.292+0.008
OBS-CPS
0.315:10.011
0.012
0.32410.019
OBS-UConf
0.354110007
0.341
0.35910.011
OBS-NoPos
0.345110009
0.32310.011
0.341=0.011
OBS-CPS-InfF
0.301++0.007
0.294 0.006
0.309
Inf-
0.34_10.004
0.328
0.005
0.34710.006
OBS-NoPos-Infa
0.337:100005
0.31910.006
0.33710.007
Total Win
3
77
RCT-50
1.430-1.0222
1.59310.025
1.73810.024
RCT-5
1.403:0.0199
1.532+0.018
1.877=0.027
OBS-CPS
1.409=0.0211
1.555=0.025
1.706=0.028
OBS-UConf
1.419-10.023
1.56310.026
1.721
0BS-NoPos
1.53:10.019
1.61240.024
1.755=0.022
0BS-CPS-InfE
0.931=0.027
1.011
1.148=0.045
Inf
0.895:10.033
0.966110.04
10.059
OBS-NoPos-InfO
0.916:10.057
1.00340.067
1.12310.086
Total Win
80
0
RCT-59
0,941
0.002+0.202
1.82:+0.200
RCT-5
1.01610.121
1.09510.123
1.21010.248
OBS-CPS
1.031+0.2588
1.882+0.264
1.188+0.345
OBS-UConf
0.985
1.015+0.300
0.383
OBS-NoPas
0.967.10.238
1.03-10.249
1.10710.299
OBS-CPS-InfE
1.146=0.030
1.148=00004
1.209
OBS-UConf-InfE
1.179+0.0024
1.172+0.031
1.234+0.032
OBS-NoPos-Inf3
1..66
1.169 0.026
1.230 100028
Total Win
48
29
RCT-59
0.186
1.90610.207
1..24400.47
RCT-5
1.60410.125
1.731110.13
1.901:10.17
OBS-CPS
1.651-00161
1.79910,201
1.990=0.243
OBS-UConf
1.630-10.127
1.759
1.974.1.212
OBS-NoPos
1.69910.139
1.856110.162
2.02920.202
0BS-CPS-InfC
0.917-10.899
1.012-0.113
1.140=0.141
OBS-UConf-InfC
0.968=:0.130
1.07440.164
1.222-0.237
OBS-NoPos-InfC
0.02000.000
1.01210.063
1.130
Total Win
80
0
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Published as a conference paper at ICLR 2026
Table 21: T-Learner MAE
Survival Causal
Base Regression Model (Treated)
Base Regression Model (Control)
Scenario Configuration
Lasso Reg.
Random Forest
XGBoost
Lasso Reg. Random Forest
XGBoost
RCT-50
0.669=0.012
0.652=0.013
0.680=000055
0.652=0.019
0.657=0.019
0.685=000019
RCT-5
0.65611..04
0.64110.009
0.677:10.050
0.644-0.011
0.650:1.012
0,668110.014
0BS-CPS
0.711+0.012
0.697+0.012
0.727+0.012
0.595+0.0014
0.621+000118
0BS-UConf 0.640=0.0099
0.641=0.007
0.668:+0.000
0.588-0.012
0.566=20.013
0.593=0.015
A
0BS-NoPos
0..011
0.56110.013
0,587110.016
0.733 4.733_0.015
0.747100016
0.776.10.016
08S-CPS-InfC 0.799=00.020
0.797=0.022
0.838+00023
0.646=0.023
0.699+00.029 0.664+0.025
0BS-UConf-InfC
0.723=0.023
0.740=0.031
0.778:10:030
0.614=0.019
0.633-10.023
0.668+1.0225
065-NoPos-Inff 1.018
0..0910.011
0.642.10.020
0.824:0.022
0.855:10.021
0.895
Total Win
52
77
3
RCT-50
0.375::0.02
0.014
0.374:1.016
0.279-
0.007
0.281 000008
0.303-10.006
RCT-5
0.393=0.051
0.383=0.047
0.404+0.043
0.271=0.005
0.273=#0005
0.287=+.0006
0BS-CPS
0.326110004
0.302-10014
0,322:10.016
0.011
0.313:10012
0.338.10.015
0BS-UConf
0.375+0.008
0.348+0.009
0.371+00011
0.327-0.008
0.334+0.007
0.363+00011
8
0BS-NoPos
0.425=0.004
0.411=0.015
0.442:400017
0,231=0.007
0,235
0.253++0.008
065-CPS-InfC 0.31110.007
0.29210.006
0.311
0.201
0.297.100010
0.322.10.011
IBS-UConf-InfC 0.365=0.004
0.344=0.007
0.370+00000
0.310=0.007
0.313+00007
0.337+0.008
OBS-NoPos-InfC 0.41520.009
0.406=0.009
0.438:0.001
0.228=0.005
0.233=00006
0.2491100006
Total Win
12
RCT-50
1.534:1.037
1.653-1.041
1.89910.048
1.387=0.029
1.542:10.020
1.747.10.02 027
RCT-5
1.643:0.099
1.751
1.935
1.393=0.020
0.52
0..02
0BS-CPS
1.484=0.026
1.599+0.031
1.797+0.036
1.379=0.030
1.529=0.0099
1.726+00033
0B5-UConf
1.493-1.037
1.61710.034
1.80910.028
0.069
1.52810.021
1.740110.227
0BS-NoPos
1.568+0.044
1666++0.038
1.860+0.037
0,037
0.0677
1.763+0.035
OBS-CPS-InfC
0.909=0.047
1.002:+00522
1.14440.050
0,953=0.042
1.040=0.048
1.198+0.060
0BS-UConf-InfC
0.876.10.039
1.08810.070 0..012
1.166 1.0001
OBS-NoPos-InfC 0.902
1.009
1. 1.149+0.088
1.928-0.007
1.016+00.087
1.122+0.088
Total Win
80
RCT-50
0.302-0.083
0.316+0.093
0.339=0.11
1.546=0.304
1.691
1.767+0.429
RCT-5
0.284=100444
0.29610.049
0.312:10052
1.051=0.127
1.11810.129
1.285-10.304
065-CPS
0.347:0.084
0.36610.087
0.38411.094
16611=0.416
1.758
1.924410.594
0BS-UConf
0.328=00134
0.343+0.130
0.362+0.118
1.691=0.564
1.797=0.529
1.09++0.705
OBS-NoPos
0.304.10.105
0.342-10.117
0.366 129
1.571=0.382
1.69910.392
1.93910.612
06S-CPS-Inf
1.138+00.029
1.997+0.027
1.771+0.028
1.147-0.041
1.201+0.051
1.300+0.056
OBS-UConf-InfC
1.206=0.029
1.166=0.043
1.240=+00044
1.146=0.023
1.197=0.028
1.298=0.0029
OBS-NoPos-InfC
1.21610.030
1.198 1.19810.033 10.035
1.297.0.006
1.100
10.000
1. 1..03
1.202
Total Win
45
35
0
66
10
4
RCT-50
1.784.10.30
1.955
2.22.10.100
1.720 10115
1. 1.89911.188
2.108.10.
RCT-5
1.607=00.244
1.859-10.436
1.969+0..335
1.605=0.121
1.733++0111
1.894+0.114 147
OBS-CPS
1.670-1.194
1.852200261
2.092-1.312
1.637=0.141
1.785=0.158
1.99310.200
OBS-UConf 1.650:0..15
1.809:0.167
2.033.10.339
1.763-10.144
1.982
E
0BS-NoPos 1.740=0.161
1.007=0.200
2.198-+0.338
1.663=0.140
1.804=0.144
2.027+00167
0BS-CPS-InfC 0.111
1.007-0.123
1.146.10.14
0.925
1.015-10.09
1.158.10.1 104
OBS-UConf-InFE
0.953++0.10 0017
1.049+0.11 118
1.22 +0 146
0.987
- 0.159
1.103+0.222
1.27 +0.228
OBS-NoPos-InfC
0.949-0.085
1.04--0.095
1.2112
0.046
1.000-1.0044
1.136:0.0064
Total Win
80
0
80
0
0
51

---

Published as a conference paper at ICLR 2026
Table 22: X-Learner MAE
Survival Causal
Base Regression Model (Treated)
Base Regression Model (Control)
Scenario Configuration
Lasso Reg.
Random Forest
XGBoost
Lasso Reg.
Random Forest
XGBoost
RCT-50
0.620=0.011
0.622=0.013
0.631
0.624=0.019
0.624=0.019
0.631=0.0118
RCT-5
0.613
0.62410.056
0.63410.050
0.618-0.012
0.617
0.623-10.010
0BS-CPS
0.664
0.667+0.010
0.675+0.012
0.561-0.00
0.562+0.014
0.568+0.011
0BS-UConf 0.608=0.008
0.610=0.008
0.616::0.008
0.530=0.012
0.531=0.012
0.538:0.012
A
0BS-NoPos 0.532.0.013
0,533
0.539.10.015
0.711
0.712.10.014
0.718.00015
08S-CPS-InfC
0.747=00018
0.751-0.018
0.763+0.019
0.616-0.021
0.616+0.022
0.623++0.022
08S-UConf-InfC
0.689=0.024
0.691=0.023
0.698:10.024
0.583=0.019
0.585=10.020
0.592:10.019
065-NoPos-Infe 0.016
0.570:0.011
0.578110.018
0.000:0.021
0.802:10.021
0.80910.0000
Total Win
33
RCT-50
0.339:1.012
0.328 0.012
0.333-10.012
0.265 0.007
0.201
0.264:10.007
RCT-5
0.365=0.045
0.364=0.051
0.368+00046
0.256=0.005
0.255=+.000 0.253++00044
0BS-CPS
0.296110.01
0.283-0.013
0,287100013
0.290-0.010
0.290-10.012
0.291110.01
0BS-UConf
0.339+0.009
0.327+0.008
0.331+0.008
0.312-0.008
0.309+00006
0.311+000088
8
0BS-NoPos
0.396=0.013
0.387=0.014
0.393+4.011
0.221=0.006
0.217=0.007
0.219+000077
065-CPS-InfC 0.28310.006
0.275 0.272.1.007
0.277
0.275110000
0.278.10.009
OBS-UConf-InfC
0.332+0.005
0.021+0.006
0.326+0.006
0.295=0.008
0.291=000007
0.293++0007
OBS-NoPos-InfC 0.38820.008
0.379=0.008
0.38640.008
0.219=0.005
0.215
0.216:10.005
Total Win
70
RCT-50
1.54220.041
1.54710.032
1.333
1.17=-0025
1.222:1.003
0.40311.0026
RCT-5
1.65110.092
1.662:10.09
1.640:1..087
1.11=000188
1.114:0.019
0.009
0BS-CPS
1.492+0.031
1.492+0.031
1.461=0.026
1.409=0.052
1413=400300
1.394400003
0B5-UConf
1.50910.038
1.51010.039
1.497.10.022
1.396=0.001
1.402-1.014
1.385110.016
0BS-NoPos
1.562+00.02
1.563++0.038
1.561+0.038
1.445-0.033
1.449+0.035
1.337
OBS-CPS-InfC
0.909=0.047
0.915=00048
0.909=0.046
0.952=0.043
0.959=0.041
0.954
0BS-UConf-InfC
0.876110.039
0..092
0.87511.039
0.9215
0.91910.047
OBS-NoPos-InfC 0.902=0.058
0.909+0.061
0.904+00000
11928-0.077
0.935+00.081
0.928+00004
Total Win
42
7
56
RCT-50
0.306-00088
0.300=0.089
0.292++.0083
1.333=0.342
1.613+0.503
0.506-+0.302
RCT-5
0.28310.046
0.280=0.042
0.277=1.0047
1.124=0.125
1.055-0.128
1.033:10.150
065-CPS
0.355::0.085
0.343:10.080
0.334:10.081
1.549
1..56
0.416
0BS-UConf 0.336=0.137
0.324
0.322++0.123
1.772=0.571
1.737=00498
1.517
D
OBS-NoPos
0.336110.10
0.322-10.10
0.31911.104
1.888
1.60710.383
1.540
(BS-CPS-Infe 1.067+0.026
1.043+0.025
1049++00026
1.133-0.041
1.137+0.043
1.136+0.004
OBS-UConf-InfC
1.116=0.032
1.098=0.033
1.103+0.027
1.135=0.021
1.138+0.021
1.136=0,002
OBS-NoPos-InfC 1.160.1.029
L.33
1.140.10.029
1.085
0.032
1.088
1.087.10.031
Total Win
36
40
17
21
42
RCT-50
1.771
10.237
1.772.10.20
1.734.10.15
1.748
1.721
RCT-5
1.607=0.240
1.731+0..66
1.608+0.245
1.602=0.
0.606+00.121
1.597+0.111
OBS-CPS
1.668=0.199
1.722-10.244
1.66810.197
1.638=0.138
1.652=0.139
1.633
OBS-UConf 1.661100.177
1.659:10.151
0.126:1..12
1.613
1.632-10.132
1.635
E
0BS-NoPos 1.726=0.162
1.753+0.176
1.773+
1.670=0.137
1.671
1.656+0.136
0BS-CPS-InfC 0.911
0.91910.100 108
0.913-10. 107
0.925
0.930-10.081
0.924-10.075
OBS-UConf-InfC 0,107
0.960+0.1
0.953 0. 106
0.987
1987--0.150 159
1.008+0.200 +00209
0.986+0.111
OBS-NoPos-InfC 0.949-0.005
0.947-0.077
0.951+00.88
0.908
0.923-10.043
0.910=20.047
Total Win
37
14
29
26
11
43
52

---

Published as a conference paper at ICLR 2026
Table 23: DR-Learner MAE
Survival Causal
Base Regression Model
Scenario Configuration
Lasso Reg.
Random Forest
XGBoost
RCT-59
0.661=0.012
0.658=0.013
0.685=0.013
RCT-5
0.645110.011
0.6524:0013
0.680=0.014
OBS-CPS
0.653=0.011
0.649=0.012
0.676=0.012
0BS-UConf
0.604=0.009
0.611=0.009
0.635=0.010
OBS-NoPos
0.657-10.010
0.65610.011
0.68410.014
0BS-CPS-InFC
0.727=100188
0.735=00023
0.770=0.025
OBS-UConf-Infe
0.675=#0.099
0.696=0.022
0.730=0.023
0BS-NoPos-InfC
0.724
0.735100015
0.770.0.0000
Total Win
54
26
RCT-58
0.330+0.008
0.318=0.011
0.341
0.276+0.006
0.278
0.300+0.007
OBS-CPS
0.316=0.001
0.008=0.013
0.332=0.017
OBS-UConf 0.354+0.007
0.344=0.00$
0.370=0.010
B
OBS-NoPos 0.345+000009
0.011
0.349+0.012
DDS-CPS-InfC 0.301110.007
0,295
0.31610.008
OBS-UConf-InfF 0.340=000044
0.331=0.004
0.355=0.006
OBS-NoPas-InfC 0.337+0.000
0.321+0.005
0.345+0.007
Total Win
RCT-50
1.400=1.0222
1.59110.021
1.701
RCT-5
0.009
1.540:100188
1.742.10.021
OBS-CPS
1.410-10.21
1.56410.026
1.76310.021
OBS-UConf
1.420=10.033
1.572=0.024
1.777=0.019
OBS-NoPas
1..19
1.61410.020
1.805
OBS-CPS-InFC
0.931
1.02110.030
1.17310.038
OBS-UConf-InfF
0.895:10.033
0,97710.044
1.13350.054
OBS-NoPas-InfC
0.916:0.0057
0.005
0.072
Total Win
80
RCT-50
0.943=1.180
0.986+0.18
1.096=0,253
RCT-5
1.020=00.100
1.095=0.118
1.7
OBS-CPS
1.031+00.256
1.103+0.259
1.158+0.339
OBS-UConf
0.986-2..440
1.024=0.345
1.119=0,357
0BS-NoPos
0.969=:0.238
1.038=0.292
1.124=0.243
OBS-CPS-InfC.
1.146+00030
1.154+0.087
1.238+0.048
OBS-UConf-InfC
1.179:10.024
1.17610.031
1.262-0.034
08S-NoPos-InfC
1.169=0.026
1.173=0.026
1.260=0.028
Total Win
65
RCT-50
1.753.10.185
1.917.1.200
10.244
RCT-5
1.605+0.127
1.742+0.144
1.949+0.161
OBS-CPS
1.652
0.81110.199
2.033+1.241
OBS-UConf
1.632.10.127
1.785_10.16
2.021
OBS-NoPos
1.701-t0.139
1.859+0.162
2.112+0.202
OBS-CPS-InFE
0.917:00.089
1.016+0.104
1.164+0.114
0BS-UConf-InfC
1..19
1.080.10.188
1.276.0..20
OBS-NoPos-InfC
0.928+00.000
1.022+0.068
1.182+0.096
Total Win
80
DR-Learner propensity score AUC. Note that the econml package in Python, which by default uses logistic regression for predicting the treatment assignment. Thus, we report the AUC of the treatment prediction by the logistic regression.
Table 24:
Causal Configuration Logistic Regression
RCT-50
0.501+
RCT-5
0.497-10.01
0BS-CPS
0.661+0.000
OBS-UConf
0,548++0.007
OBS-NoPos
0.820
08S-CPS-InfC
0.661#0.000
08S-UConf-InfC.
0.548-0.000
O8S-NoPos-InfC
0,820:10005
53

---

Published as a conference paper at ICLR 2026
F.6.3
BASE SURVIVAL LEARNER EVALUATION
See Table 25 26 27 for time-dependent concordance index different base survival learners by the base survival learners for S-, T-, matching-learners. We report the mean and standard deviation across 10 experimental repeats with different random splits.
Table 25: Survival S-Learner concordance index
Survival Causal
Base Regression Model
Scenario Configuration
RSF
DeepSurv
DeepHit
RCT-50
0.568110.088
0.59511.000
0.557:10.007
RCT-5
0.551+0.008
0.580+0.000
0.558+0.006
0BS-CPS
0.565++0.004
0.5%6+0.004
0.567+0.008
0BS-UConf
0.556==0.005
0.087=0.006
0.558=000010
OBS-NoPos
0.565.10.009
0.59411..044 0.553110.006
0BS-CPS-InfC
0.563:100.05
0.59711.004 0.546110.010
OBS-UConf-InfC
0.557++0.006
0.585+0.006
0.538+0.0008
OBS-NoPos-InfC
0.562:10.006
0.591::0.003
0.539:10.008
Total Win
80
RCT-50
0.640:1:.003 0.645+0.004
0.645: 0.004
RCT-5
0.616:10.003 0.622:1.0005
0.621 0.04
OBS-CPS
0.631+:0.005
0.632-+0.003
0.631
OBS-UConf
0.632++0.005
0.634+0.005
0.634+0.000
OBS-NoPos
0.650:10.003
0.656:10002 0.656:10.002
0BS-CPS-InFC
0.6301:0.004
0.632:10.004
0.629::0.003
OBS-UConf-InfC
0.6301100004
0.63311..005 0.63111.0005
OBS-NoPos-InfC
0.649+0.003
0.655+0.003 0.654+00.003
Total Win
10
50
20
RCT-50
0.545110.099 0.576110.004
0.570110.005
RCT-5
0.522+0.007 0.554+0.007
0.540++0.014
OBS-CPS
0.538+0.006
0.573++.005
0.562+00.004
0BS-UConf
0.536:20.007 0.566:1.007 0.561#0.008
08S-NoPos
0.550=+0.007
0.583=0.005 0.575+00.007
OBS-CPS-InfE
0.498:10.015
0.55810.026 0,546:10.017
OBS-UConf-Infe
0.502++0.023
0.500+0.029 0.541+0.020
XBS-NoPos-Ine 0.511100.09
0.586::.019 0.001
Total Win
70
10
RCT-50
0.633:+0.027 0.676+0.021
0.696 0.013
RCT-5
0.569:10.019 0.62610.017
0.628:10011
OBS-CPS
0.610+0.009 0.668=0.019
0.683+0.011
OBS-UConf
0.634+0.027
0.702+0.015 0.696+0.0188
OBS-NoPos
0.615=0.032 0.67810.016 0.685
0BS-CPS-InfC
0.626#0.011 0.634:0.005 0.629=0.007
OBS-UConf-InfC
0.639110.005
0.64611.005 0.64310.000
OBS-NoPos 0.635++0.006
0.644-10.006
0.640++0.005
Total Win
40
36
RCT-50
0,54410.010 0.59110.0111
0.578110.011
RCT-5
0.513+0.009 0.554+0.015
0.547+0.012
0BS-CPS
0.538+00.013 0.583+0.010
0.566+0.018
0BS-UConf
0.533+10.016 0.574:0.018 0.567+0.017
0BS-NoPos
0.544+0.015 0.599=0.000 0.589#0.012
08S-CPS-InfC
0,482-10.04] 0.54610.030 0.538-10.028
OBS-UConf-InfC
0.445:10.029
0.54210.045 0.53410.017
0BS BBS-NoPos-Infe 0.474-10.017
0..05
0.002
Total Win
60
54

---

Published as a conference paper at ICLR 2026
Table 26: Survival T-Learner concordance index
Survival Causal Scenario Configuration
Base Regression Model (Treated)
Base Regression Model (Control)
RSF
DeepSurv
Deepllit
RSF
DeepSury
Deepllit
RCT-50
0.579=0.009
0.612:1.006
0.581=0.015
0.54610.010
0.578=0.007 0.549:100014
RCT-5
0.567+0.031
0.604+0.0018
0.592+0.025 0.549+0.007
0.581 -..01 0.557++0.012
OBS-CPS
0.569+0.008
0.603+0.009
0.582+0.011
0.546+0.0066
0.577-0.007
0.548++00009
OBS-UConf
0.546:10.008
0.019=10.010
0.553=10.022
0.557=0.009
0.585=0.007 0.554+0..0 0009
0BS-NoPos
0.567=10.009
0.598::0.008
0.564:10016
0.534:10.006
0.564=0.009 0.544+0.005
OBS-CPS- InfCC
0.569:10.006
0.602:10.009
0.559=10.018
0.546:10.007
0.578=0.006
0.541=0.017
OBS-UConf-InfF
0.546:10.009
0.578:10.008
0.540:10.012
0.555=10.012
0.584=0.006
0.538:10.019
OBS-NoPos-InfC
0.564-00.009
0.598+0.006
0.545+0.013
0.531+0.009
0.004
0.537+0.010
Total Win
0
75
RCT-50
0.651=0.004
0.656:1.0044
0.654:10.005
0.610:10.005
0.618
0.616:1..005
RCT-5
0.628:000017
0.627=0.027
0.609=000022
0.610=:00007
0.619=0.004
0.620:1..004
OBS-CPS
0.630=0.000 0.637-1.000
0.634:1..005 0.605 0.612-0.006 0.607100000 007
OBS-UConf 0.644_1.0008 0.648.10.006
0.646-0.0066
0.5981000005
0.605
0.602 008
B
OBS-NoPos
0.628+00.00 0.636+0.0004
0.63++0.005
0.593+0.008
1.001-0.04
0.600+0.000
OBS-CPS- InfC
0.628=00.005 0.633::0.00
0.632=+0.003
0.603=00006
0.611=0.008 0.610=
0BS-UConf-InfC
0.642-10.004
0.645:10.005
0.646=10.05
0.598=00.009
0.605=0.004
0.603-10.007
0BS-NoPos-InfC 0.624:0.007
0.634:10.00
0.628=#0.005
0.592+00.006
0.602-0.004
0.600+00.007
Total Win
14
44
22
22
RCT-50
0.532:10.155 0.565.10.113
0.557=00015
0.512110008
0.541=0.011
0.524+1.0010
RCT-5
0.536::0.31 0.541=0.0000
0.544:0.027
0.518=0.0014 0.547=0.010
0.541
OBS-CPS
0.5361:0.008
0.56810.009 0.555=10.01
0.516:0.007 0.540=0.011 0.523 009
OBS-UConf
0.537-10.010
0.568=00.012 0.557+00.007
0.509+0.0100
0.533=0.012 0.521+0.011
OBS-NoPos
0.524+-0.06
0.555++.012
0.543+00.014
0.521+0.012
0.547-0.011
0.535+0.0008
OBS-CPS- InfCC
0.487-100041 0.550:10.032
0.5421100038
0.497.10.018
0.537-0.021 0.522
OBS-UConf-InfC
0.49111.0044
0.552.10.031
0.550:10.032
0.484:10.021
0.513=0.035 0.519-100118
OBS-NoPos-InfF
0.470=10.045
0.549::0.037
0.544=10.032
0,489:10.029
0.538=0.023
0.513++0.033
Total Win
RCT-50
0.646110.038 0.6831100084
0.727
0.565-10.025
0.614=0.018 0.623-1.002
RCT-5
0.447: 0.412++..15
0.672+0.133
0.573++0.019
0.626=0.016 0.625+00015
OBS-CPS
0.584:0.055 0.646:+0.038
0.672::0.022
0.543+10.023 0.609=0.032 0.620
OBS-UConf
0.655=100038
0.731=0..028
0.745=:00122
0.536=10.034
0.588=0.036 0.597=0.029
0BS-NoPos
0.668=10.051 0.658=10.085
0.773::0.024
0.547=100027
0.593=0.019 0.586
0BS-CPS-InfC
0.632:10.010 0.639:10.005
0.637-10.006
0.556:10.010
0.575=0.010 0.566110.110
OBS-UConf-InfC
0.673+00.00
0.675+0.007
0.676+0.007
0.549+0.011
0.569-0.005
0.556+0.008
OBS-NoPos-InfC
0.664+00.099
0.671+0.007
0.668+0.000
0.549+0.007
0.563-0.006
0.553++00009
Total Win
5
25
50
49
29
RCT-50
0.539:40.000
0.589::0.024
0.575=000017
0.514++0.020
0.547=0.019
0.537+-0.014
RCT-5
0.481+00065
0.518+0..04
0.516+0.005
0.518+0.011
0.554-0.010 0.544400.013
OBS-CPS
0.533=10.021
0.574:1.022
0.562-1.020
0,508+0.018 0.544-0.015 0.535-1.0014
QBS-UConf
0.534-10.023
0.587-10.024
0.552-10.014
0,510:1.014
0.520=0.023 0.531+0.022
OBS-NoPos
0.520:1:.024 0.539:10.032
0.547=00.22
0.516:+0.020
0.546=0.016
0.534+0.015
(BS-CPS-InfC
0.485:10.047
0.551:10.022
0.520:10.034
0.454:10.038
0.515=0.045 0.508:10.04
OBS-UConf-InfC
0.437-100004
0.525=10.048
0.541=0.065
0.455-10.025
0.495=0.037
0.499-1.0441
OBS-NoPos-InfC
0.4444-0.046 0.520+0.038
0.505+0..040
0.453+0.043
0.514-0.027
0.537+0.023
Total Win
55

---

Published as a conference paper at ICLR 2026
Table 27: Survival Matching-Learner concordance index
Survival Causal
Base Survival Model
Scenarlo Configuration
RSF
DeepSury
DeepHit
RCT-5e
0.568+0..00
0.595 0,000 0.557+0.000
RCT-5
0,551=00.00
0.580=0.004
0.558:00.006
OBS-CPS
0.556+00.005
0.596=0.004
0.567=00000
OBS-UConf
0.556110.005
0.587-10.006
0.558110.010
0BS-NePos
0.565+0.0009
0.594+0.000
0.553+000006
0BS-CPS-
0.563++0.005
0.597:10.004 0.546++0.010
OBS-UConf-InfC
0.557=+0.006
0.585=00.006
0.538=+0.008
OBS-NoPos-Inf
0.562+00.006
0.591=00.003
0.539+0.008
Total Win
80
0
RCT-50
0.640++0.003 0.645=0.004
0.645:00.004
RCT-5
0.616++0.003 0.622+00005
0.621+0.004
OBS-CPS
0.6311:0.005
0.632:1.003 0.631=0.003
OBS-UConf
0.632::0.005
0.634:0.005 0.634:1..044
OBS-NoPos
0.650.10.003
0.656110.002 0.65611..002
0BS-CPS-InfC
0.630++0.004
0.632+0.004 0.629=+0.003
OBS-UConf-InfC
0.630+00.004
0.633+0.005 0.631+0.005
OBS-NoPos-InfC
0.649:10.003
0.655-1.003
0.65410.003
Total Win
50
21
RCT-50
0.545+0.009 0.576+0.004
0.570+00.0 005
RCT-5
0.5224+0.00 0.55410.007
0.540=
0BS-CPS
0.538:40.006
0.573+0.005
0.562+00004
OBS-UConf
0.536110.077
0.56610.007 0.56110.008
OBS-NoPos
0.550:10.007
0.583100000 0.575=10.007
0BS-CPS-InFC
0.498:+0.015
0.558:0.026 0.54610.017
08S-UConf-InfC
0.502+00003
0.560=0.029 0.541=0.020
OBS-NoPos-InfC
0.511+0.029
0.586=0.019
0.561+0.025
Win
70
RCT-50
0.633:+0.027 0.676:1.021
0.69:
RCT-5
0.569+00.019 0.626+0.011
0.628
OBS-CPS
0.610:10.029 0.66810.019 0.68310.011
0BS-UConf
0.634:10.027 0.702:10.155 0.696::0.018
OBS-NoPos
0.615:10.032
0.67810.016 0.015
OBS-CPS-InfE
0.626.10.011
0.634.1.005 0.629110007
OBS-UConf-InfC
0.639+-0.005
0.646+0.005
0.643+0.007
OBS-NoPos-InfC
0.635:10.006
0.64410.006
0.640+4..005
Total Win
40
36
RCT-50
0.544+00.11 0.591+0.011
0.578+0.011
RCT-5
0.513+40.009 0.55410.015
0.547+0.012
0BS-CPS
0.538+000013
0.583=0.010
0.566+00018
OBS-UConf
0.533-10.016
0.57410.018 0.56710.017
OBS-NoPos
0.544=10.015
0.59910.010
0.58910.012
0BS-CPS-Inf
0.482:+0.041
0.546-1.030 0.538+10.028
OBS-UConf-InfC
0.445:+0.029
0.542+0.005 0.534+0.017
OBS-NoPos-InfE
0.474:+0.017
0.565-0.035
0.563+0.022
Total Win
60
20
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F.7 CONVERGENCE RESULTS
Figure 18 presents the convergence behavior of different causal inference methods under eight con- figurations of assumptions, all within Scenario which was the main focus in Section 4. The x-axis shows increasing training set sizes (ranging from 50 to 10,000), while the y-axis plots the root mean squared error (RMSE) of the estimated CATE on the test set. (Note that, all models are selected based performance the validation set).
Across all configurations, we observe general convergence trends where CATE RMSE decreases as training size increases. Among the survival methods, the T-Learner-Survin the slowest, especially under small training sizes. This may be due to the model requiring sufficient uncensored samples per treatment arm to function effectively. Double-ML also tends to require more data to stabilize, particularly in the presence of low treatment rate or lack of positivity. The Causal Survival Forests shows slower convergence under settings with non-ignorable censoring positiv- ity violations, reflecting its convergence sensitivity to these assumptions despite its nonparametric structure. Overall, while standard meta-learners and tree-based methods show relatively stable con- vergence behavior, survival-specific adaptations appear more data-hungry and assumption-sensitvy for convergence. These trends highlight the importance of choosing appropriately robust methods with respect to the dataset size in practice, especially in real-world settings where assumptions like positivity or ignorability may be compromised.
consistently converges
Trestar
(a) RCT: (50%)) Ignorability: V. Positivity: V. Ign Censoring: /
(b) RCT: (55)) Ignorability: V. Pusitivity: v. Ign Censoring:
Tiasnar
(6) RRRCT:X X. Ignorability: /. Posilivityy V. Ignocable Censoring:
(d) RCT: X. Ignorability: X, Posiivity: V. Ignorable Censering:
Silemerr
ONe
30
(0) RCT: X. Ignorability: V. Positivity: X. Ignorable Cemseing::
(O) RCT: X. Ignorability: /. Positivity V. Ignorable Censering:
Silemner
Letmer
T-asnar
Tuasnerr
(g) RCT: Ignorability: Posilivity: v. Ignorable Censoring: X
(l) RCT: X, ..ggurraility: V. Positivvty X. Ignoraale Censoring:
Figure 18: Convergence properties: CATE RMSE in Scenario C as number of training data increases.
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G SEMI-SYNTHETIC DATASETS: SETUP AND ADDITIONAL RESULTS
G. SEMI-SYNTHETIC DATASETS SETUP
To complement synthetic benchmarks and real-world case studies, we construct semi-synthetic datasets that pair real covariates with simulated treatment assignment and survival outcomes. This strategy preserves realistic covariate distributions and correlations while enabling controlled eval- uation against known ground-truth CATES, We consider two covariate sources: the ACTG HIV trial and MIMIC-IV ICU records. Table 28 summarizes dataset sizes, covariate counts, treatment and censoring rates, and whether the treatment-ssignmenn and event-time mechanisms depend on covariates through linear versus non-linear functions; full generative details are provided in Ap- pendix G.2 and G.3 Figure 19 shows Kaplan-Metts curves for event and censoring in the treatment and control groups for each semi-synthetic dataset.
Table 28: Semi-synthetic datasets overview. The last two columns summarize how treatment assign- ment and event-time generation depend on covariates. 1inear indicates dependence through linear predictor with no quadratic or interaction terms; non-linear includes quadratic and/or interaction terms. independent indicates covariate- indeeeedent treatment assignment.
Data size
No. covariates
Treatment rate
Censoring. rate
Treatment assignment mechanism
Event time
mechanism
ACTG
2,139
23
56.15%
51.19%
linear independent
non-lineat
MIMIC-i
25,170
36
49.92%
88.49%
linear
MIMIC-ii
25,170
36
49.92%
81.65%
independent
linear
MIMIC-ii
25.170
36
49.92%
74.10%
independent
linear
MIMIC-iv
25,170
36
49.92%
66.34%
independent
1 linear
MIMIC-
25.170
36
49.92%
53.35%
independent
linear
MIMIC-vi
25,170
36
53.54%
53.07%
linear
linear
MIMIC-vii
25.170
36
54.26%
52.66%
linear
non-linear
MIMIC-viti
25,170
36
50.94%
53.26%
non-linear
linear
MIMIC-ix
25.170
36
51.47%
52.82%
non-linear
non-linear
Event, Control
Event, Treated
Censoring, Control
1.000 Censoring, Treated
ACTG
MINIC-i
NINIC-
MIMIC-Il
MINIC-IV
ord 263
8.75
pe0.501
peb
pet 455
0.50
0.25
29
26
20
28
MIMIC -V
MIMIC-VI
CIMIC-ViI
MINIC-Viii
MIMIC-AA
p-0.403
ped
pe0.343
pe0.50 --0-500
pa5.315
9.58
8.25
9.00
28
48
20
40
29
48
28
28
40
Time
Figure 19; (Semi-synthetic datasets) Kaplan-Meier curves. Solid lines show event-time survival under control (blue) and treatment (orange): dotted lines show censoring- ttmm survival for each arm. Each panel reports the empirical censoring rate and treatment probability p.
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G.2 ACTG SEMI-SYNTHETIC DATASET
The ACTG semi-synthetic dataset is derived from the ACTG 175 HIV clinical trial (Hammer et al. 19961, which contains 23 baseline covariates. Following the construction procedure of Chaapfuaa et al. (02T). we simulate covariate-dependent treatment assignment and generate event times from Gompertz-Co model with an AFT-style censoring mechanism. This dataset exhibits realistic treatment imbalance and moderate censoring (~51%), providing clinically grounded benchmark with preserved trial covariate structure.
More concretely, following Chapfuwa et al.
202 we generate:
x ACTG covariates
1 b
P(A= 1|X x) = x (a + (MAАG - MAGE + CD40 (CDA))))
U Uniform(O,1) 1)
a logu U
TA
log
Aa exp (x² BA) log C Normal(pe: o?))
Q
= min(TA,C)
where (-) is the sigmoid function, (3A, A. As b, 1/ Me. de) are hyper-parameters taken to be the same as described at https: / thub. cww/co/c//aaooc pai http:////ooutttrtaaaaaa/a///aaaa
and (MAGE, MCD40) are the means for age and CD40 respectively.
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G.3 MIMIC SEMI-SYNTHETIC DATASETS
We construct a suite of nine semi-synthetic datasets derived from MIMIC-IV ICU records (John- al. 2023). All variants share the same covariates and sample size, and differ only in the weatment-assignmen and event/censoring mechanisms. The suite is organized into two comple- mentary subsets: (1) independent assignment with varying censoring severity (MIMIC-i-t), which isolates robustness to censoring under randomized treatment; and (2) confounded assignment with varying functional form (MIMIC-ei-izz), which evaluates robustness to observed confounding and to non-linear (itteraction-bsee) event and censoring mechanisms while keeping covariates fixed.
We extract 36 covariates spanning laboratory test abnormalities (e.g., creatinine, glucose, hemoglobin), demographic features (e.g., age, sex, race, marital status), and admission descriptors (e.g., admission type, recurrent admissions, night admission). Table summarizee covariate statis- tics; Table 30 reports demographic and categorical distributions; and Figure 20 shows correlations among covariates.
Table 29: Summary statistics MIMIC semi-synthetic covariates. Reported values are mean + standard deviation. Physiological covariates coded as indicators for abnormal values where mean reflects prevalence of abnormality.
Covariate
Mean + Std
Covariate
Mean + Std
Sodium
0.12 0.32
Admission age
61,39 + 17.97
Potassium
0.08 0.28
Sex:Male
0,51 + 0.50
Chloride
0.19 0.39
Race: White
0,70 = 0.46
Bicarbonate
0,24 0.43
Race:Black
0.14 = 0.35
Anion gap
0.09 = 0.29
Race: Hispanii
0.05 = 0.22
Creatinine
0.28 = 0.45
Race:Other
0.07 = 0.25
Urea nitrogen
0.40
Insurance:Medicure
0.42 = 0.49
Glucose
0.65 = 0.48
Insurance:Other
0.52 + 0.50
Calcium total
0.29 00.45
Marital status: Married
0.45 + 0.50
Magnesium
0.09 + 0.28
Marital status:Single
0.33 + 0.47
Phosphate
0.28 + 0.45
Marital status: Widowed
0.14 + 0.34
Hemoglobin
0.73 - 0.44
Direct emergency: Yes
0.11 = 0.31
Hematocrit
0.69 + 0.46
Night admission: Yes Previous admission
0.54 + 0.50
MCV
0.20 0.40
0.08 0.27
this month: Yes Admissions number:2
MCH
0.26 - 0.44
0.16 = 0.37
MCHC
0.31 = 0.46
Admissions number:3+
0.22 = 0.42
Platelet count
0.29 - 0.45
RDW
0.29 + 0.45
White blood cells
0.40 0.49
Red bloud cells
0.76 0.43
We now introduce some shared notation all of the MIMIC semi-synthetic datasets. Let X1:5 denote the first five binary covariates corresponding to abnormal laboratory values (Anion gap, Bi- carbonate, Calcium total, Chloride, Creatinine), and let X38 denote the standardized Admission age. We define the abnormal-lab burden as
S
X,
Across all MIMIC variants, we generate potential event times T(0), and a censoring time C, and observe
T= WT(1) + - WYT(0), = min (TT,) C,C), = 1(T s C}.
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Table 30: Demographic and categorical distributions in MIMIC semi-synthetic datasets. Reported values are proportions.
Demographics
Admission-related
Variable
Proportion
Variable
Proportion
Sex
Direct emergency
Male
0.512
Yes
0.110
Female
0.488
No
0.890
Race
Night admission
White
0.699
Yes
0.539
Black
0.141
No
0.461
Other
0,066
Previous admission this month
Hispanic
0.053
Asian
0,041
Yes
0.081
Insurance
No
0.919
Other
0,522
A Admissions number
Medicare
0,421
1
0.615
Medicaid
0.057
2
0.164
Marital status
3+
0.222
Married
0.449
Single
0,334
Widowed
0.136
Divorced
0.081
Correlation of Semi-Synthetic MIMIC Covariates
hight udmisiinn:We
Admis un age
1.0
Insurance Other
Morital stotus Willowed
slatcaMerred
Race Hisganic
Race
0.5
Racac/Niite
Pearson Correlation
Admisaions numberc:
Previous admission this
number:3+
Clucose
Pot aitassium
Chloride
Phosphate
Creatinine
Antion
Bicarbonabe
MCHC
RDW
Hatwart
calcium total
Hemoglobin
Dinegt
Premmnt Admiosaai
Witte
Figure 20: Correlation heatmap of the 36 semi-synthetic MIMIC covariates. Variables include de- mographic features, admission descriptors, insurance and marital status indicators, and laboratory measurements. Most correlations weak to moderate, with stronger dependencies visible among related laboratory values (e.g., hematocrit, hemoglobin, and red blood cell count).
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G.3.1 INDEPENDENT-ASSIINNN VARYING CENSORING (MIMIC-
This subset follows the event-time construction of Meir et (2025) and varies censoring severity to span moderate to extreme censoring regimes.
Treatment assignment.
Treatment is assigned independently of covariates:
W (erroouli(003),
yielding balanced treatment groups with W X.
Potential outcomes.
Potential event times are Poisson with means depending on and X36:
T(0) ~ Poisson (30 + 0.75. + 3.75.3a),
T(1) Poisson (30 0.75.X36 0.45).
We define the conditional average treatment effect (CATE) as rΛx) [B[((1) - T(0) = x] and record unit-level ground truth CATE T(1) - T(0).
Censoring. Censoring is independent and varies across dataset variants:
C' Poisson
where Ae E {21, 23, 24.7, 26.5, 29} controls censoring severity for MIMIC-i-e, yielding censoring rates from approximately 53% to 88%.
G.3.2 CONFOUNDED ASSIGNMENT, VARYING FUNCTIONAL FORM (MIMIC-vri-iz)
This subset reuses the same covariate backbone but introduces covariate-dependent treatment as- signment (observed confounding) with propensity and varies whether the event-time and censoring mechanisms are linear or non-linear in covariates. The four variants correspond to the following combinations:
MIMIC-ri: Propensity score=linear, event/censoring time=linear;
MIMIC-cii: Propensity score=linears event/censoring time=non-linear;
MIMIC-viri: Propensity score=non-linedt event/censoring
scoermoonniieeerrreveedtennnnnnn time=linear;
MIMIC-ir: Propensity score=mon-linear, event/censoring time=non-linear.
Covariate-dependent treatment assignment (propensity score). We consider two propensity- score families:
Linear (no interactions or quadratic terms).
7イx) = oo + an Xas + 02S,
e(x) Pr(W W X = = =(((x)) W X (ernoolli(e(X)),
with (oo, 01, 42) (-0.25, 0.8, 0.4);
Non-linear (quadratic + interaction).
7(x) 90 + Xas + 325 + Bx + 84 3 e(x) Pr(W = X 2) [(n(z)) W X Bemoolli(e(X)),
with (by. by b2, by. bu) = ( 0.2, 0.8, 0.4, 0.3, 0.5).
where o--) is the sigmoid function. We clip e(x) into 0.005 0.95] to avoid near-deterministcc treat- ment assignment and preserve overlap. Note that the coefficients chosen (by checking the real- ized [E[)) so that the treatment rate remains close to 0.5 while inducing confounding through Xa and S.
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Event-time and censoring mechanisms. Potential outcomes and censoring are defined through Poisson means with an identity link and are clipped below at 1 to ensure positivity.
Linear (no interactions or quadratic terms).
(o(x) = 1/00 + 4o0 336
14 (ar) 1/10 + V1s X36.
with (1h0, Vol, 102) = (25.0, 0.75, 0.75) and (1/10 11 412) (25.0, 0.0, 0.75), and
T(0) ~ (oisson(max(11, (o))))
T(1) ~ (oisson(max(L, (I
Censoring is
Ax(x) wn w/S + W23 with (Wo, Wi, w2) (24.0, 0.2, 0.2).
C Poisson (max (x))))))))
Non-linear (quadratic + interaction).
[o(x) = 2/00 + e'o1 + X36 + Vo3 + X311
(1(x) = v/1o + +115 X + tha Whaxx X + th14 X3aS,
with
(woo, voo too,, s/o3, 4/04)
(25.0, 0.75, 0.75, 0.3, 0.5)
and
(110, Vi1, 1/ 1ha 114) (25.0, 0.0, 0.75, 0.2, 0.4). and
T(0) ~ Poisson(max (X)))), T(1) ~ Poisson (max (X))).
Censoring is
Aa(x) = wp wiS + w2 X + w3 S365, C ~ Poisson (max {1, (X))).
with (wo, w1, W2, w3, w4) = (24.0, 0.2, 0.2, 0.3, 0.4)
These mechanisms allow survival outcomes and censoring to vary non-linearly with baseline severity (lab abnormalities) and age, thereby creating heterogeneous and more realistic treatment effects.
Fixed-horizon survival probabilities. Because event times are Poisson-distributed, the condi- tional survival probability for arm w E {0, 1} at discrete horizon è
[t]
Pm (X)*
S. | x) (r(T(w) X) =1
k!
For each dataset, we compute unit-level ground-truth survival probabilities at horizons correspond- ing to the empirical 25th, 50th, and 75th percentiles of the realized event-time distribution, and use these when evaluating survival-probability CATE estimands.
Across all MIMIC variants, the sample size is = 25,170 and the covariate distributions in Ta- bles 29 and are identical. The subset MIMIC-i-W spans censoring rates from approximately 53% to 88 % under wwwariate-iddpendeer treatment assignment (Pr(W=1] so 0.5), isolating the effect of censoring severity. The subset MIMIC-vi-ia keeps censoring moderate (around 53% in our instanti- ation) while introducing covariate-dependee treatment assignment and varying whether event-time and censoring mechanisms are linear non-linear in covariates, providing complementary stress tests for both confounding and misspecified or non-linear hazard/censoring relationships.
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G.4 SEMI-SYNTHETIC RESULTS: FULL MIMIC SUITE AND ADDITIONAL ESTIMANDS
This section extends the semi-synthetic evaluation in Section 4.2 First, we complete coverage of the full MIMIC semi-synthetic suite by reporting RMST-based CATE RMSE on MIMIC-vi-ir under the same primary estimand used in the main paper (RMST evaluated at the maximum observed time max). Second, we report results for additional estimands that probe time-horizon sensitivity: Norizon-specing survival -robbbbiyy CATEs and RMST evaluated at a shorter horizon (the median event time T med)).
G.4.1 PRIMARY ESTIMAND: RMST AT Taax (FULL MIMIC SUITE)
The main paper reports RMST-based CATE RMSE on ACTG and the censoring-severije subset MIMIC-i-U (Table 3. Table 3T reports CATE RMSE on MIMIC-vi-ir using the same estimand as in the main paper: RMST evaluated at the maximum observed time in each dataset. These variants reuse the same covariates as MIMIC-i-U but introduce covariate-dependem treatment assignment and/or non-linear event-time and censoring mechanisms (Appendix G.3.2p. Across MIMIC-i-ix, mean RMSE values typically lie a narrow band, so practical differences are often reflected more strongly in stability (variance across repetitions) than in average erтor.
Dataset-dependent performance patterns. The ACTG dataset (Table exhibits clearer separa- tion among methods, whereas the MIMIC variants (TablesBann [nd33] show substantially tighter clus- tering. This reinforces that method rankings can depend on covariate structure and data data-gened getteratnnningggg mechanisms: approaches that perform well in trial-like settings (ACTG) need not be the strongest in high- figgh-dimessonal EHR-like settings (MIMIC), and vice versa.
Censoring- graiiinnt and stability under MIMIC-i-U. The censoring sweep MIMIC-i-U (53%- 88% censoring) provides granular view of censoring sensitivity. Several methods maintain stable mean RMSE as censoring increases, but standard deviation can change markedly for some learners under extreme censoring (Table 3) As result, stability considerations (e.g.. standard deviation across repeats) can be as important as mean RMSE when operating highly censored regimes typical of EHR studies.
Robustness across mechanism complexity (MIMIC-oi-iz). Moving from MIMIC-i-o to the mechanism-comppexiiy subset MIMIC-vi-ir does not qualitatively change the overall picture: mul- tiple methods remain competitive and the nop-perforning group (Causal Survival Forests and S- Searner-Survivll is often tightly clustered (Table 31). This suggests that the primary conclusions drawn from MIMIC-i-u are not driven solely by covariate ewvaraat-inddeendeen treatment assignment; rather, they persist under observed confounding and non-linear outcomeecensoring mechanisms within the same covariate support.
G.4.2 ADDITIONAL ESTIMAND: HORIZON-SPECIER SURVIVAL-PROBABILITY CATES
In addition RMST-based CATES, we consider treatment effects defined on the survival function a fixed horizon. Let (w; h) Pr(TT (w) > h) denote the potential-outcome survival probability for unit under treatment E {0, horizon h. In this case, the transformation y(-) in equation is replaced by
y (T:(w)) = Si(w; h).
The corresponding CATE is:
= E[S,(L) - Se(0;)) X; =
(6)
We evaluate Th (æ)) at three dataset-specific horizons given by the empirical 25th, 50th, and 75th percentiles of the realized event-time distribution.
We evaluate Th (z: at three dataset-specific horizons given by the empirical 25th, 50th, and 75th percentiles of the realized event-time distribution. We report results for methods that explicitly model conditional survival functions (direct-survival CATE methods and survival meta-learners). Our nutcome-imputatiie ditional survival curve, and therefore not included for this estimand. Tables 32 34 summarize RMSE across the MIMIC semi-synthetic datasets for the 25th, 50th, and 75th percentile horizons, respectively.
baselines impute event times (or RMST) rather than estimating a full con-
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Table 31: CATE RMSE (mean std over 10 repeats) on MIMIC-ri-iz, using RMST evaluated at the maximum observed time maax of each dataset as the estimand. Best two methods per dataset are bolded.
Method Family
MIMIC-ei
MIMIC-uii
MIMIC-vii
MIMIC-ir
Outcome Imputation Methods
T-Learner
7.184 +: 0.052 7.374 1 0.067 7.220 + 0.046 7.354 + 0.048
S-Learner
7.176 0.048 7.308 1 0.068 7.197 1 0.049 7.275 0.061
X-Learner
7.182 0.053 7.318 1 0.069 7.203 1 0.045 7.273 0.044
DR-Learner
7.145 1 0.054 7.295 1 0,061 7.167 1 0.046
7.263 1 0.045
Double-ML
7.127 0.051 7.259 - 0.072 7.147 1 0.049 7.226 0.056
Causal Forest
7.142 0.052 7.288 1 0.068 7.162 1 0.047 7.247 0.043
Direct-Survival CATE Methods
Causal Survival Forests 7.123
0.048 7.281 0.064 7.149 + 0.045 7.227 0.054
SurvITE
7.169 0.042 7.286 + 0.059 7.184 + 0.043 7.265 0.055
Survival Meta LearneLssss
T-Learner- -uLearnerSSurvival
7.168 0.035 7.332 + 0.071 7.188 + 0.040 7.358 0.047
S-Learner-Survivee
7.138 + 0.048 7.285 + 0.064 7.163 1 0.041 7.239 0.055
Matching Survival
7.163 0.050 7.340 + 0.062 7.199 + 0.043 7.297 0.050
Table 32: CATE RMSE (mean + std over 10 repeats) MIMIC semi-synthetic datasets, using survival probability at 25th quantile event time each dataset as the estimand. Best method per dataset is bolded.
Method Family
MIMIC-i
MIMIC-i
MIMIC-ii
MIMIC-iu
MIMIC-6
Direct-Survivel CATE Methods Causal Survival Forests
0.051 + 0.003
0.045 1 0.005
0.039 1 0.002
0.037 + 0.003
0.034 1: 0.002
SurvITE
0.066 1 0.009
0.060 1 0.004
0.057 1 0.008
0.055 + 0.005
0.055 1 0.005
Survival Meta- Learners
T-Leamee-SSrvival
0.083 + 0.011
0.077 +: 0.040
0.049 + 0.008
0.047 + 0.007
0.045 + 0.005
S-Learner-Survive
0.053 0.006
0.050 + 0.006
0.053
0.010
0.051 + 0.004
0.046 + 0.004
Matching Survival
0.061 + 0.006
0.058 + 0.005 0.058 + 0.008
0.055 + 0.004 0.050 + 0.003
Method Family
MIMIC-vi
MIMIC-eii
MIMIC-vit
MIMIC-ir
Direct-Survival CATE Methods
Causal Survival Forests 0.044 + 0.003
0.035 + 0.003
0.038 + 0.005
0.041 + 0.003 0.076 0.009
SurvITE
0.070 + 0.011
0.066
0.011
0.068 + 0.007
Survival Meta-Learners
Te-Lermer-SSrvive
0.057 + 0.007
0.068 + 0.016
0.074 + 0.014
0.069 0.010
S-I B-L.camer-Survin
0.051 0.005
0.049 + 0.006
0.054 + 0.008
0.055 0.005
Matching Survival
0.060 + 0.005
0.062 + 0.004
0.067 = 0.005
0.071 0.002
Horizon effects. Across MIMIC variants, performance gaps are generally more pronounced at carlier horizons (25th percentile) and become more compressed at later horizons (75th percentile). This is consistent with the intuition that carly-horizon survival probabilities can be more sensitive to misspecification and estimation error, whereas later-horizon estimates may be less discriminative across methods in these settings.
Method family patterns. Across horizons, Causal Survival Forests tends to achieve the lowest RMSE among the survival CATE estimators, while survival meta-learners remain competitive but display method-specific sensitivity. In particular, S-Leevner-Survival is typically among the most stable meta-learners across horizons and variants, whereas Matching Survival shows larger degra- dation for hoer-horizon survival probabilities in several variants (Tables 32 34 SurvITE is consis- tently less accurate than Causal Survival Forests under this estimand, with the gap more salient at earlier horizons.
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Table 33: CATE RMSE (mean + std over 10 repeats) on MIMIC semi-synthetic datasets, using survival probability at 50th quantile event time of each dataset as the estimand. Best method per dataset is bolded.
Method Family
MIMIC-
MIMIC-i
MIMIC-ii
MIMIC-iU
MIMIC-
Direct-Survivee CATE Methods
Causal Survival Forests
0.086 + 0.008
0.077 + 0.008
0.059 1 0.003
0.063 + 0.005
0.051 + 0.002
SurvITE
0.086 0.011
0.081 + 0.009
0.065
0.010
0.070 + 0.006
0.066 1 0.007
Survival Meta-Learners
T-Learner-Survive Survival
0.144 0.006
0.096 1 0.018
0.092
0.018
0.068 1 0.011
0.065 0.009
S- S-Leaaner-Srrvval
0.069 1 0.008
0.064 + 0.008
0.061 1 0.007
0.064 1 0.005
0.058 1 0.005
Matching Survival
0.083 + 0.007
0.078 1 0.007 0.073 1 0.007
0.072 + 0.004
0.066 1 0.005
Method Family
MIMIC-vi
MIMIC-eii
MIMIC-viie
MIMIC-ir
Direct-Survivee CATE Methods
Causal Survival Forests
0.052 + 0.005
0.044 1 0.006
0.054 + 0.005
0.054 1 0.004
SurvITE
0.076 0.012
0.071
0.010
0.079 + 0.009
0.081
0.009
Survival Meta-Learners
T-Learner-Survite Survival
0.084 0.013
0.098 + 0.028
0.093 + 0.020
0.091
0.014
S-Lecveer-Survival
0.063 + 0.007
0.059 + 0.009
0.065 + 0.010
0.066 0.006
Matching Survival
0.077 = 0.007
0.081 = 0.006
0.085 = 0.007
0.091 + 0.002
Table 34: CATE RMSE (mean + std over 10 repeats) MIMIC semi-synthetic datasets, using survival probability at 75th quantile event time of each dataset as the estimand. Best method per dataset is bolded.
Method Family
MIMIC-
MIMIC-i
MIMIC-ii
MIMIC-iu
MIMIC-#
Direct-Surviver CATE Methods
Causal Survival Forests 0.104 + 0.020
0.088 + 0.012
0.066 + 0.007
0.054 + 0.006
0.052 + 0.003 0.059 + 0.007
SurvITE
0.093 0.020
0.065 + 0.010
0.064 + 0.010
0.055 + 0.005
Survival Meta-Learners
Lxcamee--Surivee
0.137 0.041
0.097 = 0.009
0.085
0.014
0.065 = 0.012
0.059 + 0.007
S- Scarner-Survvall
0.061 + 0.008
0.056 = 0.007
0.052 + 0.010
0.049 = 0.003
0.046 + 0.006
Matching Survival
0.077 + 0.008
0.071 = 0.008
0.065 + 0.009
0.060 = 0.003
0.055 + 0.006
Method Family
MIMIC-vi
MIMIC-ei
MIMIC-viti
MIMIC-iz
Direct-Survival CATE Methods
Causal Survival Forests 0.053 + 0.004
0.050 + 0.002
0.047 = 0.004
0.056 + 0.005 0.066 0.009
SurvITE
0.066 0.013
0.058 = 0.008
0.059 = 0.003
Survival Meta- Learners
Learner-Survive
0.086 0.013
0.078 = 0.012
0.067 = 0.011
0.088 0.014
S S-Leamer- Survivall
0.052 = 0.007
0.054 = 0.009
0.051 = 0.008
0.059 + 0.006
Matching Survival
0.065 + 0.008
0.079 + 0.005
0.072 + 0.006
0.087 + 0.002
Overall, the methods' relative performance appears stable across the 25th, 50th, and 75th percentile horizons, with no major reversals as h changes.
G.4.3 ADDITIONAL ESTIMAND: RMST HORIZON SENSITIVITY
The main paper reports RMST-based CATES evaluated large horizon h Tmax (the maximum observed time in each dataset). To probe horizon sensitivity, we additionally evaluate RMST at a shorter horizon h Tiedt the median of the realized event-time distribution in each dataset. Table 35 compares CATE RMSE under both horizons across the full MIMIC suite.
Robustness to horizon choice. Shortening the horizon typically reduces absolute RMSE (as ex- pected for less variable target), but the relative behavior of method families is largely preserved:
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methods that competitive at T max tend to remain competitive at med. and large ranking reversals are uncommon. Differences are more apparent in the stability of certain learners (e.g., matching- based survival approaches), which remain more sensitive to horizon choice (Table 35).
G.4.4 DETAILED ANALYSIS AND PRACTICAL IMPLICATIONS
This subsection provides consolidated interpretation of the semi-synthetic results across datasets
and estimands (Tables 3 for method selection.
31
32 34 and 35 focusing on stability characteristics and implications
No universally best method across realistic data structures. Across ACTG and the MIMIC suite, single method dominates uniformly. ACTG resembles trial-like setting with moderate dimensionality and covariate-dependent assignment, where flexible doubly robust estimators can perform strongly (Table 3) In contrast, the high-dimensional. EHR-like MIMIC variants yield tighter performance bands, and survival-oriented approaches are frequently competitive (Tables and BT. This highlights limitation of relying on single data structure: rankings can shift when covariate support, censoring regime, and assignment mechanisms change.
Mean performance versus stability. In MIMIC, mean RMSE values are often close, so variability across repetitions provides additional signal for method selection. Under extreme censoring (MIMIC-i-it). some approaches exhibit noticeably higher variability, whereas others remain stable across censoring levels (Table When performance differences are small, stability be the more actionable differentiator.
Estimand dependence and time-horizon effects. Comparing RMST-based CATES to horizon- specific survival-probability CATES illustrates that estimand choice can change how clearly methods separate. Survival-probabiiity CATES at earlier horizons tend to be more discriminative (Tables 332 34 while RMST-based targets can compress differences by integrating over time. The RMST horizon sensitivity analysis further indicates that shortening the horizon changes the scale of errors but rarely overturns broad conclusions (Table 35).
Practical guidance. Taken together, the semi-synthetic results suggest the following heuristics. () In trial-like settings with moderate dimensionality and covariate-dependent assignment (e.g., ACTG), flexible causal estimators can provide strong accuracy (Table 33. (ii) In highly censored, high-dimensional EHR- like settings (e.g., MIMIC), survival-oriented estimators and stable meta- learner variants are often competitive, and stability under censoring becomes particularly impor- tant (Tables 3 and 31). (iii) When multiple methods fall within a tight RMSE band, secondary considerations--taeee stability, interpretability, and computational cost-may dominate method choice.
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Table 35: CATE RMSE (mean + std over 10 repeats) on MIMIC semi-synthetic datasets, comparing
RMST estimands at different horizons h max (maximum observed time) and h T (median
event time). Best two methods per dataset are bolded.
4,360 + 0.039 4.387 + 0.039 7.958 0.048
4,387 + 0.039
4.360 + 0.039
4.360 0.039
4.354 + 0.040
4.363 + 0.037
4.357 + 0.035
4,376 0.037
4.360 + 0.036 4.361 # 0.038 7,901 = 0.046 4,361 # 0.037 7.897 = 0.042
4,358 # 0.038 7.912 + 0.042
4.735 # 0.058
h Taad
MIMIC-U
Tinax
4,361 + 0.039 7.908 = 0.043
4.361 1 0.039 7.908 0.043
7,9099 = 0.043
7.891 = 0.050
7,909 + 0.044
7.893 = 0.042
7,906 # 0.066
7.902 7.902 0.046
f-- Tiest
3.709 2: 0.032
3.747 1 0.034
3.769 - 0.032
3.737 0.034
3.732 0.033
3.739 0.029
3.725 0.032
3.755 0.031
3.762 0.026
3.735 0.031
4.283 1: 0.063
MIMIC-i2
h
4.361 = 0.039
4,356 # 0.040
4.36440... 0.040
4,357 + 0.036
4,374 d: 0.038
4,361 # 0.038
4.652 0.065 7,921 = 0.046 4,714 0.086
0.048
0.061
7.273 + 0.044
7.263 # 0.045
7.226 + 0.056
0.043
0.054
0.05
7.358 0.47
7,239 0.055
7.297 0.000
= Tindd
h mmax
MIMIC-iu -i
4.364
7.354
7.275
7,247
7.227
7.265
7,959 0,046
7.912 2 0.043
7.911 7.911 0.043
7.917 + 0.046
7,931 7.931 0.047
4.364 = 0.037 7.911 = 0.051
0.058
7.902 = 0.042
0,031
3,854 1 0.032
3,866 + 0.031
3,846 + 0.032
3.849 0.035
3,852 0.033
0,031
0,029
0.025
0,030
4,255 1 0.028
h Tmax
h- Tusi
7.907
MIMIC-URR
3,866
3.839
3.859
3,861
3,845
4.361 0.039
4.387 0.039
4.361 0,039
4.361 = 0.039
4.355 # 0.040
0.039
0.04
4. 1.464 0.034
3.772 0.027 7.220 0.046
3.873 = 0.037 7.308 + 0.068 3,770 0.026 7.197 0.049
3,772 # 0.027 7,203 0.045
7.167 0.046
7.147 0,049
0.047
7.149 0.045
0.043
0.040
3.751 # 0.024 7.163 0.041
7.199 0.043
Timd
h TURa
MIMIC-iL iii
h
4.365
4.375
7.162
7.184
7.188
7.915 + 0.043
4,390 0,042 7,956 0,050
7.915 + 0,043
7.911 = 0,043
7,919 # 0,044
# 0.033
0.038 7,929 # 0X037
7.906 # 0,071
7,911 = 0.154
7.900 0,045
7,920 1 0.047
3,751 1 0.026
3,743 # 0.028
0.026
3,740 = 0.025
3.766 0.025
3.761 + 0.031
4.233 1 0.039
= Tmox
h - Tond
7,934
MIMIC-ei
3.753
3.766
h T
0.040
4,363 + 0,040
4.363 = 0,004
4,357 + 0.041
0.041
4,363 1.03300030
0.038
4,777 0.344
4,363 0.036
7.935 = 0.053 4.600 0.070
T
7.374 0.067
7.318 = 0.069
7.295 = 0.061
7.259 # 0.072
7.288 0.068
7.281 + 0.064
0.059.
7.332 + 0.071
7.285 0.064
7.340 0.062
MIMIC-i
4,363
4.365
4,377
7.286
h
7.912 # 0.046
7.968 + 0.047
7.912 = 0.046
7.912 = 0.047
7,936 # 0.045
7.949 = 0.044
4,376 0.035 7.942 = 0:039
7.908 # 0.065
7.980 = 0.233
7.912 = 0.052
3. 866 # 0.036
3. 3.865 = 0.036
3.854 : 0.035
3.855 = 0.038
0.035
3,850 # 0.032
0.034
3. 3,860 = 0.039
3,856 # 0.031
4.238 1 0.038
mmxx
4- Tind
3 3.860
3.878
MIMIC-
h
4,367 0.038
4,387 0.040
4.367 0.038
4.367 + 0.038
7.954 0.047 4.365 + 0.040
0.039
0.035
4.391 + 0.000
4,362 # 0.039
4,603 0.140
1.184 0,052
7.176 = 0.048
7.182 - 0.053
7.145 = 0.054
7.127 0.051
0,052
Causal Survival Forests 7.123 0.048
7.169 # 0.042
7.168 0,055
7.138 0M048
7.163 1 0,050
h = Tmmel
T
MIMIC-
4,367
4,371
4,381
Outcome Imputation Methods
7.142
Direct- Survival CATE Methods
7.964 + 0.046
7,977 + 0,044
7,964 0.046
7.964 0.046
7.967 0.045
Causal Sarvival Forests 7,963 + 0.057
7,931 0,050
8.007 + 0.075
7,921 # 0.044
7,949 + 0.043
Survival Meta- Meta-Leumert Leurners
Timxx
Laaeerr--SSS Survival
S-1 Leeame--Suruee Survival
Matching Survival
Direct- Direct-St Strvival CATE Methods
Method Family
Outcome Imputation Methods
Causal Forest
DR- LR-Leaeer
Double-ML. ML
T- F-L.ammer
L-Lameer
X Leeamee
Survivaa Meta- Learness
SurvITE
1- "LLeane--Suree Survival
S- Learner Survival
Matching Survival
Method Family
Forest
Causal Forest
Double-MI.
T- F-Leaner
S-Leaner
X- Leeuner
DR-Learne
SurvITE
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H REAL-WORLDE DATASETS: SETUP AND ADDITIONAL RESULTS
We evaluate our benchmark on two real-world datasets: the Twins dataset (with known ground truth) and the ACTG 175 HIV clinical trial dataset (without known ground truth). This section provides detailed descriptions of data preprocessing and additional experimental results.
H.1
TWINS DATASET
The Twins dataset is derived from all births in the USA between 1989-1991 (Almond et al. 2005) focusing twin births. Following Curth et al. (2021a), we artificially create a binary treatment where W = (W = 0) denotes being born the heavier (lighter) twin. The outcome interest is the time-to-mont mo-rtaltty (in days) of each twin in their first year, administratively censored at 365 days. Since we have records for both twins, we treat their time-to-event outcomes as two potential outcomes T(1) and r(0) with respect the treatment assignment of being born heavier. While the Twins dataset is a widely used benchmark (Louizos et al. 2017 Du et al. 202T] Curth et al.) 2021a Curth & Van der Schaar 2021, Curth al. 2021b), we note that treating twins as perfect counterfactuals at best is an approximation. The "ground-truth" relies on the assumption that the unobserved potential outcome of one twin is identical the observed of their sibling, which in reality may not fully capture genetic or environmental heterogeneity.
We obtained 30 features (43 feature dimensions after one-hot encoding categorical features) for each twin relating to the parents, pregnancy, and birth characteristics including marital status, race, residence, number previous births, pregnancy risk factors, quality of care during pregnancy, and number of gestation weeks prior to birth. We select only twins weighing less than 2kg and without missing features, resulting in more than 11,000 twin pairs.
To create observational time-to-event dataset with known ground truth, we follow the semi- synthetic experimental design from Curth et al. (202Ta). The treatment assignment given by W|z ~ Bernoulli (a [8] e)) where 31 Uniform( 00.1, 0.1)43x1 and ~ N(, 12). The time- to-censoring is given by ~ Exp(100~ (83 x)) where 32 ~ (0, 12). This results in a treatment rate of 68.1 % and censoring rate of 84.8%.
We split the data 50/25/25 for times with different random splits. CATE RMSE are reported on the testing sets. In Section display the CATE RMSE with horizon h 30 days, Here, we show CATE RMSE results for the Twins dataset with horizon h 180 days in Figure 21 and we can see it indicates similar results as = 30.
samples and repeat all the experiments 10
CATE MASE
T-Learner
S-Learner
Z-Learnor
DR. Le Learner
Double ML.
Caural Forest
Causal Survival Forest
raey SurviTe
Sur vival
S-Leamop Survivat
Matching Surviva vel
Figure 21: CATE RMSE for twin birth data using different estimator families with 180 days
across 10 experimental runs.
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H.2 ACTG 175 HIV CLINICAL TRIAL DATASET
We use data from the AIDS Clinical Trials Group Protocol 175 (ACTG 175) (Hammer et al. 1996). double-blind, randomized controlled trial that compared four treatment regimens in adults infected with HIV type I: monotherapy with zidovudine (ZDV), monotherapy with didanosine (ddI), com- bination therapy with ZDV and ddI, or combination therapy with ZDV and zalcitabine (Zal). The publicly available datase includes 2.139 HIV-infected patients randomized into four groups with assigned treatments: ZDV, ZDV+ddI, ZDV+Zal, and ddl. An event occurrence was defined as the first of either decline in CD4 cell count, an event indicating AIDS progression, or death.
Following Meir et al. 2025). after fetching raw data from the UCI Machine Learning Repository, we change the resolution from days to months and add synthetic censoring based on Bernoulli distribution with parameter p 0.6 + 0.25 Z30, where Z30 is feature that available in the data and indicates whether patient started taking ZDV prior to the assigned treatment, and it is not included in the covariates for CATE estimation. We conduct three pairwise comparisons with ZDV as the bascline treatment (W 0): ZDV vs. ZDV+ddI (HIVI), 1). ZDV vs. ZDV+Zal (HIV2), and ZDV vs. ddl (HIV3). The baseline censoring rate is less than 15% for different treatment groups. After applying the censoring injection procedure from Meir et al. (2025), increasing censoring rates to over 90%. For each treatment group, we establish baseline CATE estimates by running Causal Survival Forests 10 times and averaging the estimated conditional average treatment effects. Since there are many variants of outcome imputation and survival meta-learner families due to different imputation and base learner options, for display purposes in the HIV dataset results, we use a model selection criterion based on closeness (CATE RMSE) to estimation by Causal Survival Forests. We have looked at the results using other variants of same CATE estimator as well, and similar trends are observed.
In Section 4.3 we display the comparisons of CATE estimates between baseline and high-censoring conditions for group HIVI. Here we display the same sets of results for HIV2 and HIV3 groups in Figure 23 Consistent patterns emerge across all three treatment comparisons: Causal Survival Forests produces estimates that cluster tightly around their baseline CATE estimations data be- fore additional censoring injection; outcome imputation methods show higher variation in baseline estimates but more concentrated predictions under high censoring. and survival meta-learners dis- play substantial deviations from the 45-degree line, indicating sensitivity to censoring conditions. The consistency of these patterns across different treatment pairs reinforces the robustness of our findings regarding how different estimator families respond to increased censoring.
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T-Learser
S-Leareer
L-Learner
BR Learner
Douhh Le-HL
Cousal. Forest
Cessal. Survicnl Forest
SurvITE
T-lmarser Sereival
S-Leamer Survival
Matching Servivel
Jnstirs
Samiiir
Figure 22: CATE Estimation comparison between baseline and high-censoring conditions under ZDV ZDV+Zal treatments (HIV2). Each point represents individual patient in test sets, with the dashed diagonal line indicating perfect consistency between baseline CATE estimation and that with the additional censoring injected.
Cossal: Survivel Forest
SurvETE
T-teirser Survival
5-teamer Survival
Matching Survival
D42 Dt. Dewiire
Figure 23: CATE Estimation comparison between baseline and high-censoring conditions under ZDV vs. ddl treatments (HIV3). Each point represents an individual patient in test sets, with the dashed diagonal line indicating perfect consistency between baseline CATE estimation and that with the additional censoring injected.
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I ADDITIONAL INFORMATIVE CENSORING VIA UNOBSERVED CONFOUNDING
In the main paper, we model informative censoring by making censoring times stochastically depen- dent on event times, reflecting realistic scenarios where patients with shorter expected survival may drop out earlier. Here we complement this setting with alternative mechanism where the ignor- able censoring assumption is violated due to unobserved confounding. This extension demonstrates the flexibility of our modular data generation framework.
Data generation process. We follow the same covariate generation procedure as in synthetic datasets: observed covariates X Uniform (0, 1) and an unobserved covariate U ~ Uniform(O, (0, 1). Treatment assignment follows the OBS-UConf configuration, where U enters into both treatment assignment and outcome generation but remains unobserved during estimation.
We focus survival Scenario C (Poisson hazards with medium censoring). Event times and soring times are generated as follows, where w E {0, 1] the treatment indicator:
X(w) = X2 + X3 +6+ 2
0.3 X1 + - 0.3) w +
(7)
T(w) ~ Poisson(X(w))
(8)
x
if S 0.6,
C
(9)
1 < 0.5) otherwise,
where (O, 0.1) adds stochastic variation. The censoring distribution thus depends directly on the unobserved variable U, creating dependence between censoring and survival that cannot be explained away by the observed X alone.
Summary statistics Similar to the other synthetic datasets, we include up to 50,000 samples with treatment assigned according to an observational study mechanism. The treatment rate is 53.9%, the censoring rate is 39.7 99.7% (driven by U/), and the population-Ieve ATE is 0.7737 (computed from the 50,000 samples by averaging the CATEs). This setup mirrors real-world contexts such clinical trials with dropout patterns influenced by latent health status.
Experimental results
We evaluated representative estimators from all three method families. Fig- ure 24 reports CATE RMSE and ATE bias (mean = standard error) across 10 random splits.
Launner
D6 Learapy
Danki m.
Surtiar
Sertty Sertovel
Sarching
I-lenner
S0 Learee
Suatle Me
Furest
Chaut Serveios
borsty percival
(a) RCTX, Ignorability:X, Positivitys/ Igmorable Censoring:
(b) RCTX Ignorability: X. Posilivity:/ Ignorable Censoring:
Figure 24: CATE RMSE (left) and ATE bias (right) under informative censoring induced by unob- served confounding.
The results indicate that Causal Survival Forests and survival meta-learnen with matching tend to perform best under this setting, consistent with findings from the main synthetic datasets.
Extensibility to other settings. Here we illustrate one case: OBS-UConf combined with Sce- nario C. However, the same mechanism be straightforwardly extended to other causal config- urations (c.g., randomized trials with imbalance) and survival scenarios (c.g.. AFT or Cox models). We leave systematic exploration of these additional combinations for future work, but their ease of inclusion highlights the flexibility of SURVHTE-BENCH to accommodate alternative censoring mechanisms.
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Reviews:
[{"review_id": "gnxGJiS2nT", "reviewer": "Reviewer_yGg8", "summary": "The authors propose survHTE-Bench, a benchmark for estimating heterogeneous treatment effects (HTE) with right-censored survival outcomes. The paper summaries 52 estimators across three families, and evaluate them on 40 synthetic datasets, 6 semi-synthetic datasets, 2 real datasets. Results are reported through Borda count rankings, RMSE metrics.", "questions": "1. The benchmark defines CATE in terms of RMST up to a time horizon $h>0$ time horizon $h$. If I am correct, $h$ is the maximum observed time per dataset. If this is the case, $h$ varies across datasets (and splits for some methods), so different runs are literally evaluating different estimates. When censoring is heavy or tails differ, this changes both identifiability and difficulty in a way unrelated to the method, it can confound any cross dataset ranking. Then, there should be a sensitivity report with respect to $h$ and include additional estimates such as median survival. Please clarify this.\n\n2.\tThe benchmark mentions serval references within the direct-survival CATE models in section 2. but  why you only include and evaluate causal survival forest in this family in your experiments? Am I missing the results of other models, for example SurvITE in [Alicia C., et al. 2021 NeurIPS]?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper is well written with a clear scope. The benchmark topic is important and interesting in the study of treatment effect on health science datasets.\n\n2. The paper considers a large set of HTE estimators, the evaluations are done on multiple settings. \n\n3. The paper includes a very complete reproducibilities resources.", "weaknesses": "1. A complete benchmark on HTE with survival datasets is surely needed in the community. There are some benchmark papers on HTE (not on survival setting), including [Crabbé, J., et al. 2022], [Shimoni, Y., et al. 2018], [Kapkiç, A. et al. 2024] and others. However, extending the benchmark on HTE from complete datasets to right-censored datasets can be a weak improvement. There can be overlaps among those benchmarks. I believe a comprehensive benchmark named by survHTE-Bench should include methods and datasets with all types of censoring.\n\nCrabbé, J., Curth, A., Bica, I., & Van Der Schaar, M. (2022). Benchmarking heterogeneous treatment effect models through the lens of interpretability. Advances in Neural Information Processing Systems, 35, 12295-12309.\n\nShimoni, Y., Yanover, C., Karavani, E., & Goldschmnidt, Y. (2018). Benchmarking framework for performance-evaluation of causal inference analysis. arXiv preprint arXiv:1802.05046.\n\nKapkiç, A., Mandal, P., Wan, S., Sheth, P., Gorantla, A., Choi, Y., ... & Candan, K. S. (2024, October). Introducing causalbench: A flexible benchmark framework for causal analysis and machine learning. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management (pp. 5220-5224).\n\n2. Synthetic data design: The data generation process is too simple and not realistic, especially in health science. For example, all five covariates are **independently** generated from Uniform(0,1); treatment assignment is simple and have weak dependence on covariates. The benefits of using simulation studies is we can include all possible settings with ground truth, therefore, the data generation should include more settings, such as low/high dimensional, unbalanced cases, correlated features, causal related features, various tail behaviors, non-smooth hazards, treatment policy with feedbacks and so on.\n\n3. Semi-synthetic data design: I have the similar comments as in weakness 2. The treatment assignment is independent and Bernoulli(0.5). Censoring times are independently drawn from Poisson($\\lambda_c$), $\\lambda_c$ is constant.  The potential outcomes are Poisson with means linearly depends either on $(S,X_{36})$ or $X_{36}$. Semi-synthetic datasets are combinations of real data with reasonable synthetic data, the simple setting on treatment assignment and censoring generation can be non-realistic. \n\n4. Synthetic data design: The violation severity is binary. Authors acknowledge violations are binary (present or absent). But realistic applications require graded severities (e.g., overlap quantified by min propensity, MNAR censoring strength). It would be great if you can provide dose response grids of violation magnitude.\n\n5. I think Twins “ground truth” for survival is debatable. The Twins setting is typically used for counterfactual outcomes like birthweight; “ground truth” for survival times under treatment and control is not fully inherent and is partly constructed (randomized treatment assignment and censoring). The authors should justify why observed twin outcomes constitute true counterfactual survival outcomes and clarify how censoring was constructed (84.8% is extremely high).\n\n6. The benchmark considers multiple assumptions and considers the cases when the assumptions hold or not (binary). However, there are cases when certain assumption is not simply satisfied or not satisfied. In application, we also want sensitivity analysis, for example, if those assumptions are a little bit wrong, how much would the conclusions change? There are methods for such sensitivity analysis, for example, Rosenbaum’s $\\Gamma& for unmeasured cofounding.\n\n7. Methods: The benchmark includes three families of models. This is good. However, there are models that are closely related, but are not included. For example, TMLE, IV-based survival HTE, Dynamic treatment cases, Bayesian survival HTE. Here I list several references.\n\nStitelman, O. M., Wester, C. W., De Gruttola, V., & van der Laan, M. J. (2011). Targeted maximum likelihood estimation of effect modification parameters in survival analysis. The international journal of biostatistics, 7(1), 19.\n\nTchetgen, E. J. T., Walter, S., Vansteelandt, S., Martinussen, T., & Glymour, M. (2015). Instrumental variable estimation in a survival context. Epidemiology, 26(3), 402-410.\n\nCho, H., Holloway, S. T., Couper, D. J., & Kosorok, M. R. (2023). Multi-stage optimal dynamic treatment regimes for survival outcomes with dependent censoring. Biometrika, 110(2), 395-410.\n\nChen, X., Harhay, M. O., Tong, G., & Li, F. (2024). A Bayesian machine learning approach for estimating heterogeneous survivor causal effects: applications to a critical care trial. The annals of applied statistics, 18(1), 350.\n\n8. Borda count ranking averages hide effect sizes and are sensitive to the method set and dataset composition. It would be better to add uncertainty quantification.\n\n9. For a benchmark paper, the evaluation of using only RMSE is restricted. Quantile based treatment effect or other rank based treatment effect would be robust in certain cases. For  survival data, fixed time survival probability difference can be meaningful in clinic study. These alternative considerations would improve the novelty of the benchmark.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kE2OCLVu9d", "reviewer": "Reviewer_Yomt", "summary": "The authors propose a benchmark for evaluating models which estimate a heterogeneous treatment effect from survival data. The benchmark consists of 40 synthetic, 6 semi-synthetic, and 2 real datasets. The synthetic and semi-synthetic datasets include ground truth HTEs which realistically violate standard assumptions in causal inference to different degrees. One of the two real datasets, Twins, is conducted so that one twin receives treatment and one does not; as close to a ground truth as can be obtained in reality. The other dataset is from an HIV clinical trial. The authors also implement 52 methods for survival HTE estimation and compare their efficacy on the benchmark. They find that there is no single dominant method, with the best method frequently depending on which causal inference assumptions are violated. Based on their observations, they provide guidelines suggesting which method or class of methods to use in a given scenario.", "questions": "How were the coefficients chosen for the synthetic data generation? How robust are your conclusions to variations in these coefficients?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The paper is clearly written and easy to follow.\n\nThe proposed benchmark is thorough and does an excellent job of covering many different scenarios of practical relevance for HTE estimation with survival data. The motivation for the construction of the different synthetic datasets (in particular, tying each one to a combination of the \"causal configuration\" and survival analysis setup) makes it clear exactly what is being tested by each synthetic dataset. The semi-synthetic and real datasets are also constructed sensibly. The semi-synthetic data tests a method's ability to cope with more realistic covariate distributions (as the fully synthetic datasets only use uniformly distributed covariates) while still maintaining access to a ground truth CATE. For the real data, the Twins dataset seems to be the closest possible thing to having a ground truth measurement with real data. Modulating the censoring pattern on the HIV clinical trial dataset is an effective method for testing the robustness of each method to censoring on real data without a ground truth. I found Fig. 4 related to this dataset to be particularly interesting, as it shows that *none* of the existing methods have completely desirable behavior in the case of increasing censoring on real-world data. The CATE either changes drastically under increased censoring, or (as in the case of the CSF) the CATE estimate is simply very insensitive to the covariates.\n\nIn addition to providing a consolidated benchmark for HTE estimation with survival data--already useful in its own right to standardize the evaluation of these methods--the authors make good use of their benchmark to derive practical recommendations for the strenghts and weaknesses of existing methods. Access to these results as well as the collected implementations of a large number of relevant baselines should be of great use to other researchers working in this area.", "weaknesses": "While the types of CI assumption violations considered are extensive, the ground truth CATEs used for the synthetic data generation (discussed in Appendix A.3) are somewhat limited. In particular, the functional form of the ground truth consists of mostly linear components, with a couple of instances of quadratic terms, square root terms, or threshold discontinuities. Of particular note is that there are no interaction terms between covariates. Examining the effect of more severe nonlinearities, as well as interactions between the covariates, would strengthen the baselines. There are also a large number of presumably hand-picked constants used to define the ground truth. Some justification for how these particular constants were chosen, or else results showing that the conclusions of the paper are robust to the particular choice of constants, would also help greatly. I believe these are the most pressing issues and I would happily raise my score for the paper if they were addressed.\n\nThe CATE is defined to be the difference of some function of the survival time with and without the binary treatment. This is a reasonable design choice which is common in causal inference settings. However, in practical settings such as the analysis of clinical trials, treatment is often measured as a change in the underlying hazard function, and it is not immediately clear if this quantity can be represented in the form of equation (1).\n\nLastly, as the authors acknowledge, the evaluation is limited to binary, static treatments and static covariates, with time-varying or more complicated treatment variables left for future work. While this is a limitation, I agree with the authors that the scope they consider is already of great value.\n\nTypos:\n1. Lines 82-83: $T_i$ and $\\widetilde{T}_i$ are reversed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Naiq9wWxFK", "reviewer": "Reviewer_qN3T", "summary": "This work introduces a benchmark for evaluating estimators of the CATE in right-censored survival settings. The benchmark considers several violations or near violations of the assumptions that these methods commonly rely on (overlap, ignorability, etc.). The authors then evaluate a variety of existing learners for survival functions, which they classify into 3 categories: outcome imputation, direct methods, and meta-learners.", "questions": "The proposed methods seem to require the set of covariates you're conditioning on in the CATE to be the same as the ones to be used to satisfy the ignorability assumptions. This is somewhat restrictive, as it means that using this CATE in the future requires measuring all of X, which may be infeasible. For non-survival CATE estimation, people get around this by instead considering the CATE conditional on a user-specified subvector V of X. The identifiability assumptions remain unchanged, and many methods (e.g., DR-learner) also work in these cases. Can your benchmark be used in these settings as well?\n\nWould it be easy to extend your benchmark to other types of coarsened data - e.g., left-truncated data?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "To my knowledge, this is the first large-scale benchmark for CATE estimation in the context of right-censored outcomes.\n\nThe benchmark covers a wide mix of datasets, including semi-synthetic and real ones.\n\nReports a comprehensive set of metrics.\n\nProvides reproducible code.", "weaknesses": "The provided README in the anonymized GitHub doesn't make it clear how to add new learners to the benchmark. For this benchmark to be widely adopted, this should be described (and made as simple as possible).\n\nMinor point, but TMLE can't generally be used to estimate the CATE. The parameter isn't smooth enough for TMLE to be used to estimate it. An exception to this occurs when measuring effect modification with respect to a discrete summary of the baseline covariates (e.g., Stitelman et al., 2010), but that doesn't seem to be your main case of interest.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mrpcJUcMaP", "reviewer": "Reviewer_FuYz", "summary": "This paper introduces a comprehensive benchmark designed to evaluate methods estimating heterogeneous treatment effects (HTEs) from (right-censored) survival data. Estimating HTEs in survival analysis is vital for applications such as precision medicine but remains challenging due to censoring, unobserved counterfactuals, and complex modeling assumptions. This paper addresses these challenges by providing a unified categorization of survival HTE methods into three families—outcome imputation, direct-survival CATE models, and survival meta-learners—along with modular implementations of their variants. It also includes synthetic datasets with known ground-truth HTEs that systematically vary causal assumptions (e.g., randomization, confounding, positivity, informative censoring) and survival dynamics (e.g., Cox, AFT, Poisson models with varying censoring rates). Additionally, it offers multiple semi-synthetic datasets and two real-world datasets.", "questions": "-\tIf ground-truth hazard functions are available, it would be more meaningful to evaluate HTE performance with respect to the hazard functions themselves. Since many of the evaluated methods are capable of directly estimating conditional hazards from data, it is unclear why these performance results are not reported in the paper.\n-\tRegarding Weakness 2, it remains unclear how the benchmark results can be practically leveraged when applying the methods to new datasets or models.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-\tAddresses a Critical Need: The paper tackles a significant gap in the causal inference and survival analysis literature -- the lack of standardized evaluation practices for HTE estimation with survival data. \n-\tThe benchmark incorporates multiple data types (synthetic, semi-synthetic, real). The synthetic data explores a wide range of crucial factors: different causal assumption violations (i.e., confounding, positivity, informative censoring) and commonly used survival/censoring distributions (Cox, AFT, Poisson).", "weaknesses": "Major comments:\n\n-\tLimited synthetic data generation processes: The synthetic datasets are restricted to three survival time generation mechanisms—Cox, AFT, and Poisson—which may not capture more complex, non-parametric scenarios. For instance, SurvITE defines discrete hazards and samples time-to-event or censoring outcomes based on those hazards. Also, the validity and representativeness of such synthetic data remain unclear. In particular, how treatment effects, selection biases, and covariate shifts influence the generated time-to-event outcomes is not well articulated, as the datasets are primarily described in terms of their underlying hazard functions.\n- Lack of actionable insights from the benchmark: The benchmark results do not provide sufficient insight into how model design decisions should be made based on the findings. As a result, the analysis feels largely descriptive rather than being guided by principled intuitions or hypotheses about model behavior. The paper could better highlight how specific model characteristics or data properties influence performance, offering clearer guidance for model selection and application.\n-\tThe paper introduces a category of \"Direct-Survival CATE Models\", but, deep survival models that directly estimate the conditional average treatment effect (CATE) (such as SurvITE) on survival outcomes are not included. \n-\tAlthough the paper claims to provide a unified framework for handling various survival models, it does not address models that directly predict time-to-event outcomes (e.g., Chafuwa et al., 2021). It is unclear how such models would be integrated into the proposed benchmark.\n-\tEstimates of hazard or survival functions can vary substantially depending on the chosen time horizon, yet the benchmark does not clearly specify or analyze how this dependency affects the evaluation results.\n\nMinor comments:\n\n-\tVisualizations (e.g., conditional hazard and survival function plots) for synthetic datasets under different causal configurations would help clarify and validate the underlying data generation processes.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ppuuECEYXY", "reviewer": "Reviewer_m4FZ", "summary": "This paper is a benchmark comparing many methods for time-dependent conditional average treatment estimation, which is key in survival analysis.", "questions": "Why is there no RCT scenario with non-ignorable (informative) censoring? Since informative censoring can occur even in randomized studies, such a configuration would seem important for completeness.\n\nWould it be possible to present the results more clearly by scenario, explicitly showing which methods perform best under each assumption violation (e.g., lack of ignorability, positivity, or informative censoring)? This would make the benchmark’s insights much easier to interpret.\n\nWhat is the motivation for including IPCW-based estimators in settings where censoring is already ignorable? Their inclusion in those cases seems less informative, as IPCW adjustments are designed specifically for informative censoring scenarios.\n\nHow do you interpret the strong performance of DeepSurv-based meta-learners compared to Double-ML in high-censoring settings?\n\nCould you explain why Double-ML performs relatively poorly on the Twins dataset, despite ranking highly in synthetic experiments? Does this reflect differences in sample size, feature distribution, or unmeasured confounding?\n\nCould you include more references to existing papers that explicitly state which methods they use for survival CATE estimation? This would help situate your benchmark within the current methodological landscape.\n\nWould it be possible to provide clearer results by scenario, highlighting which methods work best under which assumption violations?\n\nIn Figure 1, DeepSurv-based methods achieve overall strongest RMSE performance across many scenarios, likely due to their overparameterization and resulting robustness to model misspecification. How do these methods perform in simpler, well-specified settings such as the Cox proportional hazards scenario? Do they still outperform other approaches when the underlying model assumptions hold?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "This paper tackles the important evaluation of the plural methods existing for HTE with survival outcomes. The benchmark evaluates methods under a grid of relevant synthetic scenarios in a structured way, and on real-world datasets.", "weaknesses": "While the paper presents a valuable and ambitious benchmarking effort, I found it somewhat difficult to read due to repetition, particularly concerning the repeated description of the three families of survival HTE estimators. Streamlining these sections could make the paper more concise and readable.\n\nA major omission in the related work is the lack of reference to existing benchmarks for survival ATE, such as [1]. This recent contribution on causal inference for survival outcomes and meta-learning estimators is highly relevant to the present study. Including and situating the current benchmark within that context would strengthen the paper’s positioning.\n\nIn Table 1, the RCT/Observational distinction is presented as an assumption being held or violated, whereas it is in fact a study design choice rather than an assumption. I would recommend removing that column or clearly separating design factors from causal assumptions.\n\nRegarding the simulation scenarios, the rationale for comparing RCTs with 50% versus 5% treated participants is not entirely clear. Since randomization guarantees ignorability regardless of treatment imbalance, it is not obvious what this variation adds conceptually beyond a variance stress test. Similarly, it is surprising that there is no RCT scenario with non-ignorable censoring, given that informative censoring can occur even in randomized studies.\n\nThere is also a typo at line 227, where “2,500 points” is reported twice.\n\nConceptually, the description of informative censoring is somewhat unclear. The paper defines A4 as conditional independence between censoring and event time given covariates and treatment, but it remains ambiguous how this assumption is violated across scenarios (e.g., whether censoring depends on T directly, on unobserved confounders, or both). In the causal configurations labeled A–D, several aspects appear to change simultaneously, making it difficult to isolate the effect of each violation. Similarly, in Figure 2, it is confusing that the paper refers to “Scenario C” while ignorable and non-ignorable censoring seem to coexist.\n\nFigure 1 is not very easy to read; in addition to being small, it may not fully respect the ICLR template in terms of spacing between the plot and caption. Moreover, I am not convinced that evaluating estimators’ average performance across all scenarios is particularly informative. It would be much more insightful to emphasize “which method works best under which conditions.” In particular, comparing IPCW-based estimators outside of the informative censoring (InfC) settings does not seem meaningful, since those estimators are specifically designed for that violation.\n\nFrom a results standpoint, Figure 2 shows relatively small differences in RMSE across estimators, suggesting that performance gaps may not be statistically significant—perhaps because ten repetitions are insufficient for stable estimates.\n\nOverall, I find that a great deal of work was put into this paper, but more attention is needed to the presentation and analysis of results, so that the article can better answer questions such as “which method works best for a given scenario?” Knowing which method performs best on average is less informative, since some assumptions are testable and practitioners often operate under known or partially known conditions.\n\nFinally, while the benchmark is well implemented, it remains somewhat descriptive. The paper would benefit from a stronger analytical component—focusing less on global rankings and more on interpretable insights about which methods are most reliable under specific types of assumption violations. This would make the contribution more actionable for practitioners.\n\nAlso, I do not really see a large difference in RMSEs in Figure 2 across estimators—perhaps ten repeats is not sufficient for clear differentiation.\n\nFinally, I am willing to increase my grade if the authors answer my concerns, especially concerning the \"when does each method works best\" issue.\n\n[1] Voinot, Charlotte, et al. “Causal survival analysis, Estimation of the Average Treatment Effect (ATE): Practical Recommendations.” arXiv preprint arXiv:2501.05836 (2025).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)