The Use of a Finite Mixture of Beta Distributions in the Analysis of Microarray Data

The analysis of microarray data from designed experiments are used to illustrate the application of finite mixtures of Beta distributions. Instead of the usual log-transformed ratio of Cy5 and Cy3 intensities in a two-colour microarray experiment we use the proportion of Cy5 of the total light intensities - possibly normalised by a covariate to allow differences in microarray slides. By using finite mixtures - in combination with treatment effect - we overcome the problem of multiplicity as encountered with testing by ANOVA or t-test for each gene separately. We motivate our alternative choice of response variable by looking at the kinetics of the binding of free mRNA to the spots on the slide. For the analysis of one colour designs, e.g., Affymetrix TM slides, we propose a similar response variable and analysis - using both the perfect matches and the mismatches for each gene. In the end each gene is assigned a posterior class membership probability (under- or overexpressed) while allowing the use of a threshold value to set aside genes for which no decision could be made yet.

[1]  E. Wit.  Design and Analysis of DNA Microarray Investigations , 2004, Human Genomics.

[2]  Paul H. C. Eilers,et al.  Enhancing scatterplots with smoothed densities , 2004, Bioinform..

[3]  J. D. den Dunnen,et al.  Intensity-based analysis of two-colour microarrays enables efficient and flexible hybridization designs. , 2004, Nucleic acids research.

[4]  Gordon K Smyth,et al.  Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments , 2004, Statistical applications in genetics and molecular biology.

[5]  J. Wade Davis,et al.  Statistical Pattern Recognition , 2003, Technometrics.

[6]  Felix Naef,et al.  Absolute mRNA concentrations from sequence-specific calibration of oligonucleotide arrays. , 2003, Nucleic acids research.

[7]  Paola Sebastiani,et al.  Statistical Challenges in Functional Genomics , 2003 .

[8]  S. Dudoit,et al.  Multiple Hypothesis Testing in Microarray Experiments , 2003 .

[9]  Raymond J Carroll,et al.  DNA Microarray Experiments: Biological and Technological Aspects , 2002, Biometrics.

[10]  Jonathan Pevsner,et al.  SNOMAD (Standardization and NOrmalization of MicroArray Data): web-accessible gene expression data analysis , 2002, Bioinform..

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

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

[13]  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..

[14]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[15]  Walter R. Gilks,et al.  Hypothesis testing and model selection , 1995 .

[16]  D. Altman,et al.  STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT , 1986, The Lancet.

[17]  R. Plackett.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[18]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[19]  Sylvia Richardson,et al.  Bayesian Hierarchical Model for Identifying Changes in Gene Expression from Microarray Experiments , 2002, J. Comput. Biol..

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

[21]  David M. Rocke,et al.  A Model for Measurement Error for Gene Expression Arrays , 2001, J. Comput. Biol..

[22]  P. Green,et al.  Corrigendum: On Bayesian analysis of mixtures with an unknown number of components , 1997 .

[23]  Edward H. Ip,et al.  Stochastic EM: method and application , 1996 .

[24]  Adrian E. Raftery,et al.  Hypothesis testing and model selection , 1996 .

[25]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[26]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .