# OPSurv: Orthogonal Polynomials Quadrature Algorithm for Survival Analysis

arXiv: https://arxiv.org/abs/2402.01955 · HTML: https://mlsanity.com/paper/2402.01955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [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)
- [Neural Fine-Gray: Monotonic neural networks for competing risks](https://mlsanity.com/paper/2305.06703/) (2023)
- [Deep Learning for Patient-Specific Kidney Graft Survival Analysis](https://mlsanity.com/paper/1705.10245/) (2017)

## Abstract (arXiv)

This paper introduces the Orthogonal Polynomials Quadrature Algorithm for Survival Analysis (OPSurv), a new method providing time-continuous functional outputs for both single and competing risks scenarios in survival analysis. OPSurv utilizes the initial zero condition of the Cumulative Incidence function and a unique decomposition of probability densities using orthogonal polynomials, allowing it to learn functional approximation coefficients for each risk event and construct Cumulative Incidence Function estimates via Gauss--Legendre quadrature. This approach effectively counters overfitting, particularly in competing risks scenarios, enhancing model expressiveness and control. The paper further details empirical validations and theoretical justifications of OPSurv, highlighting its robust performance as an advancement in survival analysis with competing risks.