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

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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.