Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form
Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form
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DOI：
10.1111/j.1541-0420.2005.00519.x
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发表时间：
2006-09-01
期刊：
影响因子：
1.9
通讯作者：
Liu, Linxu
中科院分区：
文献类型：
--
作者：
Huang, Jianhua Z.;Liu, Linxu
考克斯比例风险模型通常假设风险函数对协变量的依赖性为指数形式。然而，在实践中，这一假设可能会被违反，其他相对风险形式可能更合适。本文考虑了具有未知相对风险形式的比例风险模型。模型解释中的问题得到解决。我们提出了一种方法来估计相对风险的形式和回归参数同时通过第一近似的对数的相对风险的形式由样条，然后采用最大偏似然估计。一个迭代交替优化程序开发的有效实施。讨论了基于参数渐近理论的回归系数和相对风险形式的统计推断。所提出的方法进行了说明，使用模拟和退伍军人管理局肺癌数据的应用程序。
The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data.