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Linear models and empirical bayes methods for assessing differential expression in microarray experiments.
- Stat. Appl. Genet. Mol. Biol.
, 2004
"... Abstract The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. ..."
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Cited by 1321 (24 self)
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Abstract The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.
Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation
, 2002
"... There are many sources of systematic variation in cDNA microarray experiments which affect the measured gene expression levels (e.g. differences in labeling efficiency between the two fluorescent dyes). The term normalization refers to the process of removing such variation. A constant adjustment is ..."
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Cited by 718 (9 self)
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There are many sources of systematic variation in cDNA microarray experiments which affect the measured gene expression levels (e.g. differences in labeling efficiency between the two fluorescent dyes). The term normalization refers to the process of removing such variation. A constant adjustment is often used to force the distribution of the intensity log ratios to have a median of zero for each slide. However, such global normalization approaches are not adequate in situations where dye biases can depend on spot overall intensity and/or spatial location within the array. This article proposes normalization methods that are based on robust local regression and account for intensity and spatial dependence in dye biases for different types of cDNA microarray experiments. The selection of appropriate controls for normalization is discussed and a novel set of controls (microarray sample pool, MSP) is introduced to aid in intensity-dependent normalization. Lastly, to allow for comparisons of expression levels across slides, a robust method based on maximum likelihood estimation is proposed to adjust for scale differences among slides.
Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments
- STATISTICA SINICA
, 2002
"... DNA microarrays are a new and promising biotechnology whichallows the monitoring of expression levels in cells for thousands of genes simultaneously. The present paper describes statistical methods for the identification of differentially expressed genes in replicated cDNA microarray experiments. A ..."
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Cited by 438 (12 self)
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DNA microarrays are a new and promising biotechnology whichallows the monitoring of expression levels in cells for thousands of genes simultaneously. The present paper describes statistical methods for the identification of differentially expressed genes in replicated cDNA microarray experiments. Although it is not the main focus of the paper, new methods for the important pre-processing steps of image analysis and normalization are proposed. Given suitably normalized data, the biological question of differential expression is restated as a problem in multiple hypothesis testing: the simultaneous test for each gene of the null hypothesis of no association between the expression levels and responses or covariates of interest. Di erentially expressed genes are identified based on adjusted p-values for a multiple testing procedure which strongly controls the family-wise Type I error rate and takes into account the dependence structure between the gene expression levels. No specific parametric form is assumed for the distribution of the test statistics and a permutation procedure is used to estimate adjusted p-values. Several data displays are suggested for the visual identification of differentially expressed genes and of important features of these genes. The above methods are applied to microarray data from a study of gene expression in the livers of mice with very low HDL cholesterol levels. The genes identified using data from multiple slides are compared to those identified by recently published single-slide methods.
On Differential Variability of Expression Ratios: Improving . . .
- JOURNAL OF COMPUTATIONAL BIOLOGY
, 2001
"... We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates o ..."
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Cited by 265 (7 self)
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We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates of gene expression changes are derived within a simple hierarchical model that accounts for measurement error and fluctuations in absolute gene expression levels. Significant gene expression changes are identified by deriving the posterior odds of change within a similar model. The methods are tested via simulation and are applied to a panel of Escherichia coli microarrays.
Assessing Gene Significance from cDNA Microarray Expression Data via Mixed Models
, 2001
"... The determination of a list of differentially expressed genes is a basic objective in many cDNA microarray experiments. We present a statistical approach that allows direct control over the percentage of false positives in such a list and, under certain reasonable assumptions, improves on existing m ..."
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Cited by 218 (6 self)
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The determination of a list of differentially expressed genes is a basic objective in many cDNA microarray experiments. We present a statistical approach that allows direct control over the percentage of false positives in such a list and, under certain reasonable assumptions, improves on existing methods with respect to the percentage of false negatives. The method accommodates a wide variety of experimental designs and can simultaneously assess significant differences between multiple types of biological samples. Two interconnected mixed linear models are central to the method and provide a flexible means to properly account for variability both across and within genes. The mixed model also provides a convenient framework for evaluating the statistical power of any particular experimental design and thus enables a researcher to a priori select an appropriate number of replicates. We also suggest some basic graphics for visualizing lists of significant genes. Analyses of published experiments studying human cancer and yeast cells illustrate the results.
A Model Based Background Adjustment for Oligonucleotide Expression Arrays.
- Journal of the American Statistical Association
, 2004
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Cluster Analysis for Gene Expression Data: A Survey
- IEEE Transactions on Knowledge and Data Engineering
, 2004
"... Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity f ..."
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Cited by 149 (5 self)
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Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field. Index Terms—Microarray technology, gene expression data, clustering.
Issues in cDNA microarray analysis: quality filtering, channel normalization, models of variations and assessment of gene effects
, 2001
"... We consider the problem of comparing the gene expression levels of cells grown under two different conditions using cDNA microarray data. We use a quality index, computed from duplicate spots on the same slide, to filter out outlying spots, poor quality genes and problematical slides. We also perfor ..."
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Cited by 147 (5 self)
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We consider the problem of comparing the gene expression levels of cells grown under two different conditions using cDNA microarray data. We use a quality index, computed from duplicate spots on the same slide, to filter out outlying spots, poor quality genes and problematical slides. We also perform calibration experiments to show that normalization between fluorescent labels is needed and that the normalization is slide dependent and non-linear. A rank invariant method is suggested to select nondifferentially expressed genes and to construct normalization curves in comparative experiments. After normalization the residuals from the calibration data are used to provide prior information on variance components in the analysis of comparative experiments. Based on a hierarchical model that incorporates several levels of variations, a method for assessing the significance of gene effects in comparative experiments is presented. The analysis is demonstrated via two groups of experiments with 125 and 4129 genes, respectively, in Escherichia coli grown in glucose and acetate.
Resampling-Based Multiple Testing for Microarray Data Analysis
, 2003
"... The burgeoning field of genomics has revived interest in multiple testing procedures by raising new methodological and computational challenges. For example, microarray experiments generate large multiplicity problems in which thousands of hypotheses are tested simultaneously. In their 1993 book, We ..."
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Cited by 145 (3 self)
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The burgeoning field of genomics has revived interest in multiple testing procedures by raising new methodological and computational challenges. For example, microarray experiments generate large multiplicity problems in which thousands of hypotheses are tested simultaneously. In their 1993 book, Westfall & Young propose resampling-based p-value adjustment procedures which are highly relevant to microarray experiments. This article discusses different criteria for error control in resampling-based multiple testing, including (a) the family wise error rate of Westfall & Young (1993) and (b) the false discovery rate developed by Benjamini & Hochberg (1995), both from a frequentist viewpoint; and (c) the positive false discovery rate of Storey (2002), which has a Bayesian motivation. We also introduce our recently developed fast algorithm for implementing the minP adjustment to control familywise error rate. Adjusted p-values for different approaches are applied to gene expression data from two recently published microarray studies. The properties of these procedures for multiple testing are compared.
Statistical Design and the Analysis of Gene Expression Microarray Data
- Genet. Res
, 2001
"... INTRODUCTION Gene expression microarrays are an exciting new tool in molecular biology (Brown & Botstein, 1999). Geneticists are intrigued by the prospect of collecting and mining expression data for thousands of genes. Statisticians have taken a correspondingly enthusiastic interest in the man ..."
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Cited by 129 (3 self)
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INTRODUCTION Gene expression microarrays are an exciting new tool in molecular biology (Brown & Botstein, 1999). Geneticists are intrigued by the prospect of collecting and mining expression data for thousands of genes. Statisticians have taken a correspondingly enthusiastic interest in the many quantitative issues that arise with this technology. These issues begin with analyzing scanned array images and extracting signal (Yang et al., 2000a). After one has estimates of relative expression in hand, there are problems in data visualization, dimension reduction (Hilsenbeck et al., 1999), and pattern recognition (Brown et al., 2000). In the world of gene expression, a lot of attention has been focused here, particularly on clustering tools. In contrast, our focus is on the analysis that takes place after image analysis and before clustering. Namely, how does one get from fluorescence readings o# an array to valid estimates of relat
