Survival Analysis via Ordinary Differential Equations

• 成果类型: Article
• 署名作者: Tang, Weijing; He, Kevin; Xu, Gongjun; Zhu, Ji
• 署名单位: University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2051519
• 发表日期: 2023
• 页码: 2406-2421
• 关键词: maximum-likelihood-estimation; proportional hazards model; transformation models; efficient estimation; semiparametric estimation; sensitivity-analysis; linear-regression; parameters; mortality; tests

摘要

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