Bayesian Regression Analysis in the "Large p, Small n" Paradigm with Application in DNA Microarray S
Bayesian Regression Analysis in the "Large p, Small n" Paradigm with Application in DNA Microarray S
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发表时间：
2000
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通讯作者：
M. West;J. Nevins;J. Marks;R. Spang;H. Zuzan
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作者：
M. West;J. Nevins;J. Marks;R. Spang;H. Zuzan
在应用科学和医学中，样本量远远小于可用的和潜在的有趣的预测因子（解释变量）的统计建模和推断问题比比皆是。这些“大p，小n”问题对标准统计方法提出了挑战，并要求回归和分类的新概念和模型。我们的动机应用背景是在功能基因组学;更具体地说，在表型临床或生理结果的研究中，预测因子是基于高密度DNA微阵列测量的大量基因的表达水平。在二元回归的规范框架中，我们讨论了（a）利用严重秩亏的设计矩阵的奇异值分解的回归建模问题，（B）对高维回归参数进行仔细的、信息丰富的先验规范的必要性，（c）为这个问题开发新的结构化先验分布类，及（d）发展适当的计算方法及模式，以进行回归估计的后验推断及样本外分类的预测推断。后一项事业是基因组表型分析应用的基础。我们研究和验证了新的统计方法在乳腺癌表型的问题，使用DNA微阵列表达谱作为预测因子，并在白血病类型的歧视。
Statistical modelling and inference problems in which sample sizes are substantially smaller than the number of available and potentially interesting predictors (explanatory variables) abound in applied science and medicine. These “Large p, Small n” problems pose challenges to standard statistical methods and demand new concepts and models for regression and classification. Our motivating applied context is in functional genomics; more specifically, in studies of phenotyping clinical or physiological outcomes in which the predictors are measured expression levels of large numbers of genes based on high-density DNA microarrays. In a canonical framework of binary regression, we discuss (a) issues of regression modelling utilising singular-value decompositions of design matrices that are massively rank deficient, (b) the imperatives for careful, informative prior specifications on high-dimension regression parameters, (c) the development of new classes of structured prior distributions for this problem, and (d) the development of appropriate computational methods and modes of posterior inference for regression estimation and predictive inference for out-of-sample classification. The latter enterprise is fundamental to genomic phenotyping applications. We study and exemplify the new statistical methodology in a problem of breast cancer phenotyping using DNA microarray expression profiles as predictors, and in discrimination of leukemia types.