Hotelling's T2 multivariate profiling for detecting differential expression in microarrays

The most widely used statistical methods for finding differentially expressed genes (DEGs) are essentially univariate. In this study, we present a new T(2) statistic for analyzing microarray data. We implemented our method using a multiple forward search (MFS) algorithm that is designed for selecting a subset of feature vectors in high-dimensional microarray datasets. The proposed T2 statistic is a corollary to that originally developed for multivariate analyses and possesses two prominent statistical properties. First, our method takes into account multidimensional structure of microarray data. The utilization of the information hidden in gene interactions allows for finding genes whose differential expressions are not marginally detectable in univariate testing methods. Second, the statistic has a close relationship to discriminant analyses for classification of gene expression patterns. Our search algorithm sequentially maximizes gene expression difference/distance between two groups of genes. Including such a set of DEGs into initial feature variables may increase the power of classification rules. We validated our method by using a spike-in HGU95 dataset from Affymetrix. The utility of the new method was demonstrated by application to the analyses of gene expression patterns in human liver cancers and breast cancers. Extensive bioinformatics analyses and cross-validation of DEGs identified in the application datasets showed the significant advantages of our new algorithm.     

Multivariate search for differentially expressed gene combinations

Background

To identify differentially expressed genes, it is standard practice to test a two-sample hypothesis for each gene with a proper adjustment for multiple testing. Such tests are essentially univariate and disregard the multidimensional structure of microarray data. A more general two-sample hypothesis is formulated in terms of the joint distribution of any sub-vector of expression signals.

Results

By building on an earlier proposed multivariate test statistic, we propose a new algorithm for identifying differentially expressed gene combinations. The algorithm includes an improved random search procedure designed to generate candidate gene combinations of a given size. Cross-validation is used to provide replication stability of the search procedure. A permutation two-sample test is used for significance testing. We design a multiple testing procedure to control the family-wise error rate (FWER) when selecting significant combinations of genes that result from a successive selection procedure. A target set of genes is composed of all significant combinations selected via random search.

Conclusions

A new algorithm has been developed to identify differentially expressed gene combinations. The performance of the proposed search-and-testing procedure has been evaluated by computer simulations and analysis of replicated Affymetrix gene array data on age-related changes in gene expression in the inner ear of CBA mice.

     

A mathematical model for the validation of gene selection methods

Gene selection methods aim at determining biologically relevant subsets of genes in DNA microarray experiments. However, their assessment and validation represent a major difficulty since the subset of biologically relevant genes is usually unknown. To solve this problem a novel procedure for generating biologically plausible synthetic gene expression data is proposed. It is based on a proper mathematical model representing gene expression signatures and expression profiles through Boolean threshold functions. The results show that the proposed procedure can be successfully adopted to analyze the quality of statistical and machine learning-based gene selection algorithms.     

Multivariate approach for selecting sets of differentially expressed genes

An important problem addressed using cDNA microarray data is the detection of genes differentially expressed in two tissues of interest. Currently used approaches ignore the multidimensional structure of the data. However it is well known that correlation among covariates can enhance the ability to detect less pronounced differences. We use the Mahalanobis distance between vectors of gene expressions as a criterion for simultaneously comparing a set of genes and develop an algorithm for maximizing it. To overcome the problem of instability of covariance matrices we propose a new method of combining data from small-scale random search experiments. We show that by utilizing the correlation structure the multivariate method, in addition to the genes found by the one-dimensional criteria, finds genes whose differential expression is not detectable marginally.     

Gene Selection for Multiclass Prediction by Weighted Fisher Criterion

Gene expression profiling has been widely used to study molecular signatures of many diseases and to develop molecular diagnostics for disease prediction. Gene selection, as an important step for improved diagnostics, screens tens of thousands of genes and identifies a small subset that discriminates between disease types. A two-step gene selection method is proposed to identify informative gene subsets for accurate classification of multiclass phenotypes. In the first step, individually discriminatory genes (IDGs) are identified by using one-dimensional weighted Fisher criterion (wFC). In the second step, jointly discriminatory genes (JDGs) are selected by sequential search methods, based on their joint class separability measured by multidimensional weighted Fisher criterion (wFC). The performance of the selected gene subsets for multiclass prediction is evaluated by artificial neural networks (ANNs) and/or support vector machines (SVMs). By applying the proposed IDG/JDG approach to two microarray studies, that is, small round blue cell tumors (SRBCTs) and muscular dystrophies (MDs), we successfully identified a much smaller yet efficient set of JDGs for diagnosing SRBCTs and MDs with high prediction accuracies (96.9% for SRBCTs and 92.3% for MDs, resp.). These experimental results demonstrated that the two-step gene selection method is able to identify a subset of highly discriminative genes for improved multiclass prediction.     

Nonparametric methods for identifying differentially expressed genes in microarray data

MOTIVATION: Gene expression experiments provide a fast and systematic way to identify disease markers relevant to clinical care. In this study, we address the problem of robust identification of differentially expressed genes from microarray data. Differentially expressed genes, or discriminator genes, are genes with significantly different expression in two user-defined groups of microarray experiments. We compare three model-free approaches: (1). nonparametric t-test, (2). Wilcoxon (or Mann-Whitney) rank sum test, and (3). a heuristic method based on high Pearson correlation to a perfectly differentiating gene ('ideal discriminator method'). We systematically assess the performance of each method based on simulated and biological data under varying noise levels and p-value cutoffs. RESULTS: All methods exhibit very low false positive rates and identify a large fraction of the differentially expressed genes in simulated data sets with noise level similar to that of actual data. Overall, the rank sum test appears most conservative, which may be advantageous when the computationally identified genes need to be tested biologically. However, if a more inclusive list of markers is desired, a higher p-value cutoff or the nonparametric t-test may be appropriate. When applied to data from lung tumor and lymphoma data sets, the methods identify biologically relevant differentially expressed genes that allow clear separation of groups in question. Thus the methods described and evaluated here provide a convenient and robust way to identify differentially expressed genes for further biological and clinical analysis.     

How many differentially expressed genes: A perspective from the comparison of genotypic and phenotypic distances

Identifying differentially expressed genes is critical in microarray data analysis. Many methods have been developed by combining p-value, fold-change, and various statistical models to determine these genes. When using these methods, it is necessary to set up various pre-determined cutoff values. However, many of these cutoff values are somewhat arbitrary and may not have clear connections to biology. In this study, a genetic distance method based on gene expression level was developed to analyze eight sets of microarray data extracted from the GEO database. Since the genes used in distance calculation have been ranked by fold-change, the genetic distance becomes more stable when adding more genes in the calculation, indicating there is an optimal set of genes which are sufficient to characterize the stable difference between samples. This set of genes is differentially expressed genes representing both the genotypic and phenotypic differences between samples.     

Gene expression analysis with the parametric bootstrap

Recent developments in microarray technology make it possible to capture the gene expression profiles for thousands of genes at once. With this data researchers are tackling problems ranging from the identification of 'cancer genes' to the formidable task of adding functional annotations to our rapidly growing gene databases. Specific research questions suggest patterns of gene expression that are interesting and informative: for instance, genes with large variance or groups of genes that are highly correlated. Cluster analysis and related techniques are proving to be very useful. However, such exploratory methods alone do not provide the opportunity to engage in statistical inference. Given the high dimensionality (thousands of genes) and small sample sizes (often <30) encountered in these datasets, an honest assessment of sampling variability is crucial and can prevent the over-interpretation of spurious results. We describe a statistical framework that encompasses many of the analytical goals in gene expression analysis; our framework is completely compatible with many of the current approaches and, in fact, can increase their utility. We propose the use of a deterministic rule, applied to the parameters of the gene expression distribution, to select a target subset of genes that are of biological interest. In addition to subset membership, the target subset can include information about relationships between genes, such as clustering. This target subset presents an interesting parameter that we can estimate by applying the rule to the sample statistics of microarray data. The parametric bootstrap, based on a multivariate normal model, is used to estimate the distribution of these estimated subsets and relevant summary measures of this sampling distribution are proposed. We focus on rules that operate on the mean and covariance. Using Bernstein's Inequality, we obtain consistency of the subset estimates, under the assumption that the sample size converges faster to infinity than the logarithm of the number of genes. We also provide a conservative sample size formula guaranteeing that the sample mean and sample covariance matrix are uniformly within a distance epsilon > 0 of the population mean and covariance. The practical performance of the method using a cluster-based subset rule is illustrated with a simulation study. The method is illustrated with an analysis of a publicly available leukemia data set.     

The effects of normalization on the correlation structure of microarray data

Background  

Stochastic dependence between gene expression levels in microarray data is of critical importance for the methods of statistical inference that resort to pooling test-statistics across genes. It is frequently assumed that dependence between genes (or tests) is suffciently weak to justify the proposed methods of testing for differentially expressed genes. A potential impact of between-gene correlations on the performance of such methods has yet to be explored.     

The optimal discovery procedure for large-scale significance testing, with applications to comparative microarray experiments

As much of the focus of genetics and molecular biology has shifted toward the systems level, it has become increasingly important to accurately extract biologically relevant signal from thousands of related measurements. The common property among these high-dimensional biological studies is that the measured features have a rich and largely unknown underlying structure. One example of much recent interest is identifying differentially expressed genes in comparative microarray experiments. We propose a new approach aimed at optimally performing many hypothesis tests in a high-dimensional study. This approach estimates the optimal discovery procedure (ODP), which has recently been introduced and theoretically shown to optimally perform multiple significance tests. Whereas existing procedures essentially use data from only one feature at a time, the ODP approach uses the relevant information from the entire data set when testing each feature. In particular, we propose a generally applicable estimate of the ODP for identifying differentially expressed genes in microarray experiments. This microarray method consistently shows favorable performance over five highly used existing methods. For example, in testing for differential expression between two breast cancer tumor types, the ODP provides increases from 72% to 185% in the number of genes called significant at a false discovery rate of 3%. Our proposed microarray method is freely available to academic users in the open-source, point-and-click EDGE software package.     

Impact of DNA microarray data transformation on gene expression analysis - comparison of two normalization methods

Two-color DNA microarrays are commonly used for the analysis of global gene expression. They provide information on relative abundance of thousands of mRNAs. However, the generated data need to be normalized to minimize systematic variations so that biologically significant differences can be more easily identified. A large number of normalization procedures have been proposed and many softwares for microarray data analysis are available. Here, we have applied two normalization methods (median and loess) from two packages of microarray data analysis softwares. They were examined using a sample data set. We found that the number of genes identified as differentially expressed varied significantly depending on the method applied. The obtained results, i.e. lists of differentially expressed genes, were consistent only when we used median normalization methods. Loess normalization implemented in the two software packages provided less coherent and for some probes even contradictory results. In general, our results provide an additional piece of evidence that the normalization method can profoundly influence final results of DNA microarray-based analysis. The impact of the normalization method depends greatly on the algorithm employed. Consequently, the normalization procedure must be carefully considered and optimized for each individual data set.     

肿瘤微阵列数据统计分析概述

微阵列技术已广泛应用于生物学和医学研究领域,如肿瘤的诊断和分型、预测和治疗,理解肿瘤的发生机制、生物学通路和基因网络。统计学方法在这一科学挑战中的地位至关重要。我们综述了微阵列实验数据分析的统计学方法最新发展,主要描述了微阵列数据的标准化、差异表达基因的统计学检验及微阵列技术在肿瘤治疗中的应用,重点介绍了时间序列微阵列数据分析方法和基因调控网络在肿瘤研究中的最新发展。     

A Robust Statistical Method for Detecting Differentially Expressed Genes

DNA microarray technology allows researchers to monitor the expressions of thousands of genes under different conditions, and to measure the levels of thousands of different DNA molecules at a given point in the life of an organism, tissue or cell. A wide variety of different diseases that are characterised by unregulated gene expression, DNA replication, cell division and cell death, can be detected early using microarrays. One of the major objectives of microarray experiments is to identify differentially expressed genes under various conditions. The detection of differential gene expression under two different conditions is very important in biological studies, and allows us to identify experimental variables that affect different biological processes. Most of the tests available in the literature are based on the assumption of normal distribution. However, the assumption of normality may not be true in real-life data, particularly with respect to microarray data.A test is proposed for the identification of differentially expressed genes in replicated microarray experiments conducted under two different conditions. The proposed test does not assume the distribution of the parent population; thus, the proposed test is strictly nonparametric in nature. We calculate the p-value and the asymptotic power function of the proposed test statistic. The proposed test statistic is compared with some of its competitors under normal, gamma and exponential population setup using the Monte Carlo simulation technique. The application of the proposed test statistic is presented using microarray data. The proposed test is robust and highly efficient when populations are non-normal.     

Relationships among murine CD11c(high) dendritic cell subsets as revealed by baseline gene expression patterns

The functional relationships and properties of different subtypes of dendritic cells (DC) remain largely undefined. To better characterize these cells, we used global gene analysis to determine gene expression patterns among murine CD11c(high) DC subsets. CD4(+), CD8alpha(+), and CD8alpha(-) CD4(-) (double negative (DN)) DC were purified from spleens of normal C57/BL6 mice and analyzed using Affymetrix microarrays. The CD4(+) and CD8alpha(+) DC subsets showed distinct basal expression profiles differing by >200 individual genes. These included known DC subset markers as well as previously unrecognized, differentially expressed CD Ags such as CD1d, CD5, CD22, and CD72. Flow cytometric analysis confirmed differential expression in nine of nine cases, thereby validating the microarray analysis. Interestingly, the microarray expression profiles for DN cells strongly resembled those of CD4(+) DC, differing from them by <25 genes. This suggests that CD4(+) and DN DC are closely related phylogenetically, whereas CD8alpha(+) DC represent a more distant lineage, supporting the historical distinction between CD8alpha(+) and CD8alpha(-) DC. However, staining patterns revealed that in contrast to CD4(+) DC, the DN subset is heterogeneous and comprises at least two subpopulations. Gene Ontology and literature mining analyses of genes expressed differentially among DC subsets indicated strong associations with immune response parameters as well as cell differentiation and signaling. Such associations offer clues to possible unique functions of the CD11c(high) DC subsets that to date have been difficult to define as rigid distinctions.     

Global gene expression profiling in Escherichia coli K12. The effects of oxygen availability and FNR

The work presented here is a first step toward a long term goal of systems biology, the complete elucidation of the gene regulatory networks of a living organism. To this end, we have employed DNA microarray technology to identify genes involved in the regulatory networks that facilitate the transition of Escherichia coli cells from an aerobic to an anaerobic growth state. We also report the identification of a subset of these genes that are regulated by a global regulatory protein for anaerobic metabolism, FNR. Analysis of these data demonstrated that the expression of over one-third of the genes expressed during growth under aerobic conditions are altered when E. coli cells transition to an anaerobic growth state, and that the expression of 712 (49%) of these genes are either directly or indirectly modulated by FNR. The results presented here also suggest interactions between the FNR and the leucine-responsive regulatory protein (Lrp) regulatory networks. Because computational methods to analyze and interpret high dimensional DNA microarray data are still at an early stage, and because basic issues of data analysis are still being sorted out, much of the emphasis of this work is directed toward the development of methods to identify differentially expressed genes with a high level of confidence. In particular, we describe an approach for identifying gene expression patterns (clusters) obtained from multiple perturbation experiments based on a subset of genes that exhibit high probability for differential expression values.