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A Scalable Discrete-Time Survival Model for Neural Networks

arXiv 1805.00917 ↗First posted 2 May 2018stat.ML cs.CY cs.LGcited by 72

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Abstract (arXiv)

There is currently great interest in applying neural networks to prediction tasks in medicine. It is important for predictive models to be able to use survival data, where each patient has a known follow-up time and event/censoring indicator. This avoids information loss when training the model and enables generation of predicted survival curves. In this paper, we describe a discrete-time survival model that is designed to be used with neural networks, which we refer to as Nnet-survival. The model is trained with the maximum likelihood method using minibatch stochastic gradient descent (SGD). The use of SGD enables rapid convergence and application to large datasets that do not fit in memory. The model is flexible, so that the baseline hazard rate and the effect of the input data on hazard probability can vary with follow-up time. It has been implemented in the Keras deep learning framework, and source code for the model and several examples is available online. We demonstrate the performance of the model on both simulated and real data and compare it to existing models Cox-nnet and Deepsurv.

Key facts. Cited by 72 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 May 2018.

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Citing papers per year: 2021: 12; 2022: 12; 2023: 12; 2024: 8; 2025: 10; 2026: 18.

72 papers.

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  1. 2023Deep Learning for Survival Analysis: A Reviewcited by 75
  2. 2021SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Datacited by 25
  3. 2022Net benefit, calibration, threshold selection, and training objectives for algorithmic fairness in healthcarecited by 16
  4. 2022DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysiscited by 12
  5. 2021DeepMTS: Deep Multi-task Learning for Survival Prediction in Patients with Advanced Nasopharyngeal Carcinoma using Pretreatment PET/CTcited by 11
  6. 2024DRIM: Learning Disentangled Representations from Incomplete Multimodal Healthcare Datacited by 10
  7. 2022Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guaranteecited by 9
  8. 2022Survival Mixture Density Networkscited by 9
  9. 2023Merging-Diverging Hybrid Transformer Networks for Survival Prediction in Head and Neck Cancercited by 9
  10. 2023DySurv: dynamic deep learning model for survival analysis with conditional variational inferencecited by 9
  11. 2026Tabular Foundation Models Can Do Survival Analysiscited by 9
  12. 2021T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLPcited by 8
38 more
  1. 2021Inverse-Weighted Survival Gamescited by 8
  2. 2023Federated Survival Forestscited by 8
  3. 2021BDNNSurv: Bayesian deep neural networks for survival analysis using pseudo valuescited by 7
  4. 2021Avoiding C-hacking when evaluating survival distribution predictions with discrimination measurescited by 7
  5. 2022BITES: Balanced Individual Treatment Effect for Survival datacited by 7
  6. 2022Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Datacited by 7
  7. 2023Scaling Survival Analysis in Healthcare with Federated Survival Forests: A Comparative Study on Heart Failure and Breast Cancer Genomicscited by 6
  8. 2022Interpretable Prediction of Lung Squamous Cell Carcinoma Recurrence With Self-supervised Learningcited by 5
  9. 2022Predicting Time-to-conversion for Dementia of Alzheimer's Type using Multi-modal Deep Survival Analysiscited by 5
  10. 2023Contrastive Learning of Temporal Distinctiveness for Survival Analysis in Electronic Health Recordscited by 5
  11. 2024Dynamic Survival Analysis for Early Event Predictioncited by 5
  12. 2025NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantificationcited by 5
  13. 2022A Federated Cox Model with Non-Proportional Hazardscited by 4
  14. 2024Toward a Well-Calibrated Discrimination via Survival Outcome-Aware Contrastive Learningcited by 4
  15. 2023AdaMSS: Adaptive Multi-Modality Segmentation-to-Survival Learning for Survival Outcome Prediction from PET/CT Imagescited by 3
  16. 2025Multimodal Masked Autoencoder Pre-training for 3D MRI-Based Brain Tumor Analysis with Missing Modalitiescited by 3
  17. 2026SVL: Goal-Conditioned Reinforcement Learning as Survival Learningcited by 3
  18. 2023Multimodal Deep Learning for Personalized Renal Cell Carcinoma Prognosis: Integrating CT Imaging and Clinical Datacited by 2
  19. 2024Interpretable Prediction and Feature Selection for Survival Analysiscited by 2
  20. 2025SurvBench: A Standardised Preprocessing Pipeline for Multi-Modal Electronic Health Record Survival Analysiscited by 2
  21. 2025Understanding Overparametrization in Survival Models through Interpolationcited by 2
  22. 2026FSL-BDP: Federated Survival Learning with Bayesian Differential Privacy for Credit Risk Modelingcited by 2
  23. 2026HEPA: A Self-Supervised Horizon-Conditioned Event Predictive Architecture for Time Seriescited by 2
  24. 2026Causal multi-modal AI for personalized chemosensitivity predictioncited by 2
  25. 2021Causal inference for observational longitudinal studies using deep survival modelscited by 1
  26. 2021L1-regularized neural ranking for risk stratification and its application to prediction of time to distant metastasis in luminal node negative chemotherapy na"ive breast cancer patientscited by 1
  27. 2021Energy-based survival modelling using harmoniumscited by 1
  28. 2021Towards modelling hazard factors in unstructured data spaces using gradient-based latent interpolationcited by 1
  29. 2022Ad Creative Discontinuation Prediction with Multi-Modal Multi-Task Neural Survival Networkscited by 1
  30. 2023Contrastive Learning for Predicting Cancer Prognosis Using Gene Expression Valuescited by 1
  31. 2025Extending Cox Proportional Hazards Model with Symbolic Non-Linear Log-Risk Functions for Survival Analysiscited by 1
  32. 2025Dual Mixture-of-Experts Framework for Discrete-Time Survival Analysiscited by 1
  33. 2026Value-Monotonicity Matters: A Concordance Loss for Deep Survival Predictioncited by 1
  34. 2021Dynamic prediction of time to event with survival curvescited by 0
  35. 2021Survival-oriented embeddings for improving accessibility to complex data structurescited by 0
  36. 2022KL-divergence Based Deep Learning for Discrete Time Modelcited by 0
  37. 2022EDEN : An Event DEtection Network for the annotation of Breast Cancer recurrences in administrative claims datacited by 0
  38. 2023Case-Base Neural Networks: survival analysis with time-varying, higher-order interactionscited by 0

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