Dimension reduction for censored regression data
Dimension reduction for censored regression data
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DOI：
10.1214/aos/1018031098
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发表时间：
1999-03
影响因子：
4.5
通讯作者：
Ker-Chau Li;Jane-ling Wang;Chun-Houh Chen
中科院分区：
文献类型：
--
作者：
Ker-Chau Li;Jane-ling Wang;Chun-Houh Chen
在没有参数假设的情况下，高维回归分析已经很复杂了。当数据受到删失时，情况会变得更加困难。在本文中，我们寻求在应用非参数平滑技术之前降低回归变量维度的方法。如果删失时间与寿命相互独立，那么切片逆回归方法可以直接应用。否则，需要进行修正以调整删失偏差。我们推导出了一个用于偏差校正的关键等式，并证明了修正估计量的$\sqrt{n}$一致性。在类似的降维框架下也可以研究删失模式。文中还报告了一些模拟结果以及对一个实际数据集的应用。
1. 引言
生存数据经常受到删失。当这种情况发生时，观测数据的不完整性可能会在样本中导致严重的偏差。已经提出了几种方法来克服回归中相关的困难，包括加速失效时间模型、删失线性回归、考克斯比例风险模型以及许多其他模型。当回归变量的维度增加时，生存分析变得更加复杂。要应用上述任何一种方法，使用者都需要指定一个将结果变量与输入变量相关联的函数形式。然而，在现实中，用于适当模型设定所需的知识往往是不足的。事实上，获取此类信息很可能本身就是研究的主要目标之一。在这种情况下，似乎更可取的是拥有较少依赖于这种模型设定的探索性工具。这就是本文要解决的问题。李（1991）的降维方法将被扩展到允许数据存在删失的情形。我们将提供寻找数据低维投影的方法，以便直观地检查删失模式。我们将展示在不预先假定函数形式的情况下如何仍然能够分析删失回归数据。
Without parametric assumptions, high-dimensional regression analysis is already complex. This is made even harder when data are subject to censoring. In this article, we seek ways of reducing the dimensionality of the regressor before applying nonparametric smoothing techniques. If the censoring time is independent of the lifetime, then the method of sliced inverse regression can be applied directly. Otherwise, modification is needed to adjust for the censoring bias. A key identity leading to the bias correction is derived and the root-n consistency of the modified estimate is established. Patterns of censoring can also be studied under a similar dimension reduction framework. Some simulation results and an application to a real data set are reported. 1. Introduction. Survival data are often subject to censoring. When this occurs, the incompleteness of the observed data may induce a substantial bias in the sample. Several approaches have been suggested to overcome the associated difficulties in regression, including the accelerated failure time model, censored linear regression, the Cox proportional hazard model and many others. Survival analysis becomes even more intricate when the dimension of the regressor increases. To apply any of the aforementioned methods, users are required to specify a functional form which relates the outcome variables to the input ones. However, in reality, knowledge needed for an appropriate model specification is often inadequate. As a matter of fact, the acquisition of such information may well turn out to be one of the primary goals of the study itself. Under such circumstances, it seems preferable to have exploratory tools that rely less on such model specification. This is the issue to be addressed in this article. The dimension reduction approach of Li Ž. 1991 will be extended to settings which allow for censoring in the data. We shall offer methods of finding low-dimensional projections of the data for visually examining the censoring pattern. We shall show how censored regression data can still be analyzed without assuming the functional form a priori.