SurvivalPFN, a prior-data fitted network that amortizes Bayesian survival prediction via in-context learning, is pretrained on synthetic right-censored data-generating processes that assume event and censoring times are conditionally independent given covariates; under dependent censoring the event-time distribution is not nonparametrically identifiable from observed data alone, and the method is invalid. The open problem is to construct an identifiable dependent-censoring formulation of amortized in-context survival prediction — a prior over synthetic data-generating processes in which the event time and censoring time are dependent given covariates and the inference target remains identifiable — and to pretrain a prior-data fitted network on such a prior that performs valid, calibrated amortized posterior survival inference on datasets with dependent censoring, where SurvivalPFN and all current tabular survival foundation models fail.

Background

Survival analysis models the time until an event of interest (e.g., patient death, customer churn), where for some individuals only a lower bound on that time is observed — an event known as right censoring (for instance, a study ends before the event occurs, so one observes the censoring time rather than the event time). Classical estimators such as the Kaplan–Meier curve (a nonparametric step-function estimate of the survival probability over time) and the Cox proportional-hazards model (a regression model relating event risk to covariates) rely on an independent-censoring assumption: conditional on covariates, the event time and the censoring time are independent. When this fails — when sicker patients are also more likely to drop out of follow-up — the observed-data likelihood confounds the two processes, and without further assumptions the event-time distribution is not nonparametrically identifiable: many different joint distributions of (event time, censoring time) produce exactly the same observed data. Copulas (functions coupling marginal distributions into a joint distribution via a dependence parameter) are the standard device for modeling such dependence; the classical copula-graphic estimators recover the marginal survival function only when the copula (the dependence structure) is known, and recent deep models have broadened this — Foomani et al. (UAI 2023) built per-dataset copula-based deep survival models relaxing conditional independence, and Zhang, Ling and Zhang (AAAI 2024) proved identifiability of a deep copula-based model under a broad family of copulas and survival distributions without requiring the practitioner to specify the ground-truth copula. In parallel, prior-data fitted networks (PFNs) — transformers trained once on large corpora of synthetic datasets sampled from a prior, so that Bayesian posterior prediction on a new dataset happens in-context, in a single forward pass without retraining (Müller et al., 2022; TabPFN, Hollmann et al., Nature 2025) — have been extended to censored outcomes. SurvivalPFN (Qi, Balazadeh, Cooper, Greiner and Krishnan, arXiv:2605.15488, 2026) pretrains a PFN on a diverse family of synthetic, identifiable, right-censored data-generating processes and matches or beats established survival models across 61 datasets without any per-dataset fitting. Its validity, however, is tied to conditional independent censoring: the pretraining prior only generates identifiable DGPs under that assumption. The authors state explicitly that under dependent censoring the method is not valid, and that extending it to identifiable dependent-censoring priors, such as copula-based approaches, is an important open direction. Notably, the two existing deep copula censoring models are per-dataset trained, so the question of what prior family over dependent-censored synthetic DGPs supports valid amortized (pretrained, in-context) inference is untouched: it couples the statistical identifiability question with the PFN questions of prior design and posterior-predictive consistency.

Problem Statement

Construct an identifiable dependent-censoring formulation of amortized in-context survival prediction, as called for by the SurvivalPFN authors. Concretely: (1) define a prior over synthetic right-censored data-generating processes in which the event time and the censoring time are dependent given covariates, such that the inference target (the conditional event-time, i.e., survival, distribution) is identifiable from observed right-censored data under stated assumptions; (2) pretrain a prior-data fitted network on datasets sampled from this prior, so that amortized Bayesian survival prediction still happens in a single forward pass without per-dataset fitting; and (3) demonstrate that the resulting model performs valid inference under dependent censoring — calibrated posterior survival distributions and consistency as the number of in-context observations grows — on data-generating processes with genuine event-censoring dependence, in regimes where SurvivalPFN and other current amortized survival models are invalid or biased. Steps (1)–(3) form a single pipeline and must be completed jointly for this branch to count as resolved: an identifiability result for a prior alone (1), without the pretrained network (2) and the demonstration of valid inference (3), is not a resolution. An acceptable theoretical alternative is a rigorous characterization — or impossibility result — for which dependent-censoring prior families admit identifiable, consistently learnable amortized inference targets; on this branch the task is resolved only by a complete classification — of which prior-family assumptions yield identifiable, consistently learnable amortized targets and which do not — or by an impossibility result proving that no such prior family exists. The source's second named limitation, long-context scalability of PFN-style models on large datasets, is a separable engineering direction recorded as context and not part of this problem.

References

  1. Shi-ang Qi, Vahid Balazadeh, Michael Cooper, Russell Greiner, Rahul G. Krishnan (2026). SurvivalPFN: Amortizing Survival Prediction via In-Context Bayesian Inference. arXiv:2605.15488, DOI 10.48550/arxiv.2605.15488, https://arxiv.org/abs/2605.15488
  2. Weijia Zhang, Chun Kai Ling, Xuanhui Zhang (2024). Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees. AAAI Conference on Artificial Intelligence, vol. 38, pp. 20613-20621, DOI 10.1609/aaai.v38i18.30047, arXiv:2312.15566, https://arxiv.org/abs/2312.15566
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