Devarajan Karthik, Ebrahimi Nader
Division of Population Science, Fox Chase Cancer Center, Philadelphia, PA 19111.
Comput Stat Data Anal. 2011 Jan 1;55(1):667-676. doi: 10.1016/j.csda.2010.06.010.
The assumption of proportional hazards (PH) fundamental to the Cox PH model sometimes may not hold in practice. In this paper, we propose a generalization of the Cox PH model in terms of the cumulative hazard function taking a form similar to the Cox PH model, with the extension that the baseline cumulative hazard function is raised to a power function. Our model allows for interaction between covariates and the baseline hazard and it also includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach can not be applied here to estimate the model parameters. We use the full likelihood approach via a cubic B-spline approximation for the baseline hazard to estimate the model parameters. A semi-automatic procedure for knot selection based on Akaike's Information Criterion is developed. We illustrate the applicability of our approach using real-life data.
Cox比例风险（PH）模型所基于的比例风险假设在实际中有时可能不成立。在本文中，我们根据累积风险函数提出了Cox PH模型的一种推广形式，其形式类似于Cox PH模型，扩展之处在于基线累积风险函数被提升为幂函数。我们的模型允许协变量与基线风险之间存在交互作用，并且对于两样本问题，它还涵盖了两个尺度和形状参数均不同的威布尔分布以及两个极值分布的情况。这里不能应用偏似然方法来估计模型参数。我们通过对基线风险采用三次B样条近似的全似然方法来估计模型参数。开发了一种基于赤池信息准则的半自动节点选择程序。我们使用实际数据说明了我们方法的适用性。
