# HACSurv: A Hierarchical Copula-Based Approach for Survival Analysis with Dependent Competing Risks

arXiv: https://arxiv.org/abs/2410.15180 · HTML: https://mlsanity.com/paper/2410.15180/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 19 Oct 2024.

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

- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [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)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Neural Fine-Gray: Monotonic neural networks for competing risks](https://mlsanity.com/paper/2305.06703/) (2023)
- [Copula-Based Deep Survival Models for Dependent Censoring](https://mlsanity.com/paper/2306.11912/) (2023)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [On structure, family and parameter estimation of hierarchical Archimedean copulas](https://mlsanity.com/paper/1611.09225/) (2016)

## Built on by (most cited first, 7 of 7)

- [VistaWise: Building Cost-Effective Agent with Cross-Modal Knowledge Graph for Minecraft](https://mlsanity.com/paper/2508.18722/) (2025)
- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [VideoStir: Understanding Long Videos via Spatio-Temporally Structured and Intent-Aware RAG](https://mlsanity.com/paper/2604.05418/) (2026)
- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [Overcoming Dependent Censoring in the Evaluation of Survival Models](https://mlsanity.com/paper/2502.19460/) (2025)
- [Archimedean Copula Inference via Taylor-Mode AD](https://mlsanity.com/paper/2605.23134/) (2026)

## Abstract (arXiv)

In survival analysis, subjects often face competing risks; for example, individuals with cancer may also suffer from heart disease or other illnesses, which can jointly influence the prognosis of risks and censoring. Traditional survival analysis methods often treat competing risks as independent and fail to accommodate the dependencies between different conditions. In this paper, we introduce HACSurv, a survival analysis method that learns Hierarchical Archimedean Copulas structures and cause-specific survival functions from data with competing risks. HACSurv employs a flexible dependency structure using hierarchical Archimedean copulas to represent the relationships between competing risks and censoring. By capturing the dependencies between risks and censoring, HACSurv improves the accuracy of survival predictions and offers insights into risk interactions. Experiments on synthetic dataset demonstrate that our method can accurately identify the complex dependency structure and precisely predict survival distributions, whereas the compared methods exhibit significant deviations between their predictions and the true distributions. Experiments on multiple real-world datasets also demonstrate that our method achieves better survival prediction compared to previous state-of-the-art methods.