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Model selection in a global analysis of a microarray experiment¹

C. Díaz^*,2, N. Moreno-Sánchez^*, J. Rueda, A. Reverter, Y. H. Wang and M. J. Carabaño^*

^* Departamento Mejora Genética Animal, INIA, Crta. de la Coruña km 7.5, 28040 Madrid, Spain; and Departamento Genética, Facultad de Biología, UCM, Ciudad Universitaria s/n, 28040 Madrid, Spain; and CSIRO Livestock Industries, Queensland Bioscience Precinct, 306 Carmody Rd., St Lucia 4067, Queensland, Australia

² Corresponding author: cdiaz{at}inia.es

Analysis of data from complementary DNA microarray experiments is an area of intense research. Options include models at the gene level or at the global level, the latter combining information from all of the profiled genes. In general, a joint analysis is expected to be more powerful than gene-specific analyses. Global analysis of microarray data requires fitting a model that jointly performs data normalization and analyses. The objective of this study was to assess the optimality of alternative models for data normalization and analysis in an experiment to identify differentially expressed genes between 2 muscles in Avileña Negra Ibérica calves. Three major groups of models were explored according to several aspects including spatial arrangement of spots, other technical sources of variation such as dye effects, assumptions related to effects included in the model, and gene-specific effects. In addition, 3 sources of heterogeneity of residual variance were investigated. All models were compared by Bayes factors and cross-validation predictive densities. The model that included array-block, dye, muscle, and array-dye as systematic effects and all gene-related components as random effects was the best model for normalization and analysis of these data under heterogeneity of residual variances. Furthermore, level of intensity seemed to be the major source of heteroscedasticity for all models investigated. Such models rendered the best goodness of fit without compromising the predictive ability. The best model also provided the best performance to detect genes differentially expressed with the lowest false discovery rate. The large differences found for the model comparison criteria across models indicate the importance of defining the factors that more accurately account for experiment-wide variability to ensure correct inference on differential expression of genes. Our results also illustrate the importance of the experimental setup to account for possible sources of bias in the detection of differentially expressed genes.

Key Words: Bayesian mixed linear model • differential gene expression • false discovery rate • microarray • model selection • normalization