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.

该论文介绍了正交多项式积分算法（OPSurv），它是一种为生存分析中的单一和竞争风险场景提供时间连续性功能输出的新方法。OPSurv利用累积发生率函数的初始零条件和使用正交多项式对概率密度进行独特分解的方法，通过高斯-勒让德积分学习每种风险事件的函数近似系数，并构建累积发生率函数的估计。该方法能够有效对抗过拟合，特别是在竞争风险场景中，增强了模型的表达能力和控制性能。论文还详细介绍了OPSurv的实证验证和理论证明，突出了其作为竞争风险生存分析进展的稳健性能。

OPSurv：生存分析的正交多项式积分算法