Survival Analysis via Ordinary Differential Equations

This article introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE not only provides a unified modeling framework, but more importantly, also enables the development of widely applicable, scalable, and easy-to-implement procedure estimation inference. Specifically, framework unifies many existing models, such as proportional hazards model, linear transformation accelerated failure time time-varying coefficient model special cases. generality proposed serves foundation applicable procedure. As illustrative example, we develop sieve maximum likelihood estimator general semiparametric class models. In comparison to methods, has advantages in terms computational scalability numerical stability. Moreover, address unique theoretical challenges induced by notion, establish new M-theorem bundled parameters show that is consistent asymptotically normal, achieves efficiency bound. finite sample performance examined simulation studies real-world data example. Supplementary materials this are available online.