Statistical inference for microarray experiments usually involves the estimation of error variance for each gene. Because the sample size available for each gene is often low, the usual unbiased estimator of the error variance can be unreliable. Shrinkage methods, including empirical Bayes approaches that borrow information across genes to produce more stable estimates, have been developed in recent years. Because the same microarray platform is often used for at least several experiments to study similar biological systems, there is an opportunity to improve variance estimation further by borrowing information not only across genes but also across experiments. We propose a lognormal model for error variances that involves random gene effects and random experiment effects. Based on the model, we develop an empirical Bayes estimator of the error variance for each combination of gene and experiment and call this estimator BAGE because information is Borrowed Across Genes and Experiments. A permutation strategy is used to make inference about the differential expression status of each gene. Simulation studies with data generated from different probability models and real microarray data show that our method outperforms existing approaches.
[Show abstract][Hide abstract] ABSTRACT: Covering: up to 2013Discovering molecular components and their functionality is key to the development of hypotheses concerning the organization and regulation of metabolic networks. The iterative experimental testing of such hypotheses is the trajectory that can ultimately enable accurate computational modelling and prediction of metabolic outcomes. This information can be particularly important for understanding the biology of natural products, whose metabolism itself is often only poorly defined. Here, we describe factors that must be in place to optimize the use of metabolomics in predictive biology. A key to achieving this vision is a collection of accurate time-resolved and spatially defined metabolite abundance data and associated metadata. One formidable challenge associated with metabolite profiling is the complexity and analytical limits associated with comprehensively determining the metabolome of an organism. Further, for metabolomics data to be efficiently used by the research community, it must be curated in publicly available metabolomics databases. Such databases require clear, consistent formats, easy access to data and metadata, data download, and accessible computational tools to integrate genome system-scale datasets. Although transcriptomics and proteomics integrate the linear predictive power of the genome, the metabolome represents the nonlinear, final biochemical products of the genome, which results from the intricate system(s) that regulate genome expression. For example, the relationship of metabolomics data to the metabolic network is confounded by redundant connections between metabolites and gene-products. However, connections among metabolites are predictable through the rules of chemistry. Therefore, enhancing the ability to integrate the metabolome with anchor-points in the transcriptome and proteome will enhance the predictive power of genomics data. We detail a public database repository for metabolomics, tools and approaches for statistical analysis of metabolomics data, and methods for integrating these datasets with transcriptomic data to create hypotheses concerning specialized metabolisms that generate the diversity in natural product chemistry. We discuss the importance of close collaborations among biologists, chemists, computer scientists and statisticians throughout the development of such integrated metabolism-centric databases and software.
[Show abstract][Hide abstract] ABSTRACT: Estimation of variances and covariances is required for many statistical methods such as t-test, principal component analysis and linear discriminant analysis. High-dimensional data such as gene expression microarray data and financial data pose challenges to traditional statistical and computational methods. In this paper, we review some recent developments in the estimation of variances, covariance matrix, and precision matrix, with emphasis on the applications to microarray data analysis.For further resources related to this article, please visit the WIREs website.Conflict of interest: The authors have declared no conflicts of interest for this article.
07/2014; 6(4). DOI:10.1002/wics.1308
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