Multi-Way Semilinear Methods with Applications to Microarray Data

这项研究的重点是开发统计模型、方法和理论，用于基因芯片数据和类似应用的归一化和显著性分析。微阵列技术已成为定量监测基因表达模式的重要工具，并在功能基因组学中得到了广泛应用。这位研究人员和他的合作者提出并开发了一个双向半线性模型，用于对基因芯片数据进行归一化和分析。本研究的目的是推广和发展这一方法论，并探讨其理论依据。该项目涵盖了广泛的具体问题，包括多向半线性模型，高密度寡核苷酸阵列的归一化和分析，控制/尖峰基因和生物通路信息的合并，位置-尺度归一化，噪声水平的估计，数据质量度量的合并，信息算子的可逆性，基因效应的理想/预言估计的渐近等价性等等。多向半线性模型是广泛使用的方差分析和半线性回归模型的扩展。它在微阵列实验中的应用对高维复杂数据集提出了具有挑战性的方法学和理论问题。这些数据集具有以下特征：大量的未知基因效应参数和少量样本，许多非参数分量，非参数分量和参数分量估计基数之间的共线性，具有空间不均匀分布的随机相关协变量，观察到的基因表达与可能不可观测的基因簇和生物通路之间的相互作用，不均匀噪声水平，等等。这项研究是有动力的，并将直接适用于使用微阵列和类似技术的功能基因组研究。它还将直接适用于药物发现实验中化合物的高通量筛选。这项研究将对教育产生重大影响。

This research focuses on developing statistical models, methods, and theory for normalization and significance analysis of microarray data and similar applications. Microarray technology has become an important tool for quantitatively monitoring gene expression patterns and has been widely used in functional genomics. The investigator and his collaborators have proposed and developed a two-way semilinear model for normalization and analysis of cDNA microarray data. The purpose of this research is to extend and further develop this methodology and investigate its theoretical justifications. The project covers a wide range of specific problems including multi-way semilinear models, normalization and analysis of high-density oligonucleotide arrays, incorporation of control/spike genes and biological pathway information, location-scale normalization, estimation of noise level, incorporation of data quality measurements, invertibility of information operator, asymptotic equivalence to ideal/oracle estimators of gene effects, and more.The multi-way semilinear model is an extension of widely used analysis of variance and semilinear regression models. Its applications to microarray experiments present challenging methodological and theoretical problems with high-dimensional complex datasets. These datasets have the following features: large number of unknown parameters for gene effects and small number of samples, many nonparametric components, co-linearity between bases for the estimations of nonparametric and parametric components, stochastically dependent covariates with spatially inhomogeneous distributions, interactions between observed gene expressions and possibly unobservable gene clusters and biological pathways, inhomogeneous noise level, and more. This research is motivated and will be directly applicable to functional genomic studies using microarray and similar technologies. It will also be directly applicable to high-throughput screening of chemical compounds in drug discovery experiments. This research will have significant educational impact.