# Continuous and Discrete-Time Survival Prediction with Neural Networks

arXiv: https://arxiv.org/abs/1910.06724 · HTML: https://mlsanity.com/paper/1910.06724/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 30 of 70)

- [MOTOR: A Time-To-Event Foundation Model For Structured Medical Records](https://mlsanity.com/paper/2301.03150/) (2023)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysis](https://mlsanity.com/paper/2409.04290/) (2024)
- [Net benefit, calibration, threshold selection, and training objectives for algorithmic fairness in healthcare](https://mlsanity.com/paper/2202.01906/) (2022)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis](https://mlsanity.com/paper/2202.07423/) (2022)
- [DRIM: Learning Disentangled Representations from Incomplete Multimodal Healthcare Data](https://mlsanity.com/paper/2409.17055/) (2024)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)
- [Survival Mixture Density Networks](https://mlsanity.com/paper/2208.10759/) (2022)
- [Proper Scoring Rules for Survival Analysis](https://mlsanity.com/paper/2305.00621/) (2023)
- [DySurv: dynamic deep learning model for survival analysis with conditional variational inference](https://mlsanity.com/paper/2310.18681/) (2023)
- [Comprehensive Multimodal Deep Learning Survival Prediction Enabled by a Transformer Architecture: A Multicenter Study in Glioblastoma](https://mlsanity.com/paper/2405.12963/) (2024)
- [Tabular Foundation Models Can Do Survival Analysis](https://mlsanity.com/paper/2601.22259/) (2026)
- [The structure of online social networks modulates the rate of lexical change](https://mlsanity.com/paper/2104.05010/) (2021)
- [Inverse-Weighted Survival Games](https://mlsanity.com/paper/2111.08175/) (2021)
- [Federated Survival Forests](https://mlsanity.com/paper/2302.02807/) (2023)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [DeepMMSA: A Novel Multimodal Deep Learning Method for Non-small Cell Lung Cancer Survival Analysis](https://mlsanity.com/paper/2106.06744/) (2021)
- [Avoiding C-hacking when evaluating survival distribution predictions with discrimination measures](https://mlsanity.com/paper/2112.04828/) (2021)
- [BITES: Balanced Individual Treatment Effect for Survival data](https://mlsanity.com/paper/2201.03448/) (2022)
- [Scaling Survival Analysis in Healthcare with Federated Survival Forests: A Comparative Study on Heart Failure and Breast Cancer Genomics](https://mlsanity.com/paper/2308.02382/) (2023)
- [Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2410.16765/) (2024)
- [Predicting Time-to-conversion for Dementia of Alzheimer's Type using Multi-modal Deep Survival Analysis](https://mlsanity.com/paper/2205.01188/) (2022)
- [Heterogeneous Datasets for Federated Survival Analysis Simulation](https://mlsanity.com/paper/2301.12166/) (2023)
- [NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2505.11054/) (2025)
- [A Federated Cox Model with Non-Proportional Hazards](https://mlsanity.com/paper/2207.05050/) (2022)
- [FPBoost: Fully Parametric Gradient Boosting for Survival Analysis](https://mlsanity.com/paper/2409.13363/) (2024)
- [Clustering Survival Data using a Mixture of Non-parametric Experts](https://mlsanity.com/paper/2405.15934/) (2024)

## Abstract (arXiv)

Application of discrete-time survival methods for continuous-time survival prediction is considered. For this purpose, a scheme for discretization of continuous-time data is proposed by considering the quantiles of the estimated event-time distribution, and, for smaller data sets, it is found to be preferable over the commonly used equidistant scheme. Furthermore, two interpolation schemes for continuous-time survival estimates are explored, both of which are shown to yield improved performance compared to the discrete-time estimates. The survival methods considered are based on the likelihood for right-censored survival data, and parameterize either the probability mass function (PMF) or the discrete-time hazard rate, both with neural networks. Through simulations and study of real-world data, the hazard rate parametrization is found to perform slightly better than the parametrization of the PMF. Inspired by these investigations, a continuous-time method is proposed by assuming that the continuous-time hazard rate is piecewise constant. The method, named PC-Hazard, is found to be highly competitive with the aforementioned methods in addition to other methods for survival prediction found in the literature.