Generalized multivariate analysis of variance (GMANOVA) models for high dimensional data

在复杂的时间进程基因组实验中识别具有不同表达谱的基因并根据这些差异对它们进行排名是非常具有挑战性的，并且只进行了很少的方法学研究。这些数据中的挑战出现，因为不同时间点的表达水平通常是相关的，因为测量值取自相同的生物体、组织、细胞或培养物。此外，基因表达值的时间依赖性通常是感兴趣的，并且通常是激发该问题的生物学问题。时间进程基因组实验特有的另一个挑战是基因特异性的高维性，其中通常可获得比时间点更少的重复，从而导致奇异的基因特异性协方差矩阵。这是除了所有微阵列实验共同的全局高维问题之外。高维数据不限于高通量基因组实验。这些数据也出现在广泛的应用中，包括神经学研究和信号处理。本研究计划的目的是为高维时间过程数据提供推理和诊断程序，重点是时间过程基因组数据。我们建议为广义方差分析（GMANOVA）模型提供一个统一的框架，其中包括ANOVA和MANOVA作为特殊情况。我们将使用GMANOVA模型为高维时间过程数据提供适度的检验统计量。该模型结合了内（跨时间点）的相关性和时间顺序。此外，时间作为连续变量纳入分析。我们将使用James-Stein和经验贝叶斯收缩方法来调节协方差矩阵。我们将提供适度的GMANOVA为基础的方法，基因过滤，基因排序和识别基因的不同表达谱的时间进程微阵列实验。对于生物学上感兴趣的候选遗传标记，我们将提供平均表达谱的适度似然比估计。我们还将提供适度的残差，可用于验证模型假设和识别极端观测。

Identifying genes with different expression profiles and ranking them according to these differences in complex time course genomic experiments is very challenging and only few methodological research has been conducted. Challenges in such data arise because expression levels at different time point are often correlated since measurements are taken from same organism, tissue, cell or culture. Moreover, time dependency of gene expression values are usually of interest and often are the biological question that motivates the problem. Another challenge unique to time course genomic experiments is the gene-specific high dimensionality where fewer replications than the time points are often available leading to singular gene-specific covariance matrices. This is in addition to the global high-dimensionality problem common to all microarry experiments. High-dimensional data is not limited to high-throughput genomic experiments. Such data also arises in a wide range of applications including neurological research and signal processing. The Objective of this research program is to provide inference and diagnostic procedures for high dimensional time course data with a focus on time course genomic data. We propose to provide a unified framework for Generalized Analysis of Variance (GMANOVA) models that includes ANOVA and MANOVA as special cases. We will provide moderated test statistics for high-dimensional time course data using GMANOVA models. The model incorporates the within (across time points) correlations and the temporal ordering. Moreover, time is included in the analysis as a continues variable. We will use James-Stein and empirical Bayes Shrinkage approaches to moderate the covariance matrix. We will provide moderated GMANOVA based approaches for gene filtering, gene ranking and identifying genes with different expression profiles for time course microarray experiments. For biologically interesting candidate genetic markers, we will provide moderated likelihood ratio estimates of the mean expression profile. We will also provide moderated residuals that can be used for validating model assumptions and identifying extreme observations.