Martingale difference residuals as a diagnostic tool for the Cox model
Martingale difference residuals as a diagnostic tool for the Cox model
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DOI：
10.1093/biomet/90.4.899
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发表时间：
2003-12-01
期刊：
影响因子：
2.7
通讯作者：
Winnett, A
中科院分区：
文献类型：
--
作者：
Sasieni, PD;Winnett, A
比例风险模型做了两个主要的假设：风险比随时间变化不变，风险与连续协变量之间的关系是对数线性的。检查和放松这些假设的方法是存在的，但在这两种情况下，这些方法都依赖于另一个假设为真。如果这两个假设都不合适，或者只有一个合适但不知道是哪一个，就会出现问题。我们提出了一种新的残差来同时检验这两个假设。平滑后的残差提供了风险比的灵活估计，通过具有时间相关的风险比、变换的协变量或两者兼而有之，可能偏离标准比例风险模型。这些方法是使用医学研究委员会骨髓瘤试验的数据进行说明的。
The proportional hazards model makes two major assumptions: the hazard ratio is constant over time, and the relationship between the hazard and continuous covariates is log-linear. Methods exist for checking and relaxing each of these assumptions, but in both cases the methods rely on the other assumption being true. Problems can occur if neither of the assumptions is appropriate, or even if only one of the assumptions is appropriate but it is not known which. We propose a new kind of residual for checking the two assumptions simultaneously. The smoothed residuals provide a flexible estimate of the hazard ratio, which may deviate from the standard proportional hazards model by having a time-dependent hazard ratio, transformed covariates or both. The methods are illustrated using data from the Medical Research Council's myeloma trials.