Multi-Way Semilinear Methods with Applications to Microarray Data

本研究的重点是发展统计模型、方法和理论，用于微阵列数据和类似应用的规范化和显著性分析。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广泛应用。研究者和他的合作者提出并开发了一种双向半线性模型，用于规范化和分析cDNA微阵列数据。本研究的目的是扩展和进一步发展这一方法，并探讨其理论依据。该项目涵盖了广泛的具体问题，包括多路半线性模型、高密度寡核苷酸阵列的归一化和分析、控制/尖峰基因和生物途径信息的结合、位置尺度归一化、噪声水平估计、数据质量测量的结合、信息算子的可逆性、基因效应的理想/oracle估计的渐近等价等。多元半线性模型是对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和理论问题。这些数据集具有以下特点：基因效应的未知参数大量，样本数量少，非参数成分多，非参数成分和参数成分的估计基数之间共线性，随机依赖的协变量具有空间非均匀分布，观察到的基因表达与可能无法观察到的基因簇和生物途径之间的相互作用，非均匀噪声水平等等。这项研究是有动机的，将直接适用于使用微阵列和类似技术的功能基因组研究。它也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.