c-index
SDPM: Survival Diffusion Probabilistic Model for Continuous-Time Survival Analysis
Kirpichenko, Stanislav R., Konstantinov, Andrei V., Utkin, Lev V.
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, $\mathbb{P}(T,ฮด\mid \mathbf{x})$, 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.
TabSurv: Adapting Modern Tabular Neural Networks to Survival Analysis
Kirpichenko, Stanislav, Konstantinov, Andrei, Utkin, Lev
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.
Multitask Boosting for Survival Analysis with Competing Risks
Alexis Bellot, Mihaela van der Schaar
What distinguishes ourweighting scheme from existing boosting methods isthatwhile the output ofeach weak estimator isamultivariate probability distribution, the data only provides the specific event that occurred and the time of occurrence and thus we introduce new notions of "predictioncorrectness"thatapplyinoursetting.
KAN-AFT: An Interpretable Nonlinear Survival Model Integrating Kolmogorov-Arnold Networks with Accelerated Failure Time Analysis
Jose, Mebin, Francis, Jisha, Kattumannil, Sudheesh Kumar
Survival analysis relies fundamentally on the semi-parametric Cox Proportional Hazards (CoxPH) model and the parametric Accelerated Failure Time (AFT) model. CoxPH assumes constant hazard ratios, often failing to capture real-world dynamics, while traditional AFT models are limited by rigid distributional assumptions. Although deep learning models like DeepAFT address these constraints by improving predictive accuracy and handling censoring, they inherit the significant challenge of black-box interpretability. The recent introduction of CoxKAN demonstrated the successful integration of Kolmogorov-Arnold Networks (KANs), a novel architecture that yields highly accurate and interpretable symbolic representations, within the CoxPH framework. Motivated by the interpretability gains of CoxKAN, we introduce KAN-AFT (Kolmogorov Arnold Network-based AFT), the first framework to apply KANs to the AFT model. Our primary contributions include: (i) a principled AFT-KAN formulation, (ii) robust optimization strategies for right-censored observations (e.g., Buckley-James and IPCW), and (iii) an interpretability pipeline that converts the learned spline functions into closed-form symbolic equations for survival time. Empirical results on multiple datasets confirm that KAN-AFT achieves performance comparable to or better than DeepAFT, while uniquely providing transparent, symbolic models of the survival process.
KANFormer for Predicting Fill Probabilities via Survival Analysis in Limit Order Books
Zhong, Jinfeng, Bacry, Emmanuel, Guilloux, Agathe, Muzy, Jean-Franรงois
This paper introduces KANFormer, a novel deep-learning-based model for predicting the time-to-fill of limit orders by leveraging both market- and agent-level information. KANFormer combines a Dilated Causal Convolutional network with a Transformer encoder, enhanced by Kolmogorov-Arnold Networks (KANs), which improve nonlinear approximation. Unlike existing models that rely solely on a series of snapshots of the limit order book, KANFormer integrates the actions of agents related to LOB dynamics and the position of the order in the queue to more effectively capture patterns related to execution likelihood. We evaluate the model using CAC 40 index futures data with labeled orders. The results show that KANFormer outperforms existing works in both calibration (Right-Censored Log-Likelihood, Integrated Brier Score) and discrimination (C-index, time-dependent AUC). We further analyze feature importance over time using SHAP (SHapley Additive exPlanations). Our results highlight the benefits of combining rich market signals with expressive neural architectures to achieve accurate and interpretabl predictions of fill probabilities.
Frailty-Aware Transformer for Recurrent Survival Modeling of Driver Retention in Ride-Hailing Platforms
Xu, Shuoyan, Zhang, Yu, Miller, Eric J.
Abstract--Ride-hailing platforms are characterized by high-frequency, behavior-driven environments, such as shared mobility platforms. Although survival analysis has been widely applied to recurrent events in other domains, its use for modeling ride-hailing driver behavior remains largely unexplored. T o the best of our knowledge, this study is the first to formulate driver idle behavior as a recurrent survival process using large-scale platform data. This study proposes a survival analysis framework that uses a Transformer-based temporal encoder with causal masking to capture long-term temporal dependencies and embeds driver-specific embeddings to represent latent individual characteristics, significantly enhancing the personalized prediction of driver retention risk, modeling how historical idle sequences influence the current risk of leaving the platform via trip acceptance or log-off. The model is validated on datasets from the City of T oronto over the period January 2 to March 13, 2020. The results show that the proposed Frailty-A ware Cox Transformer (F ACT) delivers the highest time-dependent C-indices and the lowest Brier Scores across early, median, and late follow-up, demonstrating its robustness in capturing evolving risk over a driver's lifecycle. This study enables operators to optimize retention strategies and helps policy makers assess shared mobility's role in equitable and integrated transportation systems. The purpose of this study is to model the driver retention behavior through a transformer-based survival model. Shared mobility services, such as ride-hailing, car-sharing, and bike-sharing, are becoming an increasingly prominent component of contemporary transportation systems. These services are central to the broader concept of Mobility as a Service (MaaS) [1], which aims to integrate various forms of transport into a unified and user-centric platform.
SurvAgent: Hierarchical CoT-Enhanced Case Banking and Dichotomy-Based Multi-Agent System for Multimodal Survival Prediction
Huang, Guolin, Chen, Wenting, Yang, Jiaqi, Lyu, Xinheng, Luo, Xiaoling, Yang, Sen, Xing, Xiaohan, Shen, Linlin
Survival analysis is critical for cancer prognosis and treatment planning, yet existing methods lack the transparency essential for clinical adoption. While recent pathology agents have demonstrated explainability in diagnostic tasks, they face three limitations for survival prediction: inability to integrate multimodal data, ineffective region-of-interest exploration, and failure to leverage experiential learning from historical cases. We introduce SurvAgent, the first hierarchical chain-of-thought (CoT)-enhanced multi-agent system for multimodal survival prediction. SurvAgent consists of two stages: (1) WSI-Gene CoT-Enhanced Case Bank Construction employs hierarchical analysis through Low-Magnification Screening, Cross-Modal Similarity-Aware Patch Mining, and Confidence-Aware Patch Mining for pathology images, while Gene-Stratified analysis processes six functional gene categories. Both generate structured reports with CoT reasoning, storing complete analytical processes for experiential learning. (2) Dichotomy-Based Multi-Expert Agent Inference retrieves similar cases via RAG and integrates multimodal reports with expert predictions through progressive interval refinement. Extensive experiments on five TCGA cohorts demonstrate SurvAgent's superority over conventional methods, proprietary MLLMs, and medical agents, establishing a new paradigm for explainable AI-driven survival prediction in precision oncology.