# Copula-Based Deep Survival Models for Dependent Censoring

arXiv: https://arxiv.org/abs/2306.11912 · HTML: https://mlsanity.com/paper/2306.11912/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 63 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [Empirical Analysis of Model Selection for Heterogeneous Causal Effect Estimation](https://mlsanity.com/paper/2211.01939/) (2022)
- [Parameter identifiability of a deep feedforward ReLU neural network](https://mlsanity.com/paper/2112.12982/) (2021)
- [Validating Causal Inference Methods](https://mlsanity.com/paper/2202.04208/) (2022)

## Built on by (most cited first, 12 of 12)

- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [HACSurv: A Hierarchical Copula-Based Approach for Survival Analysis with Dependent Competing Risks](https://mlsanity.com/paper/2410.15180/) (2024)
- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2410.16765/) (2024)
- [Benchmarking Observational Studies with Experimental Data under Right-Censoring](https://mlsanity.com/paper/2402.15137/) (2024)
- [MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation](https://mlsanity.com/paper/2409.06525/) (2024)
- [Overcoming Dependent Censoring in the Evaluation of Survival Models](https://mlsanity.com/paper/2502.19460/) (2025)
- [Predicting Long-Term Allograft Survival in Liver Transplant Recipients](https://mlsanity.com/paper/2408.05437/) (2024)
- [Teaching Models To Survive: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2406.14085/) (2024)
- [A meaningful prediction of functional decline in amyotrophic lateral sclerosis based on multi-event survival analysis](https://mlsanity.com/paper/2506.02076/) (2025)
- [Archimedean Copula Inference via Taylor-Mode AD](https://mlsanity.com/paper/2605.23134/) (2026)

## Abstract (arXiv)

A survival dataset describes a set of instances (e.g. patients) and provides, for each, either the time until an event (e.g. death), or the censoring time (e.g. when lost to follow-up - which is a lower bound on the time until the event). We consider the challenge of survival prediction: learning, from such data, a predictive model that can produce an individual survival distribution for a novel instance. Many contemporary methods of survival prediction implicitly assume that the event and censoring distributions are independent conditional on the instance's covariates - a strong assumption that is difficult to verify (as we observe only one outcome for each instance) and which can induce significant bias when it does not hold. This paper presents a parametric model of survival that extends modern non-linear survival analysis by relaxing the assumption of conditional independence. On synthetic and semi-synthetic data, our approach significantly improves estimates of survival distributions compared to the standard that assumes conditional independence in the data.