# Deep Cox Mixtures for Survival Regression arXiv: https://arxiv.org/abs/2101.06536 ยท HTML: https://mlsanity.com/paper/2101.06536/ ## Key facts - Cited by 44 papers in the map (data through 14 Oct 2026). - Builds on 20 of its 60 references that are in the map. - First posted on arXiv 16 Jan 2021. ## Builds on (most cited first, 20 of 20) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017) - [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016) - [Model Cards for Model Reporting](https://mlsanity.com/paper/1810.03993/) (2018) - [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016) - [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016) - [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019) - [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017) - [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016) - [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019) - [Posterior calibration and exploratory analysis for natural language processing models](https://mlsanity.com/paper/1508.05154/) (2015) - [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020) - [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016) - [Learning Optimized Risk Scores](https://mlsanity.com/paper/1610.00168/) (2016) - [Adversarial Time-to-Event Modeling](https://mlsanity.com/paper/1804.03184/) (2018) - [Survival Cluster Analysis](https://mlsanity.com/paper/2003.00355/) (2020) - [Causal Rule Sets for Identifying Subgroups with Enhanced Treatment Effect](https://mlsanity.com/paper/1710.05426/) (2017) - [Interpretable Subgroup Discovery in Treatment Effect Estimation with Application to Opioid Prescribing Guidelines](https://mlsanity.com/paper/1905.03297/) (2019) - [Variational Learning of Individual Survival Distributions](https://mlsanity.com/paper/2003.04430/) (2020) - [Nonlinear Semi-Parametric Models for Survival Analysis](https://mlsanity.com/paper/1905.05865/) (2019) ## Built on by (most cited first, 30 of 44) - [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023) - [A Deep Variational Approach to Clustering Survival Data](https://mlsanity.com/paper/2106.05763/) (2021) - [Healthsheet: Development of a Transparency Artifact for Health Datasets](https://mlsanity.com/paper/2202.13028/) (2022) - [CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysis](https://mlsanity.com/paper/2409.04290/) (2024) - [Neural Fine-Gray: Monotonic neural networks for competing risks](https://mlsanity.com/paper/2305.06703/) (2023) - [auton-survival: an Open-Source Package for Regression, Counterfactual Estimation, Evaluation and Phenotyping with Censored Time-to-Event Data](https://mlsanity.com/paper/2204.07276/) (2022) - [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024) - [Counterfactual Phenotyping with Censored Time-to-Events](https://mlsanity.com/paper/2202.11089/) (2022) - [SurvLatent ODE : A Neural ODE based time-to-event model with competing risks for longitudinal data improves cancer-associated Venous Thromboembolism (VTE) prediction](https://mlsanity.com/paper/2204.09633/) (2022) - [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) - [Tabular Foundation Models Can Do Survival Analysis](https://mlsanity.com/paper/2601.22259/) (2026) - [Real-time Mortality Prediction Using MIMIC-IV ICU Data Via Boosted Nonparametric Hazards](https://mlsanity.com/paper/2110.08949/) (2021) - [Neural Frailty Machine: Beyond proportional hazard assumption in neural survival regressions](https://mlsanity.com/paper/2303.10358/) (2023) - [Survival Seq2Seq: A Survival Model based on Sequence to Sequence Architecture](https://mlsanity.com/paper/2204.04542/) (2022) - [Individual Survival Curves with Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12825/) (2021) - [Efficient Training of Probabilistic Neural Networks for Survival Analysis](https://mlsanity.com/paper/2404.06421/) (2024) - [Deep conditional transformation models for survival analysis](https://mlsanity.com/paper/2210.11366/) (2022) - [Adaptive Transformer Modelling of Density Function for Nonparametric Survival Analysis](https://mlsanity.com/paper/2409.06209/) (2024) - [Calibrated Predictive Lower Bounds on Time-to-Unsafe-Sampling in LLMs](https://mlsanity.com/paper/2506.13593/) (2025) - [Competing Risks: Impact on Risk Estimation and Algorithmic Fairness](https://mlsanity.com/paper/2508.05435/) (2025) - [Variable selection for nonlinear Cox regression model via deep learning](https://mlsanity.com/paper/2211.09287/) (2022) - [Interpretable Prediction and Feature Selection for Survival Analysis](https://mlsanity.com/paper/2404.14689/) (2024) - [Aligning Data-Driven Predictors with Allocation: A Decision-Focused Approach to Survival Analysis](https://mlsanity.com/paper/2606.02671/) (2026) - [Multi-Source Survival Domain Adaptation](https://mlsanity.com/paper/2212.00424/) (2022) - [Recovering Sparse and Interpretable Subgroups with Heterogeneous Treatment Effects with Censored Time-to-Event Outcomes](https://mlsanity.com/paper/2302.12504/) (2023) - [Towards Flexible Time-to-event Modeling: Optimizing Neural Networks via Rank Regression](https://mlsanity.com/paper/2307.08044/) (2023) - [Maximum Likelihood Estimation of Flexible Survival Densities with Importance Sampling](https://mlsanity.com/paper/2311.01660/) (2023) - [Censor Dependent Variational Inference](https://mlsanity.com/paper/2502.09591/) (2025) - [Attention-Based Synthetic Data Generation for Calibration-Enhanced Survival Analysis: A Case Study for Chronic Kidney Disease Using Electronic Health Records](https://mlsanity.com/paper/2503.06096/) (2025) ## Abstract (arXiv) Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical applications, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an approximation to the Expectation Maximization algorithm for this model that does hard assignments to mixture groups to make optimization efficient. In each group assignment, we fit the hazard ratios within each group using deep neural networks, and the baseline hazard for each mixture component non-parametrically. We perform experiments on multiple real world datasets, and look at the mortality rates of patients across ethnicity and gender. We emphasize the importance of calibration in healthcare settings and demonstrate that our approach outperforms classical and modern survival analysis baselines, both in terms of discriminative performance and calibration, with large gains in performance on the minority demographics.