  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.
