Micro Array Based Gene Expression Analysis using Parametric Multivariate Tests per Gene - A Generalized Application of Multiple Procedures with Data-driven Order of Hypotheses

Micro array technology allows the simultaneous analysis of ten‐thousands of genes. Most often, however, the analysis is based on a few replications only. This causes problems in the application of classical multivariate tests which require sample sizes exceeding the number of observed variables. To...

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Bibliographic Details
Published in:Biometrical journal 2004-12, Vol.46 (6), p.687-698
Main Authors: Schuster, Ernst, Kropf, Siegfried, Roeder, Ingo
Format: Article
Language:English
Subjects:
Biological and medical sciences
Data-driven ordered hypotheses
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
Gene expression
General aspects
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Multiple tests
Multivariate analysis
Parametric inference
Probability and statistics
Sciences and techniques of general use
Score-based tests
Statistics
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Summary:Micro array technology allows the simultaneous analysis of ten‐thousands of genes. Most often, however, the analysis is based on a few replications only. This causes problems in the application of classical multivariate tests which require sample sizes exceeding the number of observed variables. To overcome these problems, a class of stable, multivariate procedures based on the theory of spherical distributions has been proposed by Läuter, Glimm, and Kropf (1996). These methods allow the use of multivariate information of many genes for testing differential gene expression. Furthermore, multiple testing procedures based on these principles have been constructed (e.g., Kropf, Läuter, 2002), which strictly keep the familywise type I error rate (FWE). In this paper, these methods have been generalized to allow for the use of full multivariate information on expression intensities of individual genes analysed by the Affymetrix GeneChip technology. In contrast to the usual strategy, which constructs an expression score for each gene, based on averaging of the different oligonucleotide (perfect‐ and miss‐match) information, and then performs some test on these summarized expression values, we suggest using a test procedure based on the complete multivariate perfect match information. We show that a multiple FWE‐controlling procedure for normally distributed data proposed by Westfall, Kropf, and Finos (2004), can be generalised to a more powerful procedure based on left‐spherically distributed scores derived from the perfect match information, without losing the FWE‐controlling property. To illustrate the proposed test procedures, which have been implemented in the statistical programming environment R, we analyse two already published data sets, comparing gene expression of tumour and healthy tissues within identical patients and between two groups of different patients, respectively. Using these examples, we demonstrated that the incorporation of the multivariate perfect match information is superior to classical expression score based methods with respect to the number of identifiable differentially expressed genes. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0323-3847
1521-4036
DOI:10.1002/bimj.200410067