REGULARIZATION FOR COX'S PROPORTIONAL HAZARDS MODEL WITH NP-DIMENSIONALITY.
REGULARIZATION FOR COX'S PROPORTIONAL HAZARDS MODEL WITH NP-DIMENSIONALITY.
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DOI：
10.1214/11-aos911
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发表时间：
2011
影响因子：
4.5
通讯作者：
Jiang J
中科院分区：
文献类型：
--
作者：
Bradic J;Fan J;Jiang J
高通量基因测序阵列，每个样本数千次测量和大量相关的经审查的临床数据，增加了对更好的测量特定模型选择的需求。本文在Cox比例风险模型的框架下，建立了非多项式(NP)维截尾数据的非凹惩罚方法的强Oracle性质。采用了一类折叠-凹形惩罚，并对套索和SCAD进行了具体的讨论。我们揭示了在哪些维度和相关性约束下可以构造和把握Oracle估计量的问题。结果表明，非凹形惩罚显著减少了套索模型选择一致性所需的“不可表示条件”。为了刻画强Oracle性质，发展了具有自身利益的大偏差结果。此外，证明了非凹正则估计渐近地达到了Oracle估计的信息界。提出了一种求解罚风险回归问题解路径网格的坐标算法，并在模拟算例和基因关联研究算例中对其性能进行了评价。
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Cox’s proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that non-concave penalties lead to significant reduction of the “irrepresentable condition” needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing the strong oracle property. Moreover, the non-concave regularized estimator, is shown to achieve asymptotically the information bound of the oracle estimator. A coordinate-wise algorithm is developed for finding the grid of solution paths for penalized hazard regression problems, and its performance is evaluated on simulated and gene association study examples.