In survival analysis the way covariates act on the risk of an event often differs between early and late failure times, yet hazard- and mean-based summaries collapse this variation into a single number. Quantile-based modeling instead describes the full conditional distribution on the original time scale, but existing censored-data methods are either inflexible or produce logically inconsistent crossing quantile curves. We propose a Censored Non-crossing Quantile (CNQ) framework for right-censored data that jointly estimates several conditional survival quantiles and guarantees valid ordering by construction, with flexibility supplied by Kolmogorov-Arnold and Transformer backbones, and we establish a finite-sample excess-risk bound holding jointly across all fitted quantile levels. Across 27 simulation settings and six cohorts the framework attains lower pinball loss than quantile-, hazard- and tree-based competitors whenever the conditional distribution is asymmetric, with interval coverage closer to nominal on all six. In two clinical case studies (METABRIC, breast cancer; FLCHAIN, population mortality) it recovers covariate effects that vary across the survival distribution and would be hidden by a single hazard ratio, and yields coherent individualized quantile milestones. Code: https://github.com/BIG-S2/deepcnq
Recovering geographic variation in survival requires separating spatial risk from patients' clinical characteristics, a problem complicated by prognostic covariates that are themselves spatially structured. We develop a nonparametric two-stage method for this separation. A clinical survival tree fit to the covariates alone supplies leaf Nelson-Aalen cumulative hazard residuals, transferring the censored survival structure to a clinically adjusted scale without imposing a functional form on the clinical hazard, and a second tree fit to these residuals on the coordinates recovers the spatial structure. Both stages are kernel dipole-splitting survival trees, so the resulting spatial risk map is piecewise constant, with sharp, possibly curved boundaries. We establish when the residuals recover the spatial signal: under a multiplicative frailty and an exogeneity condition, they are free of the clinical covariates given location and stochastically ordered by the frailty. An expansion of the frailty Laplace exponent quantifies their approximate exponentiality and identifies the leading remainder. These results assume consistency of the first stage rather than a model class, so the construction extends to other survival estimators. On the LeukSurv leukemia data the method agrees with a Bayesian Gaussian random field frailty about where risk is elevated while resolving sharp adjacencies the smooth surface averages away, and an unadjusted spatial analysis misattributes clinical variation to location. Simulations with known zones, including a sweep through graded violations of exogeneity, locate the point at which the two contributions cease to be separately identifiable, with the smooth benchmark degrading in parallel as that point is approached.
Lev V. Utkin, Stanislav K. Kogan, Andrei V. Konstantinovcs.LG stat.ML
This work presents a novel attention-based framework for estimating the Individual Probability of Treatment Benefit (IPTB) in survival analysis contexts. The proposed model, called Surv-IPTB, directly quantifies the probability that a specific patient will experience extended survival time under treatment versus control. We reformulate IPTB estimation as a binary classification problem, leveraging pairwise patient comparisons across treatment and control cohorts. The framework incorporates a principled handling of right-censored observations through imprecise probability representations, where uncertain treatment effects are characterized by interval-valued probabilities. An attention mechanism with learnable query-key transformations enables flexible, data-driven aggregation of pairwise comparisons, while simultaneously learning soft class probabilities for censored cases. Through extensive experiments on synthetic datasets with complex nonlinear structures, including spiral, bell-shaped, and circular feature spaces, we demonstrate that our approach maintains robust performance across varying censoring rates and treatment effect strengths. The model consistently outperforms meta-learner baselines (T-learner and S-learner) equipped with random survival forests, Cox proportional hazards, and Beran estimators, particularly in challenging nonlinear scenarios where conventional methods exhibit significant degradation. The results establish the proposed attention-based framework as a scalable and statistically principled solution for personalized treatment benefit assessment in survival settings. The code implementing the model is publicly available.
Christopher Wang, Sebastien Ouellet, Behrouz Haji Soleimani +1cs.LG cs.AI
Supplier lead time forecasting is a central input to material requirements planning, inventory optimization, and supply chain risk management. However, many industrial lead time datasets are naturally right-censored: at the time forecasts are required, some orders have not yet arrived. Standard regression and classification approaches discard this information, while conventional survival models require task-specific modeling. We propose LeadTime-ICL (LT-ICL), a censoring-aware in-context learning model for probabilistic lead time forecasting. LT-ICL combines a transformer backbone with a conditional normalizing-flow head, producing a full predictive distribution over lead times. The model is pretrained on synthetic right-censored lead time tasks, enabling in-context adaptation to new industrial datasets without task-specific parameter updates. We provide theoretical support for this formulation by showing that excess CRPS is bounded by prior misspecification and amortized approximation errors, providing clear direction for improving forecasting performance. We evaluate LT-ICL on 24 proprietary supply-chain datasets spanning seven industries. LT-ICL achieves the lowest point-forecasting error on 15 of the 24 datasets, and the lowest probabilistic forecasting error on 14 datasets, yielding the best average rank across both. These results support right-censored probabilistic forecasting as a practical formulation for supplier lead time prediction and demonstrate that pretrained in-context models can provide accurate, low-adaptation-cost forecasting for industrial planning systems.
Subgroup analysis is important in practice because real-world data typically come from heterogeneous populations, where meaningful patterns can differ substantially across subpopulations. Correctly identifying these subgroups can improve prediction accuracy, prevent biased or misleading conclusions, and support more effective, targeted decision-making. While most existing subgroup analysis methods are developed for complete data, in this paper we propose a novel and robust approach for censored data under heterogeneous accelerated failure time (AFT) models. Specifically, we combine inverse probability weighting, M-estimation, and concave pairwise fusion penalization to simultaneously identify subgroups and estimate covariate effects for heterogeneous censored data, without requiring prior knowledge of individual subgroup memberships. We further develop an efficient RISA-ADMM algorithm to implement the method and establish its convergence. Furthermore, we derive the theoretical properties of the proposed estimators under mild regularity conditions. Extensive simulations and an application to the German credit dataset demonstrate the robustness and effectiveness of our approach.
Circulating-tumour DNA (ctDNA) carries evidence of drug resistance months before imaging shows it, but the earliest evidence lives below the assay's limit of detection (LoD): a nascent subclone is detected only intermittently, producing a flickering sequence of faint detects and non-detects. Commercial liquid biopsies treat each draw as an independent snapshot and a non-detect as nothing. We argue a non-detect is a left-censored observation, and the pattern of non-detects and faint detects over time carries actionable evidence of growth before any single value is trustworthy. We introduce Span, a censored-Poisson Bayesian latent-growth change-point detector that models the binary detection process, accumulates a sequential generalised-likelihood-ratio statistic for an upward change-point in the per-variant detection rate, and raises a competing-risks alarm with calibrated false-alarm control. Span has no learned weights, so there is nothing to overfit. On a synthetic cohort of HR+/HER2- metastatic breast cancer on first-line CDK4/6-inhibitor plus endocrine therapy, at a matched 10% false-alarm rate, Span roughly doubles the fraction of impending progressions caught three months ahead (indolent regime: 25% vs 11% for the snapshot), with a falsifiable dose-response: large for indolent emergence, vanishing for fast emergence. A value-trajectory baseline performs identically to the snapshot, isolating the gain to the censored detection model. The survival backbone matches a Cox baseline on real breast-cancer data (GBSG-2, n=686; C-index 0.67 vs 0.68), and on a real longitudinal cohort with clean biomarkers (PBC2, n=312) the same pipeline correctly declines to win, a falsifiable boundary test confirming the mechanism is regime-specific. All ctDNA trajectories are synthetic.
Jef Jonkers, Glenn Van Wallendael, Luc Duchateau +1cs.LG
Proper scoring rules provide a rigorous theoretical basis for the training and evaluation of probabilistic forecasts. However, in the presence of right censoring, the event time is only partially observed, rendering conventional scoring rules inapplicable in their standard form. We propose a framework for proper scoring of right-censored survival outcomes based on a simple idea: first, map the predictive distribution through the censoring mechanism, then apply the underlying proper score on the induced observed-data law. This yields localized scores for fixed censoring times and marginalized scores when the censoring time is random or only partially observed. The resulting construction recovers familiar right-censored likelihood and IPCW-type criteria within a coherent framework, while also yielding right-censored versions of the CRPS, pinball loss, Brier score, and energy score. We show that the marginalized score is proper under conditional independent censoring and strictly proper on the identifiable region. The same principle also leads to censored engression, a sample-based learning objective for multivariate right-censored survival modeling. In experiments, our scores correctly rank the oracle forecast across several censoring regimes, whereas forecast-dependent plug-in weighted scores can exhibit ranking reversals. Censored engression likewise substantially improves over naive training on censored outcomes.
Samuel Böhm, Lennart Purucker, Frank Hutter +1cs.LG
Tabular foundation models (TFMs) have made rapid progress in standard classification and regression, but time-to-event survival prediction tasks have remained largely untouched. Unlike in standard regression tasks, survival prediction models must account for censored data. Standard TFMs cannot handle natively censored data, leading to biased and inaccurate predictions, making them unsuitable for real-world applications. To overcome this fundamental limitation, we propose \texttt{SurvPFN}, a prior-data fitted network (PFN), for survival prediction tasks. We pretrain \texttt{SurvPFN} on millions of synthetic survival prediction tasks to learn survival via distributional regression that accounts for censored data. \texttt{SurvPFN} works by (1) generating data with Weibull event times and a non-informative censoring mechanism; (2) integrating a censored event indicator; and (3) minimizing a censored negative log-likelihood. On SurvSet, a collection of real-world survival tasks, \texttt{SurvPFN} is highly competitive with classical and deep survival baselines without per-dataset fitting, a survival-specific architecture, or feature engineering. We show that survival can be treated as a continuous-time distributional regression problem with censored loss, unlocking the power of PFNs for time-to-event predictions.
Survival Analysis (SA) is a statistical framework that models the time span until some event of interest occurs. Widely used in several domains, including healthcare and churn prediction, a central challenge in its applicability stems from the time of the event being partially observed or \emph{right-censoring}. Tabular Foundation Models (TFM) have attracted significant interest in recent years due to their ability to perform prediction tasks in a single forward pass, requiring no dataset-specific parameter fitting. Despite their success, their application to prediction tasks on time-to-event data remains difficult due to right censoring. In this work, we present a training-free method to survival regression by leveraging TFMs to both predict the time of the event and iteratively impute right-censored data. Our method uses a TFM to construct an Accelerated Failure Time (AFT) model requiring no training beyond fitting a single scalar parameter. Subsequently, by building on the Buckley-James estimator, we introduce a non-parametric in-context estimator for right-censored data. Our experiments on standard survival analysis benchmarks show that our method is competitive with several parametric and semi-parametric survival regression models that require training, including Cox regression and parametric AFT models.
Stanislav R. Kirpichenko, Andrei V. Konstantinov, Lev V. Utkincs.LG cs.AI stat.CO stat.ML
Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility and introduce approximation errors. We propose the Survival Diffusion Probabilistic Model (SDPM), a generative approach to continuous-time survival analysis. SDPM models the conditional distribution of the survival outcome, represented by the pair of observed time and censoring indicator, $\mathbb{P}(T,δ\mid \mathbf{x})$, using a denoising diffusion model. Under the assumption of conditionally independent censoring, conditional samples generated by the model can be transformed into survival function estimates using the Kaplan-Meier estimator. This formulation avoids parametric assumptions on the event-time distribution and does not require a discretization of the output time space. The model operates in a transformed target space, using standardized log-times and a continuous Gaussian-mixture representation of the censoring indicator. We evaluate SDPM on ten real survival datasets and compare it with five strong baselines, including tree-based, boosting-based, and neural survival models. Results show that SDPM achieves competitive predictive performance across C-index, integrated time-dependent AUC, and integrated Brier score. A study on synthetic Cox-Weibull data demonstrates that SDPM can recover the shape of an underlying continuous survival distribution more accurately than a strong nonparametric baseline when sufficiently many samples are generated. An ablation study confirms the importance of the proposed target-space transformations, which improve event-rate calibration, reduce invalid generated times, and provide consistent gains in predictive discrimination. Codes implementing the proposed model are publicly available.