Multivariate analysis of variance test for gene set analysis

MOTIVATION Gene class testing (GCT) or gene set analysis (GSA) is a statistical approach to determine whether some functionally predefined sets of genes express differently under different experimental conditions. Shortcomings of the Fisher's exact test for the overrepresentation analysis are illustrated by an example. Most alternative GSA methods are developed for data collected from two experimental conditions, and most is based on a univariate gene-by-gene test statistic or assume independence among genes in the gene set. A multivariate analysis of variance (MANOVA) approach is proposed for studies with two or more experimental conditions. RESULTS When the number of genes in the gene set is greater than the number of samples, the sample covariance matrix is singular and ill-condition. The use of standard multivariate methods can result in biases in the analysis. The proposed MANOVA test uses a shrinkage covariance matrix estimator for the sample covariance matrix. The MANOVA test and six other GSA published methods, principal component analysis, SAM-GS, analysis of covariance, Global, GSEA and MaxMean, are evaluated using simulation. The MANOVA test appears to perform the best in terms of control of type I error and power under the models considered in the simulation. Several publicly available microarray datasets under two and three experimental conditions are analyzed for illustrations of GSA. Most methods, except for GSEA and MaxMean, generally are comparable in terms of power of identification of significant gene sets. AVAILABILITY A free R-code to perform MANOVA test is available at http://mail.cmu.edu.tw/~catsai/research.htm. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

[1]  P. Khatri,et al.  Global functional profiling of gene expression. , 2003, Genomics.

[2]  Peter Bühlmann,et al.  Analyzing gene expression data in terms of gene sets: methodological issues , 2007, Bioinform..

[3]  Aniko Szabo,et al.  Multivariate exploratory tools for microarray data analysis. , 2003, Biostatistics.

[4]  Ulrich Mansmann,et al.  Multiple testing on the directed acyclic graph of gene ontology , 2008, Bioinform..

[5]  Purvesh Khatri,et al.  Ontological analysis of gene expression data: current tools, limitations, and open problems , 2005, Bioinform..

[6]  Jurgen Lauter,et al.  Exact t and F Tests for Analyzing Studies with Multiple Endpoints , 1996 .

[7]  P. Park,et al.  Discovering statistically significant pathways in expression profiling studies. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[8]  P. O'Brien Procedures for comparing samples with multiple endpoints. , 1984, Biometrics.

[9]  Peter J. Park,et al.  A multivariate approach for integrating genome-wide expression data and biological knowledge , 2006, Bioinform..

[10]  Pablo Tamayo,et al.  Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Yudong D. He,et al.  Gene expression profiling predicts clinical outcome of breast cancer , 2002, Nature.

[12]  M. Daly,et al.  PGC-1α-responsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes , 2003, Nature Genetics.

[13]  Jelle J. Goeman,et al.  A global test for groups of genes: testing association with a clinical outcome , 2004, Bioinform..

[14]  R. Tibshirani,et al.  Significance analysis of microarrays applied to the ionizing radiation response , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Wei Li Analyzing Gene Expression Data in Terms of Gene Sets: Gene Set Enrichment Analysis , 2009 .

[16]  Qi Liu,et al.  Improving gene set analysis of microarray data by SAM-GS , 2007, BMC Bioinformatics.

[17]  Tao Chen,et al.  Significance analysis of groups of genes in expression profiling studies , 2007, Bioinform..

[18]  Qi Liu,et al.  Pathway Analysis of Microarray Data via Regression , 2008, J. Comput. Biol..

[19]  Rafael A Irizarry,et al.  Exploration, normalization, and summaries of high density oligonucleotide array probe level data. , 2003, Biostatistics.

[20]  Léon Personnaz,et al.  Enrichment or depletion of a GO category within a class of genes: which test? , 2007, Bioinform..

[21]  LuYan,et al.  Hotelling's T2 multivariate profiling for detecting differential expression in microarrays , 2005 .

[22]  R. Tibshirani,et al.  On testing the significance of sets of genes , 2006, math/0610667.

[23]  U. Mansmann,et al.  Testing Differential Gene Expression in Functional Groups , 2005, Methods of Information in Medicine.

[24]  Peng Xiao,et al.  Hotelling’s T 2 multivariate profiling for detecting differential expression in microarrays , 2005 .

[25]  Qi Liu,et al.  BMC Bioinformatics BioMed Central Methodology article Comparative evaluation of gene-set analysis methods , 2007 .

[26]  K. Gabriel,et al.  On closed testing procedures with special reference to ordered analysis of variance , 1976 .

[27]  Jun Lu,et al.  Pathway level analysis of gene expression using singular value decomposition , 2005, BMC Bioinformatics.

[28]  V. Arango,et al.  Using the Gene Ontology for Microarray Data Mining: A Comparison of Methods and Application to Age Effects in Human Prefrontal Cortex , 2004, Neurochemical Research.

[29]  K. Strimmer,et al.  Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics , 2011 .

[30]  Ulrich Mansmann,et al.  GlobalANCOVA: exploration and assessment of gene group effects , 2008, Bioinform..

[31]  Seon-Young Kim,et al.  Gene-set approach for expression pattern analysis , 2008, Briefings Bioinform..

[32]  Inyoung Kim,et al.  Statistical methods of translating microarray data into clinically relevant diagnostic information in colorectal cancer , 2005, Bioinform..

[33]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .