Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks

Dmitrii Seletkov; Paul Hager; Georgios Kaissis; Rickmer Braren; Daniel Rueckert; Raphael Rehms

cs.LGMar 31, 2026

Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks

Authors: Dmitrii Seletkov, Paul Hager, Georgios Kaissis, Rickmer Braren, Daniel Rueckert, Raphael Rehms

Organizations: Institute of Diagnostic and Interventional Radiology, Technical University of Munich, Germany · Chair for AI in Healthcare and Medicine, Technical University of Munich, Germany · Hasso Plattner Institute for Digital Engineering, University of Potsdam, Germany · University Hospital Hamburg-Eppendorf, Germany ·

Abstract

Survival analysis is crucial for many medical applications, but remains challenging for modern machine learning due to limited data, censoring, and the heterogeneity of tabular covariates. While the prior-fitted paradigm, which relies on pretraining models on large collections of synthetic datasets, has recently facilitated tabular foundation models for classification and regression, its suitability for time-to-event modeling remains unclear. We propose a flexible survival data generation framework that defines a rich survival prior with explicit control over covariates and time-event distributions. Building on this prior, we introduce Survival In-Context (SIC), a prior-fitted in-context learning model for survival analysis that is pretrained exclusively on synthetic data. SIC is trained to approximate Bayesian posterior predictive inference under the synthetic survival prior, enabling individualized survival prediction in a single forward pass, requiring no task-specific training or hyperparameter tuning. Across a broad evaluation on real-world survival datasets, SIC achieves competitive or superior performance compared to classical and deep survival models, particularly in small and medium-sized data regimes, highlighting the promise of a prior-fitted paradigm for survival analysis. The code and pretrained models will be made available upon publication.

Figures & tables

Figure 1: Survival In-context (SIC) method contains two stages. (I) Synthetic Data Generation using Structural Causal Models (SCMs) for the generation of (I.A) covariates X and the associated label nodes $\eta$ , followed by (I.B) two proposed survival priors to generate time-event labels: continuous (I.B.1) with the survival function parametrization $H_{0}^{-1}(*,\alpha,\beta)$ and discrete (I.B.2) with Monotonic Positive Network [ 66 ] $f_{\omega}$ . (II) In-context learning on synthetic data with a specialized time-event embedding and survival head and loss. Created in https://BioRender.com .

Figure 2: Visualization of a batch of 512 generated datasets using SCM $\eta_{1}=X_{1}+X_{2}\cdot X_{3}$ and $\eta_{2}=X_{1}\cdot X_{2}$ for continuous (upper) and discrete (lower) survival priors: time-dependent C-index estimated from fit CoxPH models (left), Kaplan–Meier curves (middle), and the underlying event survival curves on the normalized time scale. The proposed synthetic data generation methods demonstrate the ability to generate diverse survival curve patterns and outcome complexity.

Figure 3: Time-dependent C-index performance (mean and std) across 5 folds on 12 real-world datasets. The proposed Survival In-context (SIC) method achieves comparable performance to the baselines CoxPH [ 16 ] , DeepHit [ 45 ] , DeepSurv [ 36 ] , XGB [ 14 ] , RSF [ 33 ] , ConSurv [ 46 ] , TabICL [ 63 ] + Stacking [ 17 ] . SIC does not require hyperparameter tuning, whereas all baselines are tuned with 100 trials. * indicates p-value $<$ 0.05 for the two-sided t-test of SIC compared to the baselines.

Figure 4: Dataset-wise method ranks (best = 1) across 12 datasets, ordered by dataset size. The proposed Survival In-context (SIC) method shows the highest mean ( $\star$ ) and median ( $\triangle)$ rank compared to the baselines CoxPH [ 16 ] , DeepHit [ 45 ] , DeepSurv [ 36 ] , XGB [ 14 ] , RSF [ 33 ] , ConSurv [ 46 ] , TabICL [ 63 ] + Stacking [ 17 ] .

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Distribution	$H_{0}^{-1}(y)$
Weibull	$\displaystyle\alpha\,y^{1/\beta}\text{; }\alpha\ >0\text{, }\beta>0$
Gompertz	$\displaystyle\frac{1}{\alpha}\,\ln\!\left(1+\frac{\alpha}{\beta}\,y\right)\text{; }\alpha\ >0\text{, }\beta\neq 0$
Lognormal	$\displaystyle\exp\!\Big(\alpha+\beta\,\Phi^{-1}(1-e^{-y})\Big)\text{; }\alpha\ >0$
Log-logistic	$\displaystyle\alpha\,\big(e^{y}-1\big)^{1/\beta}\text{; }\alpha\ >0\text{, }\beta>0$
Birnbaum–Saunders	$\displaystyle\alpha\left[\tfrac{1}{2}\Big(\beta\,\Phi^{-1}(1-e^{-y})+\sqrt{(\beta\,\Phi^{-1}(1-e^{-y}))^{2}+4}\Big)\right]^{2}\text{; }\alpha\ >0\text{, }\beta>0$

Appendix

Table 1: Inverse cumulative hazard

H_{0}^{-1}(y)

for baseline survival distributions.

Figure 5: Visualization of control parameters for a discrete survival prior: survival (left) and Kaplan-Meier (right) curves for a batch of 100 datasets.

Dataset	#samples	#features	Event rate
VETERAN	137	6	93.4%
LUNG	288	10	72.4%
PBC	312	20	44.9%
WHAS500	500	14	43.0%
GBSG2	686	9	43.6%
AIDS	1,151	11	8.3%

Appendix

Table 2: Dataset statistics. UNOS and SEER datasets have restricted access and exceed the pretraining prior (sample size) of SIC.

Model	Hyperparameter	Domain
Cox [ 16 ]	l1_ratio	[0.0, 1.0]
	penalizer	[1e-6, 1]
DeepSurv [ 36 ]	optimizer	{adam, sgd}
	weight_decay	[1e-6, 1e-2]
	momentum	[0.0, 0.9]
	lr	[1e-5, 1e-2]

Appendix

Table 3: Summary of hyperparameter search spaces

Dataset	SIC	CoxPH	DeepSurv	DeepHit	XGB	RSF	TabICL + Stacking	Consurv
VETERAN	0.720 (0.020)	0.724 (0.039)	0.687 (0.044)	0.632 (0.105)	0.669 ∗ (0.031)	0.686 (0.044)	0.660 (0.076)	0.586 ∗ (0.056)
LUNG	0.615 (0.060)	0.615 (0.053)	0.577 (0.106)	0.514 (0.075)	0.562 ∗ (0.074)	0.587 ∗ (0.072)	0.565 (0.032)	0.606 (0.027)
PBC	0.819 (0.067)	0.790 (0.049)	0.793 (0.060)	0.812 (0.064)	0.814 (0.056)	0.808 (0.062)	0.747 ∗ (0.072)	0.790 (0.062)
WHAS500	0.757 (0.026)	0.766 (0.037)	0.754 (0.039)	0.765 (0.026)	0.758 (0.043)	0.773 (0.009)	0.665 ∗ (0.036)	0.747 (0.041)
GBSG2	0.691 (0.040)	0.680 (0.024)	0.656 (0.076)	0.667 (0.050)	0.671 (0.039)	0.681 (0.037)	0.558 ∗ (0.034)	0.658 ∗ (0.035)
AIDS	0.743 (0.046)	0.743 (0.030)	0.662 (0.072)	0.685 (0.073)	0.735 (0.042)	0.715 (0.048)	0.670 (0.057)	0.755 (0.026)

Appendix

Table 4: Time-dependent C-index (mean (std) across 5 folds). ∗ indicates paired t-test significance vs. SIC (

\alpha=0.05

Figure 6: Time-dependent C-index of SIC framework with different Survival Priors : Discrete-only, Continuous-only, and Mix of both (main option used in evaluation).

Dataset	SIC	CoxPH	DeepSurv	DeepHit	XGB	RSF	TabICL + Stacking	Consurv
UNOS	0.571 (0.004)	0.589 ∗ (0.005)	0.595 ∗ (0.005)	0.611 ∗ (0.006)	0.599 ∗ (0.006)	–	0.529 ∗ (0.013)	0.595 ∗ (0.004)
SEER	0.840 (0.004)	0.820 ∗ (0.003)	0.848 ∗ (0.005)	0.853 ∗ (0.004)	0.867 ∗ (0.003)	–	0.804 ∗ (0.004)	0.850 ∗ (0.004)

Appendix

Table 5: Time-dependent C-index (mean (std) across 5 folds). ∗ indicates paired t-test significance vs. SIC (

\alpha=0.05

). Consurv hyperparameter search is reduced to 20 trials compared to the other baselines due to time constraints. – indicates failed experiments (RSF outputs OOM error using sksurv [ 60 ] for larger datasets).

Figure 7: Time-dependent C-index of SIC framework with different discretization: 10 (main option used in evaluation), 50, and 100 bins.

Figure 8: Time-dependent C-index of SIC framework with different Survival Heads : DeepHit (main option used in evaluation), DeepSurv [ 36 ] and DeepEH [ 76 ] . The original implementation of the DeepEH method outputs NaN values for FLCHAIN dataset. This should not be considered for comparison.

Figure 9: D-Calibration performance (number of misscalibrated folds per dataset) across 5 folds on 12 real-world datasets. The Survival In-context (SIC) is a proposed method. SIC-PostCal is the SIC calibrated with CiPOT [ 62 ] . The baselines: CoxPH [ 16 ] , DeepHit [ 45 ] , DeepSurv [ 36 ] , XGB [ 14 ] , RSF [ 33 ] , ConSurv [ 46 ] , TabICL [ 63 ] + Stacking [ 17 ] . SIC does not require hyperparameter tuning, whereas all baselines are tuned with 100 trials. * indicates p-value $<$ 0.05 for the two-sided t-test of SIC compared to the baselines.

Figure 10: Integrated Brier Score performance (mean and std) across 5 folds on 12 real-world datasets. The Survival In-context (SIC) is a proposed method. SIC-PostCal is the SIC calibrated with CiPOT [ 62 ] . The baselines: CoxPH [ 16 ] , DeepHit [ 45 ] , DeepSurv [ 36 ] , XGB [ 14 ] , RSF [ 33 ] , ConSurv [ 46 ] , TabICL [ 63 ] + Stacking [ 17 ] . SIC does not require hyperparameter tuning, whereas all baselines are tuned with 100 trials. * indicates p-value $<$ 0.05 for the two-sided t-test of SIC compared to the baselines.

Dataset	SIC	SIC-PostCal	Delta mean (SIC-PostCal - SIC)
VETERAN	0.720 $\pm$ 0.020	0.721 $\pm$ 0.020	+0.001
LUNG	0.615 $\pm$ 0.060	0.615 $\pm$ 0.057	0.000
PBC	0.819 $\pm$ 0.067	0.821 $\pm$ 0.065	+0.002
WHAS500	0.757 $\pm$ 0.026	0.757 $\pm$ 0.030	0.000
GBSG2	0.691 $\pm$ 0.040	0.690 $\pm$ 0.040	-0.001
AIDS	0.743 $\pm$ 0.046	0.707 $\pm$ 0.092	-0.036

Appendix

Table 6: The difference in time-dependent C-intex performance between the proposed Survival In-context (SIC) and SIC after CiPOT [ 62 ] post-calibration (SIC-PostCal).

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