Survival Analysis

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.

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.

Quantization is a standard path to deploying large language models, and quantized models are typically judged acceptable when perplexity or downstream accuracy remains close to the full-precision original. But behavioral parity need not imply feature fidelity: the sparse-autoencoder (SAE) features used to interpret a full-precision model may change after weight rounding. We test this directly by using a frozen SAE as a fixed measurement basis, encoding full-precision and round-to-nearest (RTN) quantized activations on identical tokens, and measuring per-feature survival by Pearson correlation across bit-widths from INT8 to INT4 on Pythia-70M and Gemma-2-2B. Our central finding is that perplexity can miss feature damage: on Gemma-2-2B, INT7 improves perplexity while degrading 18.7% of active SAE features, and under sliding-window evaluation INT6 also improves perplexity while only 51.3% of active features survive. Feature survival is graded rather than cliff-like, with 62.4% of active Pythia features and 51.3% of active Gemma features surviving at INT6; most non-surviving features are blurred rather than fully damaged. Survival is also predictable from full-precision feature statistics alone, with cross-validated AUC 0.92--0.97 and peak activation as the strongest marginal predictor. Finally, RTN quantization and matched-perplexity magnitude pruning damage strongly overlapping feature sets, with Jaccard overlap 0.79--0.86 and damage-score Spearman correlation 0.98. These results show that behavioral metrics alone are insufficient evidence that full-precision interpretability findings transfer to quantized models, motivating feature-level audits of compression.

Machine learning predictors have become essential tools for guiding automated decision making. However, a major misalignment persists: predictive models are typically optimized in terms of standard statistical metrics in isolation from the algorithmic tasks they inform. We highlight this incongruity in the high-stakes domain of organ allocation by demonstrating that any algorithm relying on (even highly accurate) survival predictors optimized for standard metrics -- such as the Concordance index (C-index) -- can yield arbitrarily poor outcomes when used for allocation, failing to guarantee utility better than a uniform random selection. To bridge the gap between survival analysis and policy optimization, we introduce a decision-focused learning approach based on optimizing normalized discounted cumulative gain (NDCG), a mainstay metric in information retrieval. We establish the utility of NDCG in survival analysis by proving that it translates to guarantees on the performance of allocation. Empirically, we propose a bootstrapping approach to optimize the NDCG of existing survival models. Unlike prior work, we also address the challenge of right censorship when evaluating ranking. On historical heart transplant data from the US, our method dramatically boosts the NDCG of baseline models by 50-100%, which translates to tens of thousands of additional life years gained annually when deployed for transplant allocation. We anticipate that our framework will find broader applications in decision making with predictions.

Estimating the causal effect of time-varying treatments on survival outcomes in large observational studies is computationally demanding, particularly when outcomes are rare. While g-formula-based methods such as the iterative conditional expectation (ICE) estimator provide a principled framework for longitudinal causal inference, they become computationally expensive, especially when bootstrap-based variance estimation is required. In addition, outcome rarity at each time point induces severe class imbalance, leading to instability and convergence issues in logistic regression and related models. To address these challenges, we propose a principled subsampling and reweighting strategy for longitudinal survival data that can be applied to a range of existing causal effect estimators in this setting, including the ICE estimator. The proposed method substantially reduces computational burden while preserving consistency and improving estimation stability in rare-outcome settings. We evaluate the method through simulations and validate it using a large-scale EHR cohort study on social and behavioral determinants of health (SBDH) and suicide risk, demonstrating its effectiveness for modeling rare outcomes in longitudinal data.

A mobile robot following a graph of known routes can make costly navigation errors when a temporary obstacle blocks a critical edge: waiting too long behind a parked cart wastes time, but immediately rerouting around a person who would move in a few seconds is also inefficient. Standard reactive obstacle avoidance addresses local motion around obstacles, while fixed wait-or-reroute rules ignore how long different obstacle types tend to persist. We propose OSCAR: an adaptive survival-modeling framework for graph-based navigation with temporary blockages. Assuming obstacle class labels are available at encounter time, the robot learns class-conditioned residual clearance-time distributions from online experience, including right-censored observations when it reroutes before observing clearance. These survival models are integrated into a time-dependent graph planner that maintains obstacle memory and computes a patience threshold at each blocked edge: how long to wait before taking an alternate route. The method continuously updates its clearance estimates across episodes and uses them to balance waiting against rerouting. We evaluate the approach in simulation and on a real mobile robot in a university atrium with obstacles including people, chairs, bins, and tubes. In simulation, the learned policy's time-to-goal converges to within 1% of an oracle with access to ground-truth clearance distributions after fewer than 20 observations per obstacle class, outperforming all heuristic baselines. Real-world deployment confirms that the policy improves online, adapting its patience thresholds from experience across 50 navigation episodes.

The Charlson Comorbidities Index (CCI) is a weighted additive index widely used to estimate ten-year mortality risk, but its original weights may not reflect contemporary prognoses. This limitation is critical in Prostate Cancer (PCa), where radical treatment is recommended only for patients with a life expectancy of at least ten years. For candidates eligible for Radical Prostatectomy (RP), accurate estimation of ten-year other-cause mortality is essential to balance oncological benefit against competing risks and avoid overtreatment. We propose a data-driven framework to derive a comorbidity index tailored to PCa patients considered for RP. Using a retrospective single-institution cohort, we apply Population-Based Bio-Inspired Algorithms (PBBIAs) to recalibrate comorbidity weights and evolve alternative symbolic formulations optimized for ten-year survival discrimination. We compared six optimization strategies, including symbolic regression approaches based on Genetic Programming (GP), population-based metaheuristics, clinically validated baselines, and survival prediction models. Results show that GA, FST-PSO, and SLIM outperform both the original CCI and the PCCI, particularly when PCa-specific variables are included, improving the Concordance Index by up to 0.1. GPLearn yields compact and interpretable models with competitive performance. Overall, the proposed approach provides an updated and interpretable tool to improve patient selection for RP.

Survival analysis concerns the task of predicting the time until an event occurs. Often used in the medical field, survival analysis deals with incomplete (i.e., censored) data, for instance, from patients who did not experience the event during the duration of the study. For practical use, both accuracy and interpretability are important. Survival trees are easy-to-follow survival models that split the patient cohort recursively into discrete patient groups. Whilst survival trees can capture complex relationships, they typically need to grow large, threatening interpretability. Moreover, survival trees are often built using greedy approaches that may overlook globally optimal split combinations, limiting predictive performance. Shallow survival trees require expressive, higher-order feature combinations to achieve competitive accuracy. We therefore use genetic programming to multi-objectively evolve inherently inspectable feature sets and study how they interact with different tree induction strategies. We further introduce an evolutionary approach that jointly optimises the survival tree structure and the non-linear split logic. Our findings demonstrate that evolutionary feature construction improves predictive performance across different tree induction strategies on two real-world datasets and two different survival tree depths. Given its speed and flexible presentation, the multi-objective evolution of entire trees likely holds the most future promise.

In randomized trials involving multiple treatments, bivariate survival outcomes present significant analytical challenges for making decisions. This paper addresses the problem of deriving optimal individualized treatment rules to maximize the joint survival probability beyond fixed time points $(t_1, t_2)$ through deep neural networks, while accounting for right censoring. We propose a novel approach that models treatment rules via stochastic policies, coupling marginal accelerated failure time models via link function to capture bivariate dependence. To enhance robustness and effectiveness of decision making, we introduce an adaptive prediction-powered method that leverages auxiliary predictions from machine learning models.

Objective: Survival analysis is central to medical prediction, yet large language models (LLMs) are rarely used as end-to-end survival models because censoring prevents straightforward supervised fine-tuning. Here we present LLMSurvival, a framework that enables censoring-aware survival analysis with unmodified LLMs operating directly on tabular clinical data. Materials and Methods: LLMSurvival reformulates time-to-event prediction as pairwise ranking among comparable subjects, and derives test-time risk by aggregating comparisons against anchor individuals from the training cohort. Results: Across two clinical tasks (ICU mortality prediction in MIMIC-IV and fragility fracture prediction in a NewYork-Presbyterian/Weill Cornell Medicine cohort), LLMSurvival improves overall concordance over Cox proportional hazards modeling by 3.1% for ICU mortality and 0.5% for fracture risk, 2.1% on average for ICU mortality and 2.8% for fracture risk over three established deep learning survival models. Discussion: The results show that survival modeling with censoring can be made compatible with LLM fine-tuning through comparison-based reformulation. The framework demonstrates high portability and superior performance over expert curated scores like SAPS-II and FRAX scores across diverse clinical context. Furthermore, the framework supports local deployment, as compact, publicly available base models provide sufficient performance. Conclusion: The LLMSurvival framework serves as a proof of concept for an integrated, censoring-conscious approach to survival analysis via LLMs.

Integrating multimodal datasets in clinical oncology is frequently hindered by high dimensionality and blockwise missingness, where entire data sources are unavailable for specific patient subsets. Standard survival models often struggle with these gaps, leading to biased results or patient exclusion. We introduce Multimodality Stacking with Blockwise missing values (MSB), a late-fusion framework for survival analysis that independently models modality-specific features before aggregating predictions via a cross-validated stacking meta-learner. MSB was validated on the PIONeeR study (n=443 patients, 378 biomarkers across eight heterogeneous sources) to predict progression-free survival in advanced non-small cell lung cancer patients receiving immunotherapy. MSB yielded higher predictive performance (C-index) than baseline algorithms. Improvements varied by baseline strength: linear models showed a 15.9% increase (p<0.001 for the Wilcoxon signed-rank test), random survival forests gained 5.4% (p=0.002), and gradient boosting methods improved by 2.1% (p=0.030). Beyond discrimination, MSB reduced the generalization gap (train-test difference in 5 folds cross-validation repeated 3 times: 0.055 vs 0.380 for linear models). Permutation importance analysis identified routine laboratory markers, clinical features, and PD-L1 expression as primary predictive drivers. Missing block indicators showed negligible importance, suggesting the model learned from biomarker values rather than data availability patterns. MSB provides a statistically validated framework for multimodal survival prediction with blockwise missingness. By enabling systematic biomarker evaluation without requiring complete data, MSB offers a practical tool for predictive modeling in biomedical research, pending external validation. Implementation is available at https://github.com/MohamedBoussena/MSB under Inria license.

In computational pathology, Whole Slide Images (WSIs) survival analysis is crucial for patient prognosis assessment, but it faces multiple technical challenges. Although the Transformer captures long-range dependencies through its self-attention mechanism, its $O(N^2)$ time complexity causes a severe computational bottleneck in large-scale WSIs graph structures. The Mamba model breaks through the Transformer's computational bottleneck with linear complexity. But, owing to Mamba's high sensitivity to the order of input data, traditional node sorting methods in Graph Mamba, such as those based on node degree or subgraph size, fail to adequately account for the topological connectivity of graph data. This inadequacy consequently restricts the performance of Mamba's sequential modeling. Moreover, its unidirectional architecture cannot leverage the bidirectional spatial structure of images. To address these challenges, this paper proposes a novel Graph Mamba survival analysis framework based on topology-aware ordering (TopoMamSurv) to adapt to the sequential sensitivity of Mamba. Our visualization experiments further confirmed that the nodes extracted through the topology-aware ordering (TAO) strategy indeed exhibit higher similarity. Furthermore, we designed a bidirectional Mamba module and integrated a Graph Convolutional Network (GCN) to achieve bidirectional spatial context modeling of images, forming a hierarchical feature learning architecture for "local aggregation - global capture." This framework effectively reconciles the contradiction between long-range dependency modeling, computational efficiency, and spatial structure utilization in WSIs analysis through its systematic design of TAO, bidirectional semantic modeling, and hierarchical feature fusion. This framework has been validated for its comprehensive performance advantage on five TCGA datasets.

No existing nested Archimedean copula tool handles all three of (a) arbitrary per-variable (right-)censoring in survival analysis, (b) arbitrary nesting trees, and (c) exact parameter gradients. Existing implementations handle only bivariate problems, low dimensional (i.e., $d \leq 10$) cases, two layers of nesting, or only hand-derived copula nestings. We present \textsc{acopula}, a JAX-native framework that, given any Archimedean generator -- classical or neural -- evaluates exact nested-copula likelihoods and parameter gradients under arbitrary censoring masks in polynomial time. The mechanism is polynomial powering of Taylor-mode automatic differentiation output, which replaces per-family hand-derived partial Bell polynomial tables with a single differentiable computation that any user-defined generator can drive. We conduct extensive simulations to verify the correctness of \textsc{acopula}. We then demonstrate (a) per-variable censoring on $85{,}229$ MIMIC-IV ICU admissions in high dimensions with $d{=}53$, fit by both classical Archimedean families and nested neural Archimedean copulas; (b) an 11-sector hierarchical model on S&P~500 daily returns at $d{=}98$; (c) family-agnostic censored MLE across ten families, five of them with no prior implementation, on a retinopathy study; and (d) a ${\sim}650\times$ per-density speedup over R's \texttt{nacLL} at $d{=}35$, scaling quadratically to $d{=}8{,}000$.

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.

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.

Predictive modelling is important for health data analysis and data-driven clinical decision-making. However, predictive studies are challenging to design optimally by hand when tens or even hundreds of features require selection, transformation, or interaction modelling. While complex machine learning models offer high performance, their "black-box" nature limits the clinical trust, transparency, and interpretability required for decision-making. We developed and evaluated an Exploratory AI Recommender that provides data-driven recommendations to improve predictive performance of existing interpretable statistical models. The developed framework uses flexible AI modelling to capture complex data patterns and explainable AI techniques to translate the patterns into three recommendation types: feature exclusion, non-linear terms, and feature interactions. We evaluated the framework by comparing predictive performance of a baseline (i.e., no interactions or non-linear terms) Cox Proportional Hazards (CPH) model against an augmented CPH incorporating recommendations suggested by our method. The primary analysis predicts the time to the first occurrence of a fall or related injury in 245,614 patients. Our method recommended excluding 23 features, including non-linear terms for two features, and including 221 suggested feature interactions. The C-index improved from 0.805 (95% CI 0.798-0.812) to 0.815 (95% CI 0.809-0.822), and so did calibration (intercept: -0.006 to 0.003; slope: 1.063 to 0.950). All recommendations were supported by existing literature. The method also proved effective on two additional public datasets, demonstrating wider applicability. The proposed Exploratory AI Recommender demonstrates the potential of explainable AI and data-driven study design to improve the process of developing, and the performance of high-dimensional transparent predictive models.

Infrastructure deterioration poses significant challenges for asset management, yet existing approaches rely on population-averaged models that overlook equipment-specific heterogeneity. We present a novel framework that combines Bayesian hierarchical hazard modeling with causal discovery to identify operational patterns that drive heterogeneous deterioration rates in pump equipment. Our approach first estimates pump-specific random effects $u_i$ using GPU-accelerated No-U-Turn Sampling (NUTS), achieving 3--5$\times$ speedup over CPU implementations. We then employ DirectLiNGAM to discover causal relationships between 22 engineered time-series features and deterioration rates, stratified by positive ($u_i > 0$, faster deterioration) versus negative ($u_i \leq 0$, slower deterioration) random effects. Analyzing 112 pumps with 92,861 observations over 650 days, we uncover striking heterogeneity: the negative group exhibits causal effects 400$\times$ larger than the positive group, with standard deviation (std) showing a strong positive causal effect ($+1.515$) on deterioration rates in low-risk equipment. We validate linearity assumptions through NonlinearLiNGAM comparison and demonstrate practical scalability through GPU acceleration. Our findings enable targeted maintenance strategies by revealing that different operational regimes require fundamentally distinct management approaches, advancing predictive maintenance from population-averaged to heterogeneity-aware decision making.

Adaptive experimentation enables efficient estimation of causal effects, but existing methods are not designed for survival data with censoring, where event times are only partially observed (e.g., overall survival in cancer trials but with dropout). In this paper, we develop a novel framework for adaptive experimentation to estimate causal effects under right censoring. For this, we derive the semiparametric efficiency bound for the average survival effect curve as a function of the treatment allocation policy and thereby obtain a closed-form efficiency-optimal allocation policy. The policy generalizes classical Neyman allocation to survival settings by prioritizing patient strata where both event and censoring dynamics induce high uncertainty. Building on this, we propose the Adaptive Survival Estimator (ASE), an adaptive framework that learns the allocation policy and estimates the average survival effect curve sequentially. Our framework has three main benefits: (i) it accommodates arbitrary machine learning models for nuisance estimation; (ii) it is guided by a closed-form efficiency-optimal allocation policy; and (iii) it admits strong theoretical guarantees, including asymptotic normality via a martingale central limit theorem. We demonstrate our framework across various numerical experiments to show consistent efficiency gains over uniform randomization and censoring-agnostic baselines.

Time-to-event data is widespread across the life sciences and engineering, but it is typically encountered together with censoring, which complicates the application of standard machine learning methods. Deep Cox models have emerged as a popular method for analyzing time-to-event data because they gracefully handle censoring and can be used with unstructured data such as clinical text reports, genomic sequences, and pathology images. However, their predicted survival probabilities are often poorly calibrated, thus limiting their practical utility. In this paper, we propose a novel post hoc calibration method for Deep Cox models that uses isotonic regression to refine predicted survival probabilities without affecting discriminative power. We establish favorable theoretical guarantees, including a double-robustness property and asymptotic calibration. Experiments on synthetic and real-world clinical data demonstrate the empirical effectiveness of our method.

Flexible continuous-time survival modeling is critical for capturing complex time-varying hazard dynamics in high-dimensional data; however, training such models remains challenging due to the intractable integral required for likelihood estimation. We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling without relying on time discretization or restrictive distributional assumptions. We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy while facilitating efficient end-to-end training via standard backpropagation. Furthermore, to effectively capture non-stationary hazard dynamics in complex architectures, we introduce time-conditioned low-rank adaptation, a mechanism that conditions general neural backbones on time by dynamically modulating weights via low-rank updates. We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation. Comprehensive experiments across synthetic benchmarks, large-scale real-world tabular datasets, and high-dimensional medical imaging tasks demonstrate that QSurv achieves competitive predictive performance with advantages in instantaneous hazard function estimation, enabling more interpretable characterization of time-varying risk patterns.

Survival analysis provides a powerful statistical framework for modeling time-to-event outcomes in the presence of censoring. However, selecting an appropriate estimator from the many specialized survival approaches often requires substantial methodological and domain expertise. We introduce SurvivalPFN, a prior-data fitted network that amortizes Bayesian inference for censored observations through in-context learning. SurvivalPFN is pretrained on a diverse family of synthetic, identifiable, and right-censored data-generating processes, enabling it to amortize survival analysis in a single forward pass during inference. As a result, the model adapts to the effective complexity of each dataset without task-specific training or hyperparameter tuning, avoids restrictive parametric assumptions, and produces calibrated survival distributions. In a large-scale benchmark spanning 61 datasets, 21 methods, and 5 evaluation metrics, SurvivalPFN achieves strong predictive performance and often improves upon established survival models. These results suggest that SurvivalPFN offers a principled and practical foundation model for survival analysis, with potential applications in high-impact domains such as healthcare, finance, and engineering (https://github.com/rgklab/SurvivalPFN).

Large language models (LLMs) are increasingly deployed in a wide range of applications, yet remain vulnerable to adversarial jailbreak attacks that circumvent their safety guardrails. Existing evaluation frameworks typically report binary success/failure metrics, failing to capture the temporal dynamics of how attacks succeed under persistent adversarial pressure. This preliminary work proposes a novel evaluation framework that applies survival analysis techniques to characterize LLM jailbreak vuln`erability. Our approach models the time-to-jailbreak as a survival outcome, enabling estimation of hazard functions, survival curves, and risk factors associated with successful attacks. We evaluate three LLMs against a subset of prompts from the HarmBench dataset spanning three attack categories. Our analysis reveals that models exhibit distinct vulnerability profiles: while one model demonstrates rapid degradation under iterative attacks, the two other models show consistent moderate vulnerability. Our framework provides actionable insights for model and LLM application developers and establishes survival analysis as a rigorous methodology for LLM safety evaluation.

We propose a novel multimodal deep learning framework for patient-level survival prediction, which integrates whole-slide histology features, RNA-seq expression profiles, and clinical variables. Our architecture combines an ABMIL module~\cite{ilse2018attention} for slide-level representation with feedforward encoders for RNA and clinical data. These embeddings are then integrated through low-rank bilinear cross-modal fusion~\cite{liu2018efficient} to model conditional interactions across modalities while controlling parameter growth. The model outputs continuous risk scores that are subsequently mapped to survival times using a nonparametric calibration procedure based on the Kaplan--Meier estimator~\cite{kaplan1958nonparametric}. By decomposing multimodal reasoning into independent pairwise interactions, the proposed fusion design promotes structural interpretability and parameter efficiency compared with full tensor and hierarchical fusion strategies. Experiments on the CHIMERA challenge dataset demonstrate improved predictive performance over concatenation-based baselines and competitive generalization on hidden evaluation cohorts. These results indicate that the proposed framework is a promising approach for multimodal survival prediction in HR-NMIBC. The implementation is publicly available at https://github.com/hassancpu/ChimeraChallenge2025_Task_3.

In the data-driven era, large-scale datasets are routinely collected and analyzed using machine learning (ML) and artificial intelligence (AI) to inform decisions in high-stakes domains such as healthcare, employment, and criminal justice, raising concerns about the fairness behavior of these systems. Existing works in fair ML cover tasks such as bias detection, fair prediction, and fair decision-making, but largely focus on static settings. At the same time, fairness in temporal contexts, particularly survival/time-to-event (TTE) analysis, remains relatively underexplored, with current approaches to fair survival analysis adopting statistical fairness definitions, which, even with unlimited data, cannot disentangle the causal mechanisms that generate disparities. To address this gap, we develop a causal framework for fairness in TTE analysis, enabling the decomposition of disparities in survival into contributions from direct, indirect, and spurious pathways. This provides a human-understandable explanation of why disparities arise and how they evolve over time. Our non-parametric approach proceeds in four steps: (1) formalizing the necessary assumptions about censoring and lack of confounding using a graphical model; (2) recovering the conditional survival function given covariates; (3) applying the Causal Reduction Theorem to reframe the problem in a form amenable to causal pathway decomposition; (4) estimating the effects efficiently. Finally, our approach is used to analyze the temporal evolution of racial disparities in outcome after admission to an intensive care unit (ICU).

We propose non-parametric estimators for the average run length (ARL) and average detection delay (ADD) in quickest changepoint detection (QCD) under finite and irregular sequence lengths. Although ARL and ADD are widely used as optimality criteria in theoretical and simulation studies, their application to real-world datasets is hindered by limited and irregular sequence lengths. To address this issue, we propose non-parametric estimators for the ARL and ADD, termed KM-ARL and KM-ADD, by drawing an analogy between QCD and survival analysis to model detection probabilities under sequence truncation. We derive estimation bias bounds and prove that they are asymptotically unbiased unless extrapolation is required. Experiments on simulated and real-world datasets demonstrate their practical utility, enhancing robustness against limited and irregular sequence lengths, improving interpretability, and facilitating empirical, intuitive model selection. Our Python code is provided at https://github.com/TaikiMiyagawa/Kaplan-Meier-Average-Run-Length, offering ready-to-use implementations for practitioners.

Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring these networks from event-based observations, which arise naturally in finance, seismology, and neuroscience. While there is substantial algorithmic work addressing this important problem, theoretical results are scarce. In this paper we ask the following fundamental question: what is the minimum time that one must observe the dynamics in order to exactly recover the underlying network, as a function of the number $d$ of interacting entities? For a class of stationary Hawkes processes with sparse, weak interactions, we prove that an observation time of order $\log d$ is sufficient and necessary. For the upper bound we construct a two-stage estimator that uses clipped and binned event data for screening, followed by a least-squares refinement, and apply concentration bounds derived from the Poisson cluster representation. For the lower bound we combine Fano's inequality with Jacod's Girsanov formula for point processes on a suitable subclass of networks.

Protein sequence data from nature exhibits survivorship bias: we only observe data from those organisms that survive and reproduce, while non-functional protein mutations are eliminated by natural selection. Thus, predicting whether a protein sequence is functional often requires learning from positive examples alone. While positive-unlabeled (PU) learning frameworks offer a generic solution to this problem, existing PU methods ignore the evolutionary processes that shape sequence observability and cause survivorship bias. Consider a sequence that is one mutation away from a commonly-observed protein variant in a well-surveilled organism. If the sequence were functional, it would likely be observed. If it is not observed, this suggests non-functionality. In contrast, sequences that are unlikely to arise through mutation may be missing simply because they never arose. Thus, these two kinds of missing sequences should be treated differently when training models. In this work, we propose Evo-PU, a PU learning framework that uses a scientific understanding of nucleotide mutation to model survivorship bias for well-surveilled single-organism sequence data. On three prediction tasks using single-organism uniform-coverage surveillance data -- predicting results from held-out influenza and respiratory syncytial virus (RSV) mutagenesis studies, and predicting future SARS-CoV-2 variants -- Evo-PU outperforms standard PU learning, one-class classification (OCC), and protein language models (PLMs). On prediction tasks from multi-organism ProteinGym datasets with more heterogeneous surveillance coverage, we identify opportunities to generalize our approach.

Survival analysis on tabular data is a well-studied problem. However, existing deep learning methods are often highly task-specific, which can limit the transfer of new approaches from other domains and introduce constraints that may affect performance. We propose TabSurv, an approach that adapts modern tabular architectures to survival analysis using either the Weibull distribution or non-parametric survival prediction. TabSurv optimizes SurvHL, a novel histogram loss function supporting censored data. In addition to a baseline feed-forward network, we implement deep ensembles of MLPs for survival analysis within TabSurv. In contrast to prior work, the ensemble components are trained in parallel, optimizing survival distribution parameters before averaging, which promotes diversity across ensemble component predictions. We perform a comprehensive empirical evaluation of different proposed architectures on 10 diverse real-world survival datasets. Our results show that TabSurv consistently outperforms on average established classical and deep learning baselines, such as RSF, DeepSurv, DeepHit, SurvTRACE. Notably, deep ensembles with Weibull parametrization instead of non-parametric models achieve the highest average rank by C-index. Overall, our study clarifies how modern tabular neural networks can be adapted and trained to tackle survival analysis problems, offering a strong and reliable approach. The TabSurv implementation is publicly available.

``How long can I live and remain free of cancer?'' is often the first question a patient asks after receiving a cancer diagnosis and treatment. Accurate survival prediction helps alleviate psychological distress and supports risk stratification and personalized treatment planning. Recent survival prediction frameworks have shown strong performance using computed tomography (CT) images. However, variations in imaging acquisition introduce out-of-distribution (OOD) samples caused by covariate shifts that undermine model reliability. Despite this challenge, to our knowledge, no existing benchmark systematically studies OOD detection in cancer survival prediction. To address this gap, we introduce the Cancer sURvival bEnchmark for OOD Detection (CURE-OOD), the first benchmark for systematically evaluating OOD detection in survival prediction under controlled acquisition-induced distribution shifts. CURE-OOD defines scanner-parameter-based training, in-distribution (ID), and OOD test splits across four survival prediction tasks. Our experiments show that covariate shifts notably reduce survival prediction performance. It also shows that mainstream classification-oriented OOD detectors can fail in survival prediction. Finally, we include HazardDev as a simple survival-aware reference baseline for OOD detection. CURE-OOD enables systematic analysis of how distribution shifts affect both downstream survival performance and OOD detectability.

Pathology foundation models (PFMs) have recently emerged as powerful pretrained encoders for computational pathology, enabling transfer learning across a wide range of downstream tasks. However, systematic comparisons of these models for clinically meaningful prediction problems remain limited, especially in the context of survival prediction under external validation. In this study, we benchmark widely used and recently proposed PFMs for breast cancer survival prediction from whole-slide histopathology images. Using a standardized pipeline based on patch-level feature extraction and a unified survival modeling framework, we evaluate model representations across three independent clinical cohorts comprising more than 5,400 patients with long-term follow-up. Models are trained on one cohort and evaluated on two independent external cohorts, enabling a rigorous assessment of cross-dataset generalization. Overall, H-optimus-1 achieves the strongest survival prediction performance. More broadly, we observe consistent generational improvements across model families, with second-generation PFMs outperforming their first-generation counterparts. However, absolute performance differences between many recent PFMs remain modest, suggesting diminishing returns from further scaling of pretraining data or model size alone. Notably, the compact distilled model H0-mini slightly outperforms its larger teacher model H-optimus-0, despite using fewer than 8% of the parameters and enabling significantly faster feature extraction. Together, these results provide the first large-scale, externally validated benchmark of PFMs for breast cancer survival prediction, and offer practical guidance for efficient deployment of PFMs in clinical workflows.

Cancer survival prediction from multi-omics data remains challenging because prognostic signals are high-dimensional, heterogeneous, and distributed across interacting genes and pathways. We propose PathMoG, a pathway-centric modular graph neural network for multi-omics survival prediction. PathMoG reorganizes genome-scale inputs into 354 KEGG-informed pathway modules, introduces a Hierarchical Omics Modulation module to condition gene-expression representations on mutation, copy number variation, pathway, and clinical context, and uses dual-level attention to capture both intra-pathway driver signals and inter-pathway clinical relevance. We evaluated PathMoG on 5,650 patients across 10 TCGA cancer types and observed consistent improvements over representative survival baselines. The framework further provides gene-level, pathway-level, and patient-level interpretability, supporting biologically grounded and clinically relevant risk stratification.

Survival analysis is a widely used statistical framework for modeling time-to-event data under censoring. Classical methods, such as the Cox proportional hazards (Cox PH) model, offer a semiparametric approach to estimating the effects of covariates on the hazard function. Despite its importance, survival analysis has been largely unexplored in online settings, particularly within the bandit framework, where decisions must be made sequentially to optimize treatments as new data arrive over time. In this work, we take an initial step toward integrating survival analysis into a purely online learning setting under the Cox PH model, addressing key challenges including staggered entry, delayed feedback, and right censoring. We adapt three canonical bandit algorithms to balance exploration and exploitation, with theoretical guarantees of sublinear regret bounds. Extensive simulations and semi-real experiments using SEER cancer data demonstrate that our approach enables rapid and effective learning of near-optimal treatment policies.

Accurate prognostication and risk estimation are essential for guiding clinical decision-making and optimizing patient management. While radiologist-assessed features from CT scans provide valuable indicators of disease severity and outcomes, interpreting such images requires expert knowledge, and translating rich visual information into textual summaries inevitably leads to information loss. In this work, we propose a vision-language framework for 3D CT image understanding that leverages large-scale open-sourced CT images paired with radiology reports through visual instruction tuning. This pre-training enables the model to learn clinically meaningful visual-textual representations, which can then be adapted to downstream survival prediction tasks. By incorporating a survival prediction head on top of the pre-trained model, our approach improves survival prediction from CT images and clinical data while generating clinically meaningful language responses to predefined questions. Experimental results demonstrate that our method outperforms baseline methods in survival prediction, particularly, when clinical data alone is less predictive. The code will be released upon acceptance.

Standard approaches to goal-conditioned reinforcement learning (GCRL) that rely on temporal-difference learning can be unstable and sample-inefficient due to bootstrapping. While recent work has explored contrastive and supervised formulations to improve stability, we present a probabilistic alternative, called survival value learning (SVL), that reframes GCRL as a survival learning problem by modeling the time-to-goal from each state as a probability distribution. This structured distributional Monte Carlo perspective yields a closed-form identity that expresses the goal-conditioned value function as a discounted sum of survival probabilities, enabling value estimation via a hazard model trained via maximum likelihood on both event and right-censored trajectories. We introduce three practical value estimators, including finite-horizon truncation and two binned infinite-horizon approximations to capture long-horizon objectives. Experiments on offline GCRL benchmarks show that SVL combined with hierarchical actors matches or surpasses strong hierarchical TD and Monte Carlo baselines, excelling on complex, long-horizon tasks. Webpage and Code: https://simple-robotics.github.io/publications/survival-value-learning/

Decentralized Finance (DeFi) lending protocols like Aave v3 rely on over-collateralization to secure loans, yet users frequently face liquidation due to volatile market conditions. Existing risk management tools utilize static health-factor thresholds, which are reactive and fail to distinguish between administrative "dust" cleanup and genuine insolvency. In this work, we propose an autonomous agent that leverages time-to-event (survival) analysis and moves beyond prediction to execution. Unlike passive risk signals, this agent perceives risk, simulates counterfactual futures, and executes protocol-faithful interventions to proactively prevent liquidations. We introduce a return period metric derived from a numerically stable XGBoost Cox proportional hazards model to normalize risk across transaction types, coupled with a volatility-adjusted trend score to filter transient market noise. To select optimal interventions, we implement a counterfactual optimization loop that simulates potential user actions to find the minimum capital required to mitigate risk. We validate our approach using a high-fidelity, protocol-faithful Aave v3 simulator on a cohort of 4,882 high-risk user profiles. The results demonstrate the agent's ability to prevent liquidations in imminent-risk scenarios where static rules fail, effectively "saving the unsavable" while maintaining a zero worsening rate, providing a critical safety guarantee often missing in autonomous financial agents. Furthermore, the system successfully differentiates between actionable financial risks and negligible dust events, optimizing capital efficiency where static rules fail.

In evolutionary reinforcement learning tasks (ERL), agent policies are often encoded as small artificial neural networks (NERL). Such representations lack explicit modular structure, limiting behavioral interpretation. We investigate whether programmatic policies (PERL), implemented as soft, differentiable decision lists (SDDL), can match the performance of NERL. To support reproducible evaluation, we provide the first fully specified and open-source reimplementation of the classic 1992 Artificial Life (ALife) ERL testbed. We conduct a rigorous survival analysis across 4000 independent trials utilizing Kaplan-Meier curves and Restricted Mean Survival Time (RMST) metrics absent in the original study. We find a statistically significant difference in survival probability between PERL and NERL. PERL agents survive on average 201.69 steps longer than NERL agents. Moreover, SDDL agents using learning alone (no evolution) survive on average 73.67 steps longer than neural agents using both learning and evaluation. These results demonstrate that programmatic policies can exceed the survival performance of neural policies in ALife.

Multimodal survival analysis aims to improve cancer prognosis using heterogeneous biomedical data, such as histopathology images and genomic profiles. A common strategy is to align representations across modalities so that shared signals can be captured. However, strong cross-modal alignment can also remove modality-specific evidence that is critical for survival prediction. In this paper, we revisit multimodal survival learning from a simple observation: effective models should first discover shared patterns across modalities, and then preserve modality-specific signals. This motivates a representation learning principle that we refer to as Together Then Apart. Based on this idea, we propose TTA, a framework that balances cross-modal alignment and representation distinctiveness. TTA first performs prototype-based alignment to capture shared survival-related structures between modalities. It then encourages modality-specific distinctiveness through an anchor-guided contrastive objective. To further account for modality imbalance and noisy correspondences, we model cross-modal interactions using unbalanced optimal transport. We evaluate the proposed approach on multiple TCGA cancer cohorts with paired histopathology and genomic data. TTA consistently improves survival prediction over recent multimodal survival models. Moreover, the learned prototype structures reveal interpretable cross-modal patterns associated with clinical outcomes.

We revisit Cox's proportional hazards model to improve variable selection in survival analysis. A square-root transformation of the partial likelihood renders the selection of the regularization parameter pivotal, free of the unknown baseline hazard and censoring mechanism. The resulting criterion borrows from information criteria such as BIC and from penalized regression methods such as the lasso, taking the best of both. On simulated and real data, our method substantially improves upon state-of-the-art approaches used daily in support recovery.

Survival analysis plays a vital role in making clinical decisions. However, the models currently in use are often difficult to interpret, which reduces their usefulness in clinical settings. Prototype learning presents a potential solution, yet traditional methods focus on local similarities and static matching, neglecting the broader tumor context and lacking strong semantic alignment with genomic data. To overcome these issues, we introduce an innovative prototype-based multimodal framework, FeatProto, aimed at enhancing cancer survival prediction by addressing significant limitations in current prototype learning methodologies within pathology. Our framework establishes a unified feature prototype space that integrates both global and local features of whole slide images (WSI) with genomic profiles. This integration facilitates traceable and interpretable decision-making processes. Our approach includes three main innovations: (1) A robust phenotype representation that merges critical patches with global context, harmonized with genomic data to minimize local bias. (2) An Exponential Prototype Update Strategy (EMA ProtoUp) that sustains stable cross-modal associations and employs a wandering mechanism to adapt prototypes flexibly to tumor heterogeneity. (3) A hierarchical prototype matching scheme designed to capture global centrality, local typicality, and cohort-level trends, thereby refining prototype inference. Comprehensive evaluations on four publicly available cancer datasets indicate that our method surpasses current leading unimodal and multimodal survival prediction techniques in both accuracy and interpretability, providing a new perspective on prototype learning for critical medical applications. Our source code is available at https://github.com/JSLiam94/FeatProto.

Cancer survival prediction from whole slide images (WSIs) is a challenging task in computational pathology due to the large size, irregular shape, and high granularity of the WSIs. These characteristics make it difficult to capture the full spectrum of patterns, from subtle cellular abnormalities to complex tissue interactions, which are crucial for accurate prognosis. To address this, we propose CrossFusion, a novel multi-scale feature integration framework that extracts and fuses information from patches across different magnification levels. By effectively modeling both scale-specific patterns and their interactions, CrossFusion generates a rich feature set that enhances survival prediction accuracy. We validate our approach across six cancer types from public datasets, demonstrating significant improvements over existing state-of-the-art methods. Moreover, when coupled with domain-specific feature extraction backbones, our method shows further gains in prognostic performance compared to general-purpose backbones. The source code is available at: https://github.com/RustinS/CrossFusion

Dependent censoring occurs when the event time and censoring time are not conditionally independent given the observed covariates. This complicates survival model evaluation because widely used metrics, such as the Brier score, typically handle right-censoring using inverse probability of censoring weighting (IPCW). Unfortunately, IPCW is valid only when the estimated censoring distribution is independent of the event time. We propose a dependent Brier score based on an Archimedean copula and the Copula-Graphic estimator, and establish consistency and asymptotic normality of its margin-time estimator. To evaluate the metric, we introduce a semi-synthetic framework that creates realistic dependent censoring while preserving the original covariate structure and known event times. Across 12 datasets, the proposed metric reduces estimation error by 12-16% on average relative to IPCW. Source code is available at https://github.com/thecml/DependentEVAL.

Brownian motion is a compact mathematical language for continuous-time uncertainty in biostatistics. This tutorial develops the process from construction and path properties to tools that recur in applied biomedical work: the Markov and strong Markov properties, the Karhunen-Loeve expansion, functional principal component analysis (Functional PCA), reflection principles, local time, stochastic differential equations (SDEs), Brownian bridges, and empirical-process limits. The applications emphasize longitudinal biomarkers, degradation modelling, first-passage endpoints, dynamic frailty, group-sequential monitoring, calibration diagnostics, recurrent-event processes, electronic health records, and wearable streams. A short cross-domain section uses literary and historical archives to make Brownian-bridge thinking concrete without shifting the paper away from biostatistics, and includes a reproducible chapter-level experiment on Frankenstein. The Black-Merton-Scholes model is included as a solved SDE template, not as a finance application in its own right. The aim is to connect rigorous probability with modelling decisions faced by biostatisticians when biological processes evolve between noisy observation times.

Recent work has argued normatively, on synthetic data, that evaluating survival models by discrimination alone (concordance index) yields systematically misleading model comparisons, because the metric ignores calibration and time-dependent accuracy. Whether this matters for real, published, non-clinical models has not been tested. We reproduce three published survival-ML models across three structurally distinct domains -- hard-drive failure prediction, peer-to-peer credit default, and user disengagement on digital platforms -- validate our instrument against the anchor paper's own synthetic experiment, and test five pre-registered hypotheses under a Holm-corrected family-wise error rate. Three of five reject (though one pre-registered threshold clears by a narrow margin). A model reproducing the published literature's discrimination almost exactly (C = 0.9595 vs. 0.958 reported) fails a formal calibration test at p < 0.001; a broad feature-ablation search finds no single attribute responsible for its discrimination, so the calibration failure is not a trivial shortcut artifact. A lender's estimated default risk is biased upward by roughly two percentage points, growing to nearly four in the riskiest segment, when loan prepayment is treated as non-informative censoring rather than a competing risk. A platform's churn model shows probability estimates that degrade with the horizon even as global discrimination stays within the pre-registered C-index band. A direct test of whether metric choice inverts model preference does not reject, though with limited power given two to three models per domain; the failure mode we document is better characterized as misplaced confidence in a chosen model than as choosing the wrong one. We release a pre-registered evaluation harness with full code and an annotated notebook, so these results can be verified independently and the audit extended.