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doi:10.1093/nar/gkm1075

Zhijin Wu Johns Hopkins Bloomberg School of Public Health 615 North Wolfe Street zwu@jhsph.edu Rafael A. Irizarry Johns Hopkins Bloomberg School of Public Health 615 North Wolfe Street rafa@jhu.edu ABSTRACT High density oligonucleotide expression arrays are a widely used tool for the measurement of gene expression on a large scale. A#ymetrix GeneChip arrays appear to dominate this market. These arrays use short oligonucleotides to probe for genes in an RNA sample. Due to optical noise, nonspecific hybridization, probe-specific e#ects, and measurement error, ad-hoc measures of expression, that summarize probe intensities, can lead to imprecise and inaccurate results. Various researchers have demonstrated that expression measures based on simple statistical models can provide great improvements over the ad-hoc procedure o#ered by A#ymetrix. Recently, physical models based on molecular hybridization theory, have been proposed as useful tools for prediction of, for example, non-specific hybridization. These physical models show great potential in terms of improving existing expression measures. In this paper we suggest that the system producing the measured intensities is too complex to be fully described with these relatively simple physical models and we propose empirically motivated stochastic models that compliment the above mentioned molecular hybridization theory to provide a comprehensive description of the data. We discuss how the proposed model can be used to obtain improved measures of expression useful for the data analysts.

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DNA microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease. The high throughput nature of these arrays, where differential expression for thousands of genes can be measured simultaneously, creates an enormous wealth of information, but also poses a challenge for data analysis because of the large multiple testing problem involved. The solution has generally been to focus on optimizing false-discovery rates while sacri � cing power. The drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold. We introduce a new method for detecting differentially expressed genes based on a high-dimensional model selection technique, Bayesian ANOVA for microarrays (BAM), which strikes a balance between false rejections and false nonrejections. The basis of the new approach involves a weighted average of generalized ridge regression estimates that provides the bene � ts of using shrinkage estimation combined with model averaging. A simple graphical tool based on the amount of shrinkage is developed to visualize the trade-off between low false-discovery rates and � nding more genes. Simulations are used to illustrate BAM’s performance, and the method is applied to a large database of colon cancer gene expression data. Our working hypothesis in the colon cancer analysis is that large differential expressions may not be the only ones contributing to metastasis—in fact, moderate changes in expression of genes may be involved in modifying the genetic environment to a suf � cient extent for metastasis to occur. A functional biological analysis of gene effects found by BAM, but not other false-discovery-based approaches, lends support to this hypothesis. KEY WORDS: Bayesian analysis of variance for microarrays; False discovery rate; False nondiscovery rate; Heteroscedasticity; Ridge

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a family of transformations (the generalized-log family) which stabilizes the variance of microarray data up to the first order. We introduce a method for estimating the transformation parameter in tandem with a linear model based on the procedure outlined in Box and Cox (1964). We also discuss means of finding transformations within the generalized-log family which are optimal under other criteria, such as minimum residual skewness and minimum mean-variance dependency. Availability: R and Matlab code and test data are available from the authors on request. Contact:

DNA microarrays can provide insight into genetic changes that characterize different stages of a disease process. Accurate identification of these changes has significant therapeutic and diagnostic implications. Statistical analysis for multistage (multigroup) data is challenging, however. ANOVA-based extensions of two-sample Z-tests, a popular method for detecting differentially expressed genes in two groups, do not work well in multigroup settings. False detection rates are high because of variability of the ordinary least squares estimators and because of regression to the mean induced by correlated parameter estimates. We develop a Bayesian rescaled spike and slab hierarchical model specifically designed for the multigroup gene detection problem. Data preprocessing steps are introduced to deal with unique features of microarray data and to enhance selection performance. We show theoretically that spike and slab models naturally encourage sparse solutions through a process called selective shrinkage. This translates into oracle-like gene selection risk performance compared with ordinary least squares estimates. The methodology is illustrated on a large microarray repository of samples from different clinical stages of metastatic colon cancer. Through a functional analysis of selected genes, we show that spike and slab models identify important biological signals while minimizing biologically implausible false detections.

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replicated gene expression data.