Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes. A simple nonparametric empirical Bayes model is introduced, which is used to guide the ef � cient reduction of the data to a single summary statistic per gene, and also to make simultaneous inferences concerning which genes were affected by the radiation. Although our focus is on one speci � c experiment, the proposed methods can be applied quite generally. The empirical Bayes inferences are closely related to the frequentist false discovery rate (FDR) criterion. 1.

Normalization means to adjust microarray data for effects which arise from variation in the technology rather than from biological differences between the RNA samples or between the printed probes. This article describes normalization methods based on the fact that dye balance typically varies with spot intensity and with spatial position on the array. Print-tip loess normalization provides a well-tested general purpose normalization method which has given good results on a wide range of arrays. The method may be refined by using quality weights for individual spots. The method is best combined with diagnostic plots of the data which display the spatial and intensity trends. When diagnostic plots show that biases still remain in the data after normalization, further normalization steps such as plate-order normalization or scalenormalization between the arrays may be undertaken. Composite normalization may be used when control spots are available which are known to be not differentially expressed. Variations on loess normalization include global loess normalization and 2D normalization. Detailed commands are given to implement the normalization techniques using freely available software. 1

Motivation: DNA microarrays have recently been used for the purpose of monitoring expression levels of thousands of genes simultaneously and identifying those genes that are differentially expressed. The probability that a false identification (type I error) is committed can increase sharply when the number of tested genes gets large. Correlation between the test statistics attributed to gene co-regulation and dependency in the measurement errors of the gene expression levels further complicates the problem. In this paper we address this very large multiplicity problem by adopting the false discovery rate (FDR) controlling approach. In order to address the dependency problem, we present three resampling-based FDR controlling procedures, that account for the test statistics distribution, and compare their performance to that of the naïve application of the linear step-up procedure in Benjamini and Hochberg (1995). The procedures are studied using simulated microarray data, and their performance is examined relative to their ease of implementation. Results: Comparative simulation analysis shows that all four FDR controlling procedures control the FDR at the desired level, and retain substantially more power then the family-wise error rate controlling procedures. In terms of power, using resampling of the marginal distribution of each test statistics substantially improves the performance over the naïve one. The highest power is achieved, at the expense of a more sophisticated algorithm, by the resampling-based procedures that resample the joint distribution of the test statistics and estimate the level of FDR control.

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.

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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.

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.

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.

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