Empirical Bayes analysis of unreplicated microarray data

Because of the high costs of microarray experiments and the availability of only limited biological materials, microarray experiments are often performed with a small number of replicates. Investigators, therefore, often have to perform their experiments with low replication or without replication. However, the heterogeneous error variability observed in microarray experiments increases the difficulty in analyzing microarray data without replication. No current analysis techniques are practically applicable to such microarray data analysis. We here introduce a statistical method, the so-called unreplicated heterogeneous error model (UHEM) for the microarray data analysis without replication. This method is possible by utilizing many adjacent-intensity genes for estimating local error variance after nonparametric elimination of differentially expressed genes between different biological conditions. We compared the performance of UHEM with three empirical Bayes prior specification methods: between-condition local pooled error, pseudo standard error, or adaptive standard error-based HEM. We found that our unreplicated HEM method is effective for the microarray data analysis when replication of an array experiment is impractical or prohibited.

[1]  J. S. Rao,et al.  Detecting Differentially Expressed Genes in Microarrays Using Bayesian Model Selection , 2003 .

[2]  Jeffrey P. Townsend,et al.  Resolution of large and small differences in gene expression using models for the Bayesian analysis of gene expression levels and spotted DNA microarrays , 2004, BMC Bioinformatics.

[3]  Jae K. Lee,et al.  Error-Pooling Empirical Bayes Model for Enhanced Statistical Discovery of Differential Expression in Microarray Data , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[4]  C M Kendziorski,et al.  On parametric empirical Bayes methods for comparing multiple groups using replicated gene expression profiles , 2003, Statistics in medicine.

[5]  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.

[6]  Jae K. Lee,et al.  Local-pooled-error test for identifying differentially expressed genes with a small number of replicated microarrays , 2003, Bioinform..

[7]  G. A. Whitmore,et al.  Importance of replication in microarray gene expression studies: statistical methods and evidence from repetitive cDNA hybridizations. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[8]  R. Tibshirani,et al.  Empirical bayes methods and false discovery rates for microarrays , 2002, Genetic epidemiology.

[9]  Marina Vannucci,et al.  Gene selection: a Bayesian variable selection approach , 2003, Bioinform..

[10]  Christina Kendziorski,et al.  On Differential Variability of Expression Ratios: Improving Statistical Inference about Gene Expression Changes from Microarray Data , 2001, J. Comput. Biol..

[11]  G. Parmigiani,et al.  The Analysis of Gene Expression Data , 2003 .

[12]  T. Speed,et al.  Design issues for cDNA microarray experiments , 2002, Nature Reviews Genetics.

[13]  J. Ibrahim,et al.  Bayesian Models for Gene Expression With DNA Microarray Data , 2002 .

[14]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[15]  Rainer Fuchs,et al.  Bayesian Estimation of Fold-Changes in the Analysis of Gene Expression: The PFOLD Algorithm , 2001, J. Comput. Biol..

[16]  John D. Storey,et al.  Empirical Bayes Analysis of a Microarray Experiment , 2001 .

[17]  R. Lenth.  Quick and easy analysis of unreplicated factorials , 1989 .

[18]  D. Hartl,et al.  Bayesian analysis of gene expression levels: statistical quantification of relative mRNA level across multiple strains or treatments , 2002, Genome Biology.

[19]  J. Townsend,et al.  BMC Genomics BioMed Central Methodology article , 2003 .

[20]  Aaron Aragaki,et al.  Significance testing for small microarray experiments , 2005, Statistics in medicine.

[21]  Lorenz Wernisch.  Can Replication Save Noisy Microarray Data? , 2002, Comparative and functional genomics.

[22]  Pierre Baldi,et al.  A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes , 2001, Bioinform..

[23]  Christina Kendziorski,et al.  Parametric Empirical Bayes Methods for Microarrays , 2003 .

[24]  M. Oh,et al.  Issues in cDNA microarray analysis: quality filtering, channel normalization, models of variations and assessment of gene effects. , 2001, Nucleic acids research.

[25]  Mingyu Liang,et al.  Quantitative assessment of the importance of dye switching and biological replication in cDNA microarray studies. , 2003, Physiological genomics.

[26]  B. Efron.  Robbins, Empirical Bayes, And Microarrays , 2001 .