Survival Model Inference Using Functions of Brownian Motion

• 作者: John O’Quigley
• 来源期刊: 应用数学(英文)
• 学科: 医学
• 关键词: BROWNIAN MOTION BROWNIAN Bridge Cox MODEL Integrated BROWNIAN MOTION Kaplan-Meier Estimate Non-Proportional Hazards Reflected BROWNIAN MOTION TIME-VARYING Effects Weighted Score Equation
• 年，卷（期）: yysxyw_2012,（6）
• 页码范围: 641-651
• 页数: 11页
• 分类号: R73

摘要

A family of tests for the presence of regression effect under proportional and non-proportional hazards models is described. The non-proportional hazards model, although not completely general, is very broad and includes a large number of possibilities. In the absence of restrictions, the regression coefficient, β(t), can be any real function of time. When β(t) = β, we recover the proportional hazards model which can then be taken as a special case of a non-proportional hazards model. We study tests of the null hypothesis;H0:β(t) = 0 for all t against alternatives such as;H1:∫β(t)dF(t) ≠ 0 or H1:β(t) ≠ 0 for some t. In contrast to now classical approaches based on partial likelihood and martingale theory, the development here is based on Brownian motion, Donsker’s theorem and theorems from O’Quigley [1] and Xu and O’Quigley [2]. The usual partial likelihood score test arises as a special case. Large sample theory follows without special arguments, such as the martingale central limit theorem, and is relatively straightforward.