Diagnostic plots to reveal functional form for covariates in multiplicative intensity models
Diagnostic plots to reveal functional form for covariates in multiplicative intensity models
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DOI：
10.2307/2533277
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发表时间：
1995-12-01
期刊：
影响因子：
1.9
通讯作者：
Fleming, TR
中科院分区：
文献类型：
--
作者：
Grambsch, PM;Therneau, TM;Fleming, TR
我们展示了如何使用基于比例风险模型残差的图来揭示模型中协变量的正确函数形式。为此，Therneau、Grambsch 和 Fleming (1990, Biometrika 77, 147-160) 建议使用鞅残差的平滑图；然而，其一致性要求协变量是独立的。他们还指出，该图可能因较大的协变量效应而出现偏差。我们引入了两项改进来克服这些困难。第一个基于散点图平滑率，其中分子是针对协变量绘制的观察计数的平滑率，分母是预期计数的平滑率。这与 Arjas 拟合优度图相关（1988 年，美国统计协会杂志 83, 204-212）。第二种技术使用预期计数作为权重，对鞅残差除以预期计数进行平滑。后一种方法与 GLM 部分残差图以及 Hastie 和 Tibshirani (1990, Biometrics 46, 1005-1016) 以及 Gentleman 和 Crowley (1991, Biometrics 47, 1283-1296) 的迭代方法相关。给出了生存数据集的应用。
We show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model. A smoothed plot of the martingale residuals was suggested for this purpose by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160); however, its consistency required that the covariates be independent. They also noted that the plot could be biased for large covariate effects. We introduce two refinements which overcome these difficulties. The first is based on a ratio of scatter plot smooths, where the numerator is the smooth of the observed count plotted against the covariate, and the denominator is a smooth of the expected count. This is related to the Arjas goodness-of-fit plot (1988, Journal of the American Statistical Association 83, 204-212). The second technique smooths the martingale residuals divided by the expected count, using expected count as a weight. This latter approach is related to a GLM partial residual plot, as well as to the iterative methods of Hastie and Tibshirani (1990, Biometrics 46, 1005-1016) and Gentleman and Crowley (1991, Biometrics 47, 1283-1296). Applications to survival data sets are given.