Sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis

Summary Simultaneous inference for a large number, N, of parameters is a challenge. In some situations, such as microarray experiments, researchers are only interested in making inference for the K parameters corresponding to the K most extreme estimates. Hence it seems important to construct simultaneous confidence intervals for these K parameters. The naïve simultaneous confidence intervals for the K means (applied directly without taking into account the selection) have low coverage probabilities. We take an empirical Bayes approach (or an approach based on the random effect model) to construct simultaneous confidence intervals with good coverage probabilities. For N= 10,000 and K= 100, typical for microarray data, our confidence intervals could be 77% shorter than the naïve K‐dimensional simultaneous intervals.     

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.     

Covariate adjustment in the analysis of microarray data from clinical studies

There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for follow-up validation studies. We develop two approaches to the analysis of microarray data in non-randomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic (ROC) curve for the analysis of gene expression data. The ideas are illustrated using data from a prostate cancer molecular profiling study.     

基因表达数据聚类分析技术及其软件工具

随着DNA芯片技术的广泛应用,基因表达数据分析已成为生命科学的研究热点之一。概述基因表达聚类技术类型、算法分类与特点、结果可视化与注释;阐述一些流行的和新型的算法;介绍17个最新相关软件包和在线web服务工具;并说明软件工具的研究趋向。     

Sample size calculation for multiple testing in microarray data analysis

Microarray technology is rapidly emerging for genome-wide screening of differentially expressed genes between clinical subtypes or different conditions of human diseases. Traditional statistical testing approaches, such as the two-sample t-test or Wilcoxon test, are frequently used for evaluating statistical significance of informative expressions but require adjustment for large-scale multiplicity. Due to its simplicity, Bonferroni adjustment has been widely used to circumvent this problem. It is well known, however, that the standard Bonferroni test is often very conservative. In the present paper, we compare three multiple testing procedures in the microarray context: the original Bonferroni method, a Bonferroni-type improved single-step method and a step-down method. The latter two methods are based on nonparametric resampling, by which the null distribution can be derived with the dependency structure among gene expressions preserved and the family-wise error rate accurately controlled at the desired level. We also present a sample size calculation method for designing microarray studies. Through simulations and data analyses, we find that the proposed methods for testing and sample size calculation are computationally fast and control error and power precisely.     

Statistical analysis of microarray data: a Bayesian approach

The potential of microarray data is enormous. It allows us to monitor the expression of thousands of genes simultaneously. A common task with microarray is to determine which genes are differentially expressed between two samples obtained under two different conditions. Recently, several statistical methods have been proposed to perform such a task when there are replicate samples under each condition. Two major problems arise with microarray data. The first one is that the number of replicates is very small (usually 2-10), leading to noisy point estimates. As a consequence, traditional statistics that are based on the means and standard deviations, e.g. t-statistic, are not suitable. The second problem is that the number of genes is usually very large (approximately 10,000), and one is faced with an extreme multiple testing problem. Most multiple testing adjustments are relatively conservative, especially when the number of replicates is small. In this paper we present an empirical Bayes analysis that handles both problems very well. Using different parametrizations, we develop four statistics that can be used to test hypotheses about the means and/or variances of the gene expression levels in both one- and two-sample problems. The methods are illustrated using experimental data with prior knowledge. In addition, we present the result of a simulation comparing our methods to well-known statistics and multiple testing adjustments.     

A note on joint versus gene-specific mixed model analysis of microarray gene expression data

Currently, linear mixed model analyses of expression microarray experiments are performed either in a gene-specific or global mode. The joint analysis provides more flexibility in terms of how parameters are fitted and estimated and tends to be more powerful than the gene-specific analysis. Here we show how to implement the gene-specific linear mixed model analysis as an exact algorithm for the joint linear mixed model analysis. The gene-specific algorithm is exact, when the mixed model equations can be partitioned into unrelated components: One for all global fixed and random effects and the others for the gene-specific fixed and random effects for each gene separately. This unrelatedness holds under three conditions: (1) any gene must have the same number of replicates or probes on all arrays, but these numbers can differ among genes; (2) the residual variance of the (transformed) expression data must be homogeneous or constant across genes (other variance components need not be homogeneous) and (3) the number of genes in the experiment is large. When these conditions are violated, the gene-specific algorithm is expected to be nearly exact.     

On sparse Fisher discriminant method for microarray data analysis

One of the applications of the discriminant analysis on microarray data is to classify patient and normal samples based on gene expression values. The analysis is especially important in medical trials and diagnosis of cancer subtypes. The main contribution of this paper is to propose a simple Fisher-type discriminant method on gene selection in microarray data. In the new algorithm, we calculate a weight for each gene and use the weight values as an indicator to identify the subsets of relevant genes that categorize patient and normal samples. A l(2) - l(1) norm minimization method is implemented to the discriminant process to automatically compute the weights of all genes in the samples. The experiments on two microarray data sets have shown that the new algorithm can generate classification results as good as other classification methods, and effectively determine relevant genes for classification purpose. In this study, we demonstrate the gene selection's ability and the computational effectiveness of the proposed algorithm. Experimental results are given to illustrate the usefulness of the proposed model.     

Random forest for gene selection and microarray data classification

A random forest method has been selected to perform both gene selection and classification of the microarray data. In this embedded method, the selection of smallest possible sets of genes with lowest error rates is the key factor in achieving highest classification accuracy. Hence, improved gene selection method using random forest has been proposed to obtain the smallest subset of genes as well as biggest subset of genes prior to classification. The option for biggest subset selection is done to assist researchers who intend to use the informative genes for further research. Enhanced random forest gene selection has performed better in terms of selecting the smallest subset as well as biggest subset of informative genes with lowest out of bag error rates through gene selection. Furthermore, the classification performed on the selected subset of genes using random forest has lead to lower prediction error rates compared to existing method and other similar available methods.     

Statistical issues and methods for meta-analysis of microarray data: a case study in prostate cancer

With the proliferation of related microarray studies by independent groups, a natural step in the analysis of these gene expression data is to combine the results across these studies. However, this raises a variety of issues in the analysis of such data. In this article, we discuss the statistical issues of combining data from multiple gene expression studies. This leads to more complications than those in standard meta-analyses, including different experimental platforms, duplicate spots and complex data structures. We illustrate these ideas using data from four prostate cancer profiling studies. In addition, we develop a simple approach for assessing differential expression using the LASSO method. A combination of the results and the pathway databases are then used to generate candidate biological pathways for cancer.     

Discrimination and scoring using small sets of genes for two-sample microarray data

Comparison of gene expression for two groups of individuals form an important subclass of microarray experiments. We study multivariate procedures, in particular use of Hotelling's T2 for discrimination between the groups with a special emphasis on methods based on few genes only. We apply the methods to data from an experiment with a group of atopic dermatitis patients compared with a control group. We also compare our methodology to other recently proposed methods on publicly available datasets. It is found that (i) use of several genes gives a much improved discrimination of the groups as compared to one gene only, (ii) the genes that play the most important role in the multivariate analysis are not necessarily those that rank first in univariate comparisons of the groups, (iii) Linear Discriminant Analysis carried out with sets of 2-5 genes selected according to their Hotelling T2 give results comparable to state-of-the-art methods using many more genes, a feature of our method which might be crucial in clinical applications. Finding groups of genes that together give optimal multivariate discrimination (given the size of the group) can identify crucial pathways and networks of genes responsible for a disease. The computer code that we developed to make computations is available as an R package.     

Effective feature selection framework for cluster analysis of microarray data

The microarray technique has become a standard means in simultaneously examining expression of all genes measured in different circumstances. As microarray data are typically characterized by high dimensional features with a small number of samples, feature selection needs to be incorporated to identify a subset of genes that are meaningful for biological interpretation and accountable for the sample variation. In this article, we present a simple, yet effective feature selection framework suitable for two-dimensional microarray data. Our correlation-based, nonparametric approach allows compact representation of class-specific properties with a small number of genes. We evaluated our method using publicly available experimental data and obtained favorable results.     

Using ANOVA for gene selection from microarray studies of the nervous system

Methods are presented for detecting differential expression using statistical hypothesis testing methods including analysis of variance (ANOVA). Practicalities of experimental design, power, and sample size are discussed. Methods for multiple testing correction and their application are described. Instructions for running typical analyses are given in the R programming environment. R code and the sample data set used to generate the examples are available at http://microarray.cpmc.columbia.edu/pavlidis/pub/aovmethods/.     

CAP-miRSeq: a comprehensive analysis pipeline for microRNA sequencing data

Background

miRNAs play a key role in normal physiology and various diseases. miRNA profiling through next generation sequencing (miRNA-seq) has become the main platform for biological research and biomarker discovery. However, analyzing miRNA sequencing data is challenging as it needs significant amount of computational resources and bioinformatics expertise. Several web based analytical tools have been developed but they are limited to processing one or a pair of samples at time and are not suitable for a large scale study. Lack of flexibility and reliability of these web applications are also common issues.

Results

We developed a Comprehensive Analysis Pipeline for microRNA Sequencing data (CAP-miRSeq) that integrates read pre-processing, alignment, mature/precursor/novel miRNA detection and quantification, data visualization, variant detection in miRNA coding region, and more flexible differential expression analysis between experimental conditions. According to computational infrastructure, users can install the package locally or deploy it in Amazon Cloud to run samples sequentially or in parallel for a large number of samples for speedy analyses. In either case, summary and expression reports for all samples are generated for easier quality assessment and downstream analyses. Using well characterized data, we demonstrated the pipeline’s superior performances, flexibility, and practical use in research and biomarker discovery.

Conclusions

CAP-miRSeq is a powerful and flexible tool for users to process and analyze miRNA-seq data scalable from a few to hundreds of samples. The results are presented in the convenient way for investigators or analysts to conduct further investigation and discovery.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-423) contains supplementary material, which is available to authorized users.     

Comparative microarray data analysis for the expression of genes in the pathway of glioma

Our present work focuses on the set of genes, which are involved in primary brain tumors - the glioma pathway. These gliomas are mostly malignant (cancerous) in nature and are difficult to be cured and that's why they attract the attention of all the workers. To understand the relative functionality of these genes, we analyzed the expression pattern of all genes, using gene expression data, at genomic level, and then to check their universality in all other cancers, we compared their expression levels and patterns in all other types of cancers by using gene expression graphs, and observed their expression levels in all these cancers, whether they are over or under expressed. We found that every gene has its own unique expression pattern and level and on that basis it can be classified. We also found that oncogenes and tumor suppressor genes that were involved in the glioma pathway were showing similar expression patterns in other cancers too but their expression level is low.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

A new geometric biclustering algorithm based on the Hough transform for analysis of large-scale microarray data

Biclustering is an important tool in microarray analysis when only a subset of genes co-regulates in a subset of conditions. Different from standard clustering analyses, biclustering performs simultaneous classification in both gene and condition directions in a microarray data matrix. However, the biclustering problem is inherently intractable and computationally complex. In this paper, we present a new biclustering algorithm based on the geometrical viewpoint of coherent gene expression profiles. In this method, we perform pattern identification based on the Hough transform in a column-pair space. The algorithm is especially suitable for the biclustering analysis of large-scale microarray data. Our studies show that the approach can discover significant biclusters with respect to the increased noise level and regulatory complexity. Furthermore, we also test the ability of our method to locate biologically verifiable biclusters within an annotated set of genes.