Wu Baolin
Division of Biostatistics, School of Public Health, University of Minnesota, A460 Mayo Building, MMC 303, Minneapolis, MN 55455, USA.
Bioinformatics. 2006 Feb 15;22(4):472-6. doi: 10.1093/bioinformatics/bti827. Epub 2005 Dec 13.
Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p >> n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.
利用微阵列数据进行差异基因表达检测和样本分类,近年来受到了广泛的研究关注。由于基因数量(p)众多而样本数量(n)较少((p\gg n)),微阵列数据分析给统计分析带来了巨大挑战。“大(p)小(n)”带来的一个明显问题是过拟合。仅仅是偶然,我们就可能找到一些非差异表达基因,它们能很好地对样本进行分类。收缩的思想是对模型参数进行正则化,以减少噪声的影响并产生可靠的推断。收缩已成功应用于微阵列数据分析。Tusher等人提出的SAM统计量以及Tibshirani等人提出的“最近收缩质心”都是特殊的收缩方法。这两种方法都简单、直观,并且在实证研究中证明是有用的。最近,Wu通过正式使用用于两类微阵列数据的(1)惩罚线性回归模型,提出了具有收缩的惩罚(t/F)统计量,表现良好。在本文中,我们系统地讨论了惩罚回归模型在分析微阵列数据中的应用。我们将Wu提出的两类惩罚(t/F)统计量推广到多类微阵列数据。我们使用(1)惩罚回归模型正式推导了Tibshirani等人使用的特殊收缩质心。并且我们表明,惩罚线性回归模型为样本分类和差异基因表达检测提供了一个严谨统一的统计框架。