# Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees

arXiv: https://arxiv.org/abs/2312.15566 · HTML: https://mlsanity.com/paper/2312.15566/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 56 references that are in the map.
- First posted on arXiv 24 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Survival Regression with Proper Scoring Rules and Monotonic Neural Networks](https://mlsanity.com/paper/2103.14755/) (2021)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Copula-Based Deep Survival Models for Dependent Censoring](https://mlsanity.com/paper/2306.11912/) (2023)
- [A copula-based boosting model for time-to-event prediction with dependent censoring](https://mlsanity.com/paper/2210.04869/) (2022)

## Built on by (most cited first, 8 of 8)

- [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)
- [MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation](https://mlsanity.com/paper/2409.06525/) (2024)
- [CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks](https://mlsanity.com/paper/2605.12580/) (2026)
- [Overcoming Dependent Censoring in the Evaluation of Survival Models](https://mlsanity.com/paper/2502.19460/) (2025)
- [Teaching Models To Survive: Proper Scoring Rule and Stochastic Optimization with Competing Risks](https://mlsanity.com/paper/2406.14085/) (2024)
- [Multimodal Feature Prototype Learning for Interpretable and Discriminative Cancer Survival Prediction](https://mlsanity.com/paper/2510.06113/) (2025)

## Abstract (arXiv)

Censoring is the central problem in survival analysis where either the time-to-event (for instance, death), or the time-tocensoring (such as loss of follow-up) is observed for each sample. The majority of existing machine learning-based survival analysis methods assume that survival is conditionally independent of censoring given a set of covariates; an assumption that cannot be verified since only marginal distributions is available from the data. The existence of dependent censoring, along with the inherent bias in current estimators has been demonstrated in a variety of applications, accentuating the need for a more nuanced approach. However, existing methods that adjust for dependent censoring require practitioners to specify the ground truth copula. This requirement poses a significant challenge for practical applications, as model misspecification can lead to substantial bias. In this work, we propose a flexible deep learning-based survival analysis method that simultaneously accommodate for dependent censoring and eliminates the requirement for specifying the ground truth copula. We theoretically prove the identifiability of our model under a broad family of copulas and survival distributions. Experiments results from a wide range of datasets demonstrate that our approach successfully discerns the underlying dependency structure and significantly reduces survival estimation bias when compared to existing methods.