Doubly Robust Learning of Heterogeneous Survival Treatment Effects under Time-Varying Treatments

Tomàs Garriga; Munib Mesinovic; Luke De Bretton-Gordon; Gerard Sanz; Axel Brando; Tingting Zhu

cs.LGOct 19, 2026

Doubly Robust Learning of Heterogeneous Survival Treatment Effects under Time-Varying Treatments

Authors: Tomàs Garriga, Munib Mesinovic, Luke De Bretton-Gordon, Gerard Sanz, Axel Brando, Tingting Zhu

Organizations: Novartis · Barcelona Supercomputing Center · Universitat Politècnica de Catalunya · University of Oxford

Abstract

Estimating heterogeneous survival treatment effects (HSTEs) from time-to-event data under time-varying treatments is important in fields such as medicine (e.g., to decide which sequence of treatments is better in terms of survival probability). However, this task is challenging because treatment decisions, patient characteristics, and censoring probability often evolve together, requiring sequential adjustment for both treatments and censoring. Existing survival learners mostly consider a single baseline treatment assignment, while longitudinal treatment-effect learners typically assume uncensored outcomes. In this paper, we introduce a novel doubly robust learner for heterogeneous survival treatment effects under time-varying treatments and history-dependent censoring. Our framework separates the intervention window from the survival horizon, with treatment prescribed for a finite period, after which care follows its natural course. We further establish the favorable theoretical properties of Neyman-orthogonality, rate double robustness and quasi-oracle efficiency. The framework accommodates flexible machine learning models for nuisance estimation and treatment-effect regression. We evaluate our learners through several numerical experiments, demonstrating their effectiveness.

Figures & tables

Figure 1: Longitudinal intervention and survival estimand. At landmark

t

, treatment is prescribed according to

\bar{a}_{t:t+L-1}

for

L

decision times. Treatment subsequently follows its natural assignment mechanism, while survival is evaluated at

t+\tau

, where

\tau\geq L

Method	$L{=}2,\tau{=}2$	$L{=}2,\tau{=}3$	$L{=}2,\tau{=}4$	$L{=}3,\tau{=}8$
PI	0.058 $\pm$ 0.002	0.054 $\pm$ 0.005	0.047 $\pm$ 0.011	0.047 $\pm$ 0.020
RA	0.063 $\pm$ 0.009	0.055 $\pm$ 0.008	0.048 $\pm$ 0.011	0.050 $\pm$ 0.021
IPW	0.081 $\pm$ 0.013	0.086 $\pm$ 0.029	0.084 $\pm$ 0.023	0.237 $\pm$ 0.073
TV-SurvCaus	0.058 $\pm$ 0.003	0.054 $\pm$ 0.003	0.049 $\pm$ 0.003	0.051 $\pm$ 0.005
DR	0.030 $\pm$ 0.008	0.037 $\pm$ 0.013	0.031 $\pm$ 0.011	0.043 $\pm$ 0.008
DR improvement (%)	48.3	31.5	34.0	8.5

Table 1: Fully synthetic dataset.

Method	$L{=}2,\tau{=}2$	$L{=}2,\tau{=}3$	$L{=}2,\tau{=}4$	$L{=}3,\tau{=}8$
PI	0.073 $\pm$ 0.007	0.069 $\pm$ 0.011	0.063 $\pm$ 0.007	0.071 $\pm$ 0.014
RA	0.074 $\pm$ 0.012	0.068 $\pm$ 0.011	0.065 $\pm$ 0.007	0.071 $\pm$ 0.014
IPW	0.099 $\pm$ 0.007	0.116 $\pm$ 0.034	0.105 $\pm$ 0.048	0.327 $\pm$ 0.044
TV-SurvCaus	0.073 $\pm$ 0.001	0.071 $\pm$ 0.003	0.066 $\pm$ 0.002	0.074 $\pm$ 0.004
DR	0.046 $\pm$ 0.008	0.048 $\pm$ 0.008	0.047 $\pm$ 0.006	0.055 $\pm$ 0.011
DR improvement (%)	37.0	29.4	25.4	22.5

Table 2: Semi-synthetic dataset.

Method	( $L=2,\tau=8$ )	( $L=2,\tau=16$ )
PI	0.0552 $\pm$ 0.0010	0.0841 $\pm$ 0.0014
RA	0.0598 $\pm$ 0.0025	0.0882 $\pm$ 0.0029
IPW	0.0589 $\pm$ 0.0013	0.0836 $\pm$ 0.0031
TV-SurvCaus	0.0634 $\pm$ 0.0006	0.0945 $\pm$ 0.0027
DR	0.0552 $\pm$ 0.0020	0.0788 $\pm$ 0.0015
DR improvement (%)	0.0	5.7

Table 3: Real-world dataset.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description	Value
$K$	decision times	32
$\alpha$	overlap strength	0.75
$\gamma$	effect heterogeneity strength	3.0
$\phi$	treatment–confounder feedback strength	0.8
$\beta_{0}$	event intercept	$-4.0$
$c_{0}$	censoring intercept	5.2

Appendix

Table 4: Parameters of the synthetic data-generating process.

$(L,\tau)$	Best competitor	DR $-$ best competitor	Paired 95% interval
$(2,2)$	TV-SurvCaus	$-0.0272$	$[-0.0360,-0.0183]$
$(2,3)$	PI	$-0.0167$	$[-0.0323,-0.0011]$
$(2,4)$	PI	$-0.0157$	$[-0.0302,-0.0012]$
$(3,8)$	PI	$-0.0042$	$[-0.0181,0.0097]$

Appendix

Table 5: Paired difference in RMSE between DR and the competing learner with the lowest mean on the fully synthetic benchmark, with its paired 95%

t

-interval over five repetitions; a negative value favors DR.

$(L,\tau)$	Best competitor	DR $-$ best competitor	Paired 95% interval
$(2,2)$	TV-SurvCaus	$-0.0273$	$[-0.0357,-0.0190]$
$(2,3)$	RA	$-0.0199$	$[-0.0342,-0.0055]$
$(2,4)$	PI	$-0.0159$	$[-0.0278,-0.0040]$
$(3,8)$	PI	$-0.0160$	$[-0.0315,-0.0004]$

Appendix

Table 6: Paired difference in RMSE between DR and the competing learner with the lowest mean on the semi-synthetic MIMIC-IV benchmark, with its paired 95%

t

-interval over five repetitions; a negative value favors DR.

Setting	Cens.	PI	RA	IPW	TV-SurvCaus	DR	Rel. improv.	DR $-$ best competitor
Short horizon: $(L,\tau)=(2,2)$
Default	0%	0.069	0.071	0.141	0.073	0.041	+40.6%	$-0.0273$ $[-0.0403,-0.0143]$ (PI)
	20%	0.071	0.074	0.131	0.073	0.042	+40.8%	$-0.0292$ $[-0.0431,-0.0153]$ (PI)
	40%	0.073	0.075	0.178	0.073	0.041	+43.8%	$-0.0318$ $[-0.0357,-0.0278]$ (TV)
Sharp	0%	0.074	0.078	0.293	0.073	0.044	+39.7%	$-0.0291$ $[-0.0368,-0.0213]$ (TV)
	20%	0.071	0.074	0.311	0.073	0.041	+42.3%	$-0.0296$ $[-0.0331,-0.0262]$ (PI)

Appendix

Table 7: RMSE of the estimated HSTE under the stress-test conditions, averaged over five repetitions (lower is better; lowest mean in bold). Default and Sharp denote the standard and stronger history-dependent treatment-assignment mechanisms, respectively. Cens. denotes the target proportion censored before the eight-step horizon; Higher event denotes the increased-event-rate condition. Rel. improv. is the percentage reduction in RMSE of DR relative to the best competing learner; positive values favor DR. The last column gives the paired difference in RMSE between DR and the competing learner with the lowest mean (named in parentheses, with TV for TV-SurvCaus), with its 95%

t

-interval over the five repetitions; a negative value favors DR.

Horizon	Best competitor	DR $-$ best competitor	Paired 95% interval
24 hours ( $\tau=8$ )	PI	$-0.0001$	$[-0.0013,0.0012]$
48 hours ( $\tau=16$ )	IPW	$-0.0038$	$[-0.0059,-0.0018]$

Appendix

Table 8: Paired difference in weighted Brier score between DR and the competing learner with the lowest mean under continued vasopressors for the next two steps (

L=2

) in the held-out MIMIC-IV test cohort. The 95% bootstrap intervals over test patients are computed on seed-averaged predictions with the weights held fixed; a negative value favors DR.

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SurvHTE-Bench: A Benchmark for Heterogeneous Treatment Effect Estimation in Survival Analysis

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Machine Learning Department & Heinz College, Carnegie Mellon University · Heinz College, Carnegie Mellon University · National Library of Medicine, National Institutes of Health

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Estimating heterogeneous treatment effects (HTEs) from right-censored survival data is critical in high-stakes applications such as precision medicine and individualized policy-making. Yet, the survival analysis setting poses unique challenges for HTE estimation due to censoring, unobserved counterfactuals, and complex identification assumptions. Despite recent advances, from Causal Survival Forests to survival meta-learners and outcome imputation approaches, evaluation practices remain fragmented and inconsistent. We introduce SurvHTE-Bench, the first comprehensive benchmark for HTE estimation with censored outcomes. The benchmark spans (i) a modular suite of synthetic datasets with known ground truth, systematically varying causal assumptions and survival dynamics, (ii) semi-synthetic datasets that pair real-world covariates with simulated treatments and outcomes, and (iii) real-world datasets from a twin study (with known ground truth) and from an HIV clinical trial. Across synthetic, semi-synthetic, and real-world settings, we provide the first rigorous comparison of survival HTE methods under diverse conditions and realistic assumption violations. SurvHTE-Bench establishes a foundation for fair, reproducible, and extensible evaluation of causal survival methods. The data and code of our benchmark are available at: https://github.com/Shahriarnz14/SurvHTE-Bench .

Abstract

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