Lue Heng-Hui, Chen Chen-Hsin, Chang Wei-Hwa
Department of Statistics, Tunghai University, Taichung, Taiwan.
Biom J. 2011 May;53(3):426-43. doi: 10.1002/bimj.201000168. Epub 2011 Apr 15.
Dimension reduction methods have been proposed for regression analysis with predictors of high dimension, but have not received much attention on the problems with censored data. In this article, we present an iterative imputed spline approach based on principal Hessian directions (PHD) for censored survival data in order to reduce the dimension of predictors without requiring a prespecified parametric model. Our proposal is to replace the right-censored survival time with its conditional expectation for adjusting the censoring effect by using the Kaplan-Meier estimator and an adaptive polynomial spline regression in the residual imputation. A sparse estimation strategy is incorporated in our approach to enhance the interpretation of variable selection. This approach can be implemented in not only PHD, but also other methods developed for estimating the central mean subspace. Simulation studies with right-censored data are conducted for the imputed spline approach to PHD (IS-PHD) in comparison with two methods of sliced inverse regression, minimum average variance estimation, and naive PHD in ignorance of censoring. The results demonstrate that the proposed IS-PHD method is particularly useful for survival time responses approximating symmetric or bending structures. Illustrative applications to two real data sets are also presented.
针对具有高维预测变量的回归分析，已经提出了降维方法，但对于删失数据的问题却没有受到太多关注。在本文中，我们提出了一种基于主海森方向（PHD）的迭代插补样条方法，用于处理删失生存数据，以便在无需预先指定参数模型的情况下降低预测变量的维度。我们的建议是，通过使用Kaplan-Meier估计器和残差插补中自适应多项式样条回归，用其条件期望替代右删失生存时间，以调整删失效应。我们的方法中纳入了一种稀疏估计策略，以增强变量选择的可解释性。这种方法不仅可以在PHD中实现，也可以在为估计中心均值子空间而开发的其他方法中实现。针对右删失数据进行了模拟研究，将用于PHD的插补样条方法（IS-PHD）与切片逆回归、最小平均方差估计以及忽略删失的朴素PHD这两种方法进行比较。结果表明，所提出的IS-PHD方法对于近似对称或弯曲结构的生存时间响应特别有用。还给出了对两个真实数据集的说明性应用。
