# An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes

arXiv: https://arxiv.org/abs/2410.01086 · HTML: https://mlsanity.com/paper/2410.01086/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 182 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 30 of 36)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [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)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Deep Neural Networks for Survival Analysis Based on a Multi-Task Framework](https://mlsanity.com/paper/1801.05512/) (2018)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [Learning with Hyperspherical Uniformity](https://mlsanity.com/paper/2103.01649/) (2021)
- [Adversarial Time-to-Event Modeling](https://mlsanity.com/paper/1804.03184/) (2018)
- [Countdown Regression: Sharp and Calibrated Survival Predictions](https://mlsanity.com/paper/1806.08324/) (2018)
- [X-CAL: Explicit Calibration for Survival Analysis](https://mlsanity.com/paper/2101.05346/) (2021)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [A Deep Variational Approach to Clustering Survival Data](https://mlsanity.com/paper/2106.05763/) (2021)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [Neural Fine-Gray: Monotonic neural networks for competing risks](https://mlsanity.com/paper/2305.06703/) (2023)
- [An Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [Survival stacking: casting survival analysis as a classification problem](https://mlsanity.com/paper/2107.13480/) (2021)
- [Deep Kernel Survival Analysis and Subject-Specific Survival Time Prediction Intervals](https://mlsanity.com/paper/2007.12975/) (2020)
- [Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration](https://mlsanity.com/paper/2405.07374/) (2024)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)

## Built on by (most cited first, 16 of 16)

- [Tabular Foundation Models Can Do Survival Analysis](https://mlsanity.com/paper/2601.22259/) (2026)
- [Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks](https://mlsanity.com/paper/2603.29475/) (2026)
- [One Loss to Rule Them All: Marked Time-to-Event for Structured EHR Foundation Models](https://mlsanity.com/paper/2602.00541/) (2026)
- [Survival Analysis as Imprecise Classification with Trainable Kernels](https://mlsanity.com/paper/2506.10140/) (2025)
- [Stepwise Fine and Gray: Subject-Specific Variable Selection Shows When Hemodynamic Data Improves Prognostication of Comatose Post-Cardiac Arrest Patients](https://mlsanity.com/paper/2508.06023/) (2025)
- [Survival Concept-Based Learning Models](https://mlsanity.com/paper/2502.05950/) (2025)
- [dnamite: A Python Package for Neural Additive Models](https://mlsanity.com/paper/2503.07642/) (2025)
- [A novel gradient-based method for decision trees optimizing arbitrary differential loss functions](https://mlsanity.com/paper/2503.17855/) (2025)
- [Deep Kernel Aalen-Johansen Estimator: An Interpretable and Flexible Neural Net Framework for Competing Risks](https://mlsanity.com/paper/2512.08063/) (2025)
- [Counterfactual Understanding via Retrieval-aware Multimodal Modeling for Time-to-Event Survival Prediction](https://mlsanity.com/paper/2602.19987/) (2026)
- [SDPM: Survival Diffusion Probabilistic Model for Continuous-Time Survival Analysis](https://mlsanity.com/paper/2605.22776/) (2026)
- [KAPLAN: Kolmogorov-Arnold Prognostic Learnable Activation Networks for Survival Analysis](https://mlsanity.com/paper/2605.23082/) (2026)
- [Non-Crossing Deep Quantile Regression for Distributional Survival Prediction](https://mlsanity.com/paper/2608.16864/) (2026)
- [Self-supervised Pre-training Helps Retinal Disease Progression Modelling Most When Data Is Scarce](https://mlsanity.com/paper/2609.12834/) (2026)
- [Horizon-Aware Early Event Prediction for Tokamak Disruption Alarms](https://mlsanity.com/paper/2609.24443/) (2026)
- [Rank Collapse Is Recoverable, Growing |Q| Is Not: Out-of-Sample Early Warning for Value Divergence in High-UTD Soft Actor-Critic](https://mlsanity.com/paper/2609.32819/) (2026)

## Abstract (arXiv)

Many applications involve reasoning about time durations before a critical event happens--also called time-to-event outcomes. When will a customer cancel a subscription, a coma patient wake up, or a convicted criminal reoffend? Time-to-event outcomes have been studied extensively within the field of survival analysis primarily by the statistical, medical, and reliability engineering communities, with textbooks already available in the 1970s and '80s. This monograph aims to provide a reasonably self-contained modern introduction to survival analysis. We focus on predicting time-to-event outcomes at the individual data point level with the help of neural networks. Our goal is to provide the reader with a working understanding of precisely what the basic time-to-event prediction problem is, how it differs from standard regression and classification, and how key "design patterns" have been used time after time to derive new time-to-event prediction models, from classical methods like the Cox proportional hazards model to modern deep learning approaches such as deep kernel Kaplan-Meier estimators and neural ordinary differential equation models. We further delve into two extensions of the basic time-to-event prediction setup: predicting which of several critical events will happen first along with the time until this earliest event happens (the competing risks setting), and predicting time-to-event outcomes given a time series that grows in length over time (the dynamic setting). We conclude with a discussion of a variety of topics such as fairness, causal reasoning, interpretability, and statistical guarantees. Our monograph comes with an accompanying code repository that implements every model and evaluation metric that we cover in detail.