Comparing smoothing techniques in Cox models for exposure-response relationships
Comparing smoothing techniques in Cox models for exposure-response relationships
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DOI：
10.1002/sim.2848
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发表时间：
2007-09-10
影响因子：
2
通讯作者：
Eisen, Ellen A.
中科院分区：
文献类型：
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作者：
Govindarajulu, Usha S.;Spiegelman, Donna;Eisen, Ellen A.
为考虑非线性暴露 - 反应关系，我们对两个暴露分布呈偏态的职业队列中肺癌死亡时间模型应用了灵活的非参数平滑技术。我们聚焦于考克斯模型中的三种不同平滑技术：惩罚样条、受限三次样条和分数多项式。我们根据其可视化表示和模型选择标准对这三种方法的标准软件实现进行了比较。我们提出了一种基于两条曲线之间面积的曲线对差异度量方法，该面积通过曲线对下面积的平均值进行标准化。为捕捉暴露范围内差异的变化，还在暴露百分位数处计算曲线间面积，并表示为总差异的百分比。在两项研究中，三种方法得出的剂量 - 反应曲线在暴露范围较密集部分相似，曲线间直至第50百分位数的差异小于总差异的1%。对应用于暴露分布更偏态数据集的逆方差加权面积进行比较，使我们能够通过减少归因于上部1%尾区的比例，更精确地估计面积差异。总体而言，惩罚样条和受限三次样条彼此之间比它们与分数多项式更为接近。版权所有 (c) 2007约翰威立父子有限公司
To allow for non-linear exposure-response relationships, we applied flexible non-parametric smoothing techniques to models of time to lung cancer mortality in two occupational cohorts with skewed exposure distributions. We focused on three different smoothing techniques in Cox models: penalized splines, restricted cubic splines, and fractional polynomials. We compared standard software implementations of these three methods based on their visual representation and criterion for model selection. We propose a measure of the difference between a pair of curves based on the area between them, standardized by the average of the areas under the pair of curves. To capture the variation in the difference over the range of exposure, the area between curves was also calculated at percentiles of exposure and expressed as a percentage of the total difference. The dose-response curves from the three methods were similar in both studies over the denser portion of the exposure range, with the difference between curves up to the 50th percentile less than I per cent of the total difference. A comparison of inverse variance weighted areas applied to the data set with a more skewed exposure distribution allowed us to estimate area differences with more precision by reducing the proportion attributed to the upper I per cent tail region. Overall, the penalized spline and the restricted cubic spline were closer to each other than either was to the fractional polynomial. Copyright (c) 2007 John Wiley & Sons, Ltd.