A Graphical Method for Assessing Goodness of Fit in Cox's Proportional Hazards Model
评估Cox比例风险模型拟合优度的图形方法AI 解读 ↓
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评估Cox比例风险模型拟合优度的图形方法
- 研究问题
- 怎样通过直观图形检查Cox生存回归模型是否遗漏重要协变量，或错误地为不同个体设置共同基准风险？
- 方法与思路
- 作者按待检查的模型方面将个体分层，每层比较观察到与模型预期的失效频数，无需估计替代模型。
- 材料陈述的贡献
- 摘要称该方法计算简便，并通过模拟、心脏移植和黑色素瘤生存数据展示对严重模型缺陷的诊断能力。
- 阅读关注点
- 应核对分层依据、预期失效频数的计算、删失处理及图形随机波动，区分系统性偏差与偶然起伏。
- 阅读边界
- 仅据版本未注明的索引摘要，不能判断诊断的误报率、检验功效或轻微误设的可检出性，也不能推断刊本变化。
原文摘要
Suggested here is a simple graphical method for studying the goodness of fit in Cox's regression model for survival data. The method is easy to use, as it does not require the estimation of alternative models and only involves quantities similar to those already appearing in the partial likelihood expression that is needed in the parameter estimation. The rationale behind the graphs is very intuitive: They make a direct comparison between observed and expected failure frequencies, as estimated from the model. In a correctly specified model one anticipates an approximate balance between such frequencies; otherwise there will typically be groups of individuals for which the expected frequencies are systematically too high or too low to match with the data, and this shows in the graphs introduced here. In the concrete applications of the method the individuals are stratified in a way that depends on what aspect of the model is being checked against data. There is always one graph for each stratum. Simulated and real data are used to illustrate the method. In the simulations two types of defect that can come up in a Cox's model are considered: (a) an influential covariate has been deleted from the model, and (b) a common baseline hazard for all individuals has been assumed in a case in which the individuals should be stratified according to baseline hazard. Serious defects in the model are relatively easy to detect from the diagnostic graphs. As concrete applications of the method, studied briefly are the fitting of Cox's model to the well-known Stanford heart transplant data and to a data set describing the survival of malignant melanoma patients after operation. The article concludes with some general observations concerning the randomness in the graphs.