Elandt-Johnson R C, Smith F B
Department of Biostatistics-CSCC, University of North Carolina, Chapel Hill 27599.
Stat Med. 1989 Jun;8(6):703-23. doi: 10.1002/sim.4780080609.
Three kinds of generalized residuals based on probability integral transformation are defined and their roles in graphical goodness of fit testing are discussed. Although they are useful in fitting parametric distributions, their value is questionable, however, in fitting Cox's proportional hazard rate (PHR) models. They almost always appear to give a good fit because of (a) almost non-parametric nature of the PHR models; (b) heavy right-hand censoring in epidemiological data; and (c) scale adjustment in graphical presentation. Thus, the apparent overall fit has little inferential meaning, but the residuals are useful in exploratory analysis. A simple method, based on non-parametric stratified residual plots, for selection of risk factors is discussed. It is, in fact, equivalent to comparison of several empirical survival functions, one for each set of values (stratum) of a covariable under consideration. It is also suggested that for the preliminary PHR model, the continuous variables should be discretized and indicator variables used in the model to check analytically the graphical perception of the possible functional form of the contribution of each covariable to the PHR model.
定义了基于概率积分变换的三种广义残差，并讨论了它们在拟合优度图形检验中的作用。尽管它们在拟合参数分布时很有用，但在拟合考克斯比例风险率（PHR）模型时，其价值却值得怀疑。由于（a）PHR模型几乎是非参数性质；（b）流行病学数据中严重的右删失；以及（c）图形展示中的尺度调整，它们几乎总是显示出良好的拟合效果。因此，表面上的整体拟合几乎没有推断意义，但残差在探索性分析中是有用的。讨论了一种基于非参数分层残差图选择风险因素的简单方法。实际上，它等同于比较几个经验生存函数，每个经验生存函数对应于所考虑协变量的每组值（层）。还建议对于初步的PHR模型，应将连续变量离散化，并在模型中使用指示变量，以便从分析上检验每个协变量对PHR模型贡献的可能函数形式的图形感知。
