Joint estimation of time-dependent and non-linear effects of continuous covariates on survival
Joint estimation of time-dependent and non-linear effects of continuous covariates on survival
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DOI：
10.1002/sim.2519
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发表时间：
2007-01-30
影响因子：
2
通讯作者：
MacKenzie, Todd A.
中科院分区：
文献类型：
--
作者：
Abrahamowicz, Michal;MacKenzie, Todd A.
为了产生更灵活的模型，Cox回归模型lambda(t;x) = lambda(0)(t) exp(beta x)，已经使用不同的非参数模型估计技术进行了推广。一个推广是x的对数线性的松弛，lambda(t;x)=lambda(0)(t)exp[r(x)]。另一个是比例风险假设的松弛，lambda(t;x)=lambda(0)(t)exp[beta(t)x]。这些概括通常是相互独立的。我们提出了产品模型，lambda(t;x)=lambda(0)(t) exp[beta(t)r(x)]，它允许对两种效应进行联合估计，并研究其性质。描述时间相关的1 (t)和非线性r(x)效应的函数使用回归样条同时建模，并通过最大部分似然估计。提出了似然比检验来比较不同的模型。仿真表明，只要基于正确的模型，两个函数的形状恢复和测试的大小都是相当准确的。相比之下，如果模型指定错误，则类型I的错误率可能会被高度夸大，并且估计会有相当大的偏差。在癌症流行病学中的应用说明了产品模型如何对预后因素的作用产生新的见解。版权所有(c) 2006约翰威利父子有限公司
in order to yield more flexible models, the Cox regression model, lambda(t;x) = lambda(0)(t) exp(beta x), has been generalized using different non-parametric model estimation techniques. One generalization is the relaxation of log-linearity in x, lambda(t;x)=lambda(0)(t)exp[r(x)]. Another is the relaxation of the proportional hazards assumption, lambda(t;x)=lambda(0)(t)exp[beta(t)x]. These generalizations are typically considered independently of each other. We propose the product model, lambda(t;x)=lambda(0)(t) exp[beta(t)r(x)] which allows for joint estimation of both effects, and investigate its properties. The functions describing the time-dependent 1 (t) and non-linear r(x) effects are modelled simultaneously using regression splines and estimated by maximum partial likelihood. Likelihood ratio tests are proposed to compare alternative models. Simulations indicate that both the recovery of the shapes of the two functions and the size of the tests are reasonably accurate provided they are based on the correct model. By contrast, type I error rates may be highly inflated, and the estimates considerably biased, if the model is misspecified. Applications in cancer epidemiology illustrate how the product model may yield new insights about the role of prognostic factors. Copyright (c) 2006 John Wiley & Sons, Ltd.