A statistical framework for eQTL mapping using RNA-seq data

RNA-seq may replace gene expression microarrays in the near future. Using RNA-seq, the expression of a gene can be estimated using the total number of sequence reads mapped to that gene, known as the total read count (TReC). Traditional expression quantitative trait locus (eQTL) mapping methods, such as linear regression, can be applied to TReC measurements after they are properly normalized. In this article, we show that eQTL mapping, by directly modeling TReC using discrete distributions, has higher statistical power than the two-step approach: data normalization followed by linear regression. In addition, RNA-seq provides information on allele-specific expression (ASE) that is not available from microarrays. By combining the information from TReC and ASE, we can computationally distinguish cis- and trans-eQTL and further improve the power of cis-eQTL mapping. Both simulation and real data studies confirm the improved power of our new methods. We also discuss the design issues of RNA-seq experiments. Specifically, we show that by combining TReC and ASE measurements, it is possible to minimize cost and retain the statistical power of cis-eQTL mapping by reducing sample size while increasing the number of sequence reads per sample. In addition to RNA-seq data, our method can also be employed to study the genetic basis of other types of sequencing data, such as chromatin immunoprecipitation followed by DNA sequencing data. In this article, we focus on eQTL mapping of a single gene using the association-based method. However, our method establishes a statistical framework for future developments of eQTL mapping methods using RNA-seq data (e.g., linkage-based eQTL mapping), and the joint study of multiple genetic markers and/or multiple genes.     

RNA-Seq vs Dual- and Single-Channel Microarray Data: Sensitivity Analysis for Differential Expression and Clustering

With the fast development of high-throughput sequencing technologies, a new generation of genome-wide gene expression measurements is under way. This is based on mRNA sequencing (RNA-seq), which complements the already mature technology of microarrays, and is expected to overcome some of the latter’s disadvantages. These RNA-seq data pose new challenges, however, as strengths and weaknesses have yet to be fully identified. Ideally, Next (or Second) Generation Sequencing measures can be integrated for more comprehensive gene expression investigation to facilitate analysis of whole regulatory networks. At present, however, the nature of these data is not very well understood. In this paper we study three alternative gene expression time series datasets for the Drosophila melanogaster embryo development, in order to compare three measurement techniques: RNA-seq, single-channel and dual-channel microarrays. The aim is to study the state of the art for the three technologies, with a view of assessing overlapping features, data compatibility and integration potential, in the context of time series measurements. This involves using established tools for each of the three different technologies, and technical and biological replicates (for RNA-seq and microarrays, respectively), due to the limited availability of biological RNA-seq replicates for time series data. The approach consists of a sensitivity analysis for differential expression and clustering. In general, the RNA-seq dataset displayed highest sensitivity to differential expression. The single-channel data performed similarly for the differentially expressed genes common to gene sets considered. Cluster analysis was used to identify different features of the gene space for the three datasets, with higher similarities found for the RNA-seq and single-channel microarray dataset.     

Statistical significance analysis of longitudinal gene expression data

MOTIVATION: Time-course microarray experiments are designed to study biological processes in a temporal fashion. Longitudinal gene expression data arise when biological samples taken from the same subject at different time points are used to measure the gene expression levels. It has been observed that the gene expression patterns of samples of a given tumor measured at different time points are likely to be much more similar to each other than are the expression patterns of tumor samples of the same type taken from different subjects. In statistics, this phenomenon is called the within-subject correlation of repeated measurements on the same subject, and the resulting data are called longitudinal data. It is well known in other applications that valid statistical analyses have to appropriately take account of the possible within-subject correlation in longitudinal data. RESULTS: We apply estimating equation techniques to construct a robust statistic, which is a variant of the robust Wald statistic and accounts for the potential within-subject correlation of longitudinal gene expression data, to detect genes with temporal changes in expression. We associate significance levels to the proposed statistic by either incorporating the idea of the significance analysis of microarrays method or using the mixture model method to identify significant genes. The utility of the statistic is demonstrated by applying it to an important study of osteoblast lineage-specific differentiation. Using simulated data, we also show pitfalls in drawing statistical inference when the within-subject correlation in longitudinal gene expression data is ignored.     

Kernel hierarchical gene clustering from microarray expression data

MOTIVATION: Unsupervised analysis of microarray gene expression data attempts to find biologically significant patterns within a given collection of expression measurements. For example, hierarchical clustering can be applied to expression profiles of genes across multiple experiments, identifying groups of genes that share similar expression profiles. Previous work using the support vector machine supervised learning algorithm with microarray data suggests that higher-order features, such as pairwise and tertiary correlations across multiple experiments, may provide significant benefit in learning to recognize classes of co-expressed genes. RESULTS: We describe a generalization of the hierarchical clustering algorithm that efficiently incorporates these higher-order features by using a kernel function to map the data into a high-dimensional feature space. We then evaluate the utility of the kernel hierarchical clustering algorithm using both internal and external validation. The experiments demonstrate that the kernel representation itself is insufficient to provide improved clustering performance. We conclude that mapping gene expression data into a high-dimensional feature space is only a good idea when combined with a learning algorithm, such as the support vector machine that does not suffer from the curse of dimensionality. AVAILABILITY: Supplementary data at www.cs.columbia.edu/compbio/hiclust. Software source code available by request.     

EXCAVATOR: a computer program for efficiently mining gene expression data

Massive amounts of gene expression data are generated using microarrays for functional studies of genes and gene expression data clustering is a useful tool for studying the functional relationship among genes in a biological process. We have developed a computer package EXCAVATOR for clustering gene expression profiles based on our new framework for representing gene expression data as a minimum spanning tree. EXCAVATOR uses a number of rigorous and efficient clustering algorithms. This program has a number of unique features, including capabilities for: (i) data- constrained clustering; (ii) identification of genes with similar expression profiles to pre-specified seed genes; (iii) cluster identification from a noisy background; (iv) computational comparison between different clustering results of the same data set. EXCAVATOR can be run from a Unix/Linux/DOS shell, from a Java interface or from a Web server. The clustering results can be visualized as colored figures and 2-dimensional plots. Moreover, EXCAVATOR provides a wide range of options for data formats, distance measures, objective functions, clustering algorithms, methods to choose number of clusters, etc. The effectiveness of EXCAVATOR has been demonstrated on several experimental data sets. Its performance compares favorably against the popular K-means clustering method in terms of clustering quality and computing time.     

Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach

MOTIVATION: Biologists often employ clustering techniques in the explorative phase of microarray data analysis to discover relevant biological groupings. Given the availability of numerous clustering algorithms in the machine-learning literature, an user might want to select one that performs the best for his/her data set or application. While various validation measures have been proposed over the years to judge the quality of clusters produced by a given clustering algorithm including their biological relevance, unfortunately, a given clustering algorithm can perform poorly under one validation measure while outperforming many other algorithms under another validation measure. A manual synthesis of results from multiple validation measures is nearly impossible in practice, especially, when a large number of clustering algorithms are to be compared using several measures. An automated and objective way of reconciling the rankings is needed. RESULTS: Using a Monte Carlo cross-entropy algorithm, we successfully combine the ranks of a set of clustering algorithms under consideration via a weighted aggregation that optimizes a distance criterion. The proposed weighted rank aggregation allows for a far more objective and automated assessment of clustering results than a simple visual inspection. We illustrate our procedure using one simulated as well as three real gene expression data sets from various platforms where we rank a total of eleven clustering algorithms using a combined examination of 10 different validation measures. The aggregate rankings were found for a given number of clusters k and also for an entire range of k. AVAILABILITY: R code for all validation measures and rank aggregation is available from the authors upon request. SUPPLEMENTARY INFORMATION: Supplementary information are available at http://www.somnathdatta.org/Supp/RankCluster/supp.htm.     

A dynamically growing self-organizing tree (DGSOT) for hierarchical clustering gene expression profiles

MOTIVATION: The increasing use of microarray technologies is generating large amounts of data that must be processed in order to extract useful and rational fundamental patterns of gene expression. Hierarchical clustering technology is one method used to analyze gene expression data, but traditional hierarchical clustering algorithms suffer from several drawbacks (e.g. fixed topology structure; mis-clustered data which cannot be reevaluated). In this paper, we introduce a new hierarchical clustering algorithm that overcomes some of these drawbacks. RESULT: We propose a new tree-structure self-organizing neural network, called dynamically growing self-organizing tree (DGSOT) algorithm for hierarchical clustering. The DGSOT constructs a hierarchy from top to bottom by division. At each hierarchical level, the DGSOT optimizes the number of clusters, from which the proper hierarchical structure of the underlying dataset can be found. In addition, we propose a new cluster validation criterion based on the geometric property of the Voronoi partition of the dataset in order to find the proper number of clusters at each hierarchical level. This criterion uses the Minimum Spanning Tree (MST) concept of graph theory and is computationally inexpensive for large datasets. A K-level up distribution (KLD) mechanism, which increases the scope of data distribution in the hierarchy construction, was used to improve the clustering accuracy. The KLD mechanism allows the data misclustered in the early stages to be reevaluated at a later stage and increases the accuracy of the final clustering result. The clustering result of the DGSOT is easily displayed as a dendrogram for visualization. Based on a yeast cell cycle microarray expression dataset, we found that our algorithm extracts gene expression patterns at different levels. Furthermore, the biological functionality enrichment in the clusters is considerably high and the hierarchical structure of the clusters is more reasonable. AVAILABILITY: DGSOT is available upon request from the authors.     

Using DNA microarrays to study gene expression in closely related species

MOTIVATION: Comparisons of gene expression levels within and between species have become a central tool in the study of the genetic basis for phenotypic variation, as well as in the study of the evolution of gene regulation. DNA microarrays are a key technology that enables these studies. Currently, however, microarrays are only available for a small number of species. Thus, in order to study gene expression levels in species for which microarrays are not available, researchers face three sets of choices: (i) use a microarray designed for another species, but only compare gene expression levels within species, (ii) construct a new microarray for every species whose gene expression profiles will be compared or (iii) build a multi-species microarray with probes from each species of interest. Here, we use data collected using a multi-primate cDNA array to evaluate the reliability of each approach. RESULTS: We find that, for inter-species comparisons, estimates of expression differences based on multi-species microarrays are more accurate than those based on multiple species-specific arrays. We also demonstrate that within-species expression differences can be estimated using a microarray for a closely related species, without discernible loss of information. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Genetic network inference: the effects of preprocessing

Clustering of gene expression data and gene network inference from such data has been a major research topic in recent years. In clustering, pairwise measurements are performed when calculating the distance matrix upon which the clustering is based. Pairwise measurements can also be used for gene network inference, by deriving potential interactions above a certain correlation or distance threshold. Our experiments show how interaction networks derived by this simple approach exhibit low-but significant-sensitivity and specificity. We also explore the effects that normalization and prefiltering have on the results of methods for identifying interactions from expression data. Before derivation of interactions or clustering, preprocessing is often performed by applying normalization to rescale the expression profiles and prefiltering where genes that do not appear to contribute to regulation are removed. In this paper, different ways of normalizing in combination with different distance measurements are tested on both unfiltered and prefiltered data, different prefiltering criteria are considered.     

From protein microarrays to diagnostic antigen discovery: a study of the pathogen Francisella tularensis

MOTIVATION: An important application of protein microarray data analysis is identifying a serodiagnostic antigen set that can reliably detect patterns and classify antigen expression profiles. This work addresses this problem using antibody responses to protein markers measured by a novel high-throughput microarray technology. The findings from this study have direct relevance to rapid, broad-based diagnostic and vaccine development. RESULTS: Protein microarray chips are probed with sera from individuals infected with the bacteria Francisella tularensis, a category A biodefense pathogen. A two-step approach to the diagnostic process is presented (1) feature (antigen) selection and (2) classification using antigen response measurements obtained from F.tularensis microarrays (244 antigens, 46 infected and 54 healthy human sera measurements). To select antigens, a ranking scheme based on the identification of significant immune responses and differential expression analysis is described. Classification methods including k-nearest neighbors, support vector machines (SVM) and k-Means clustering are applied to training data using selected antigen sets of various sizes. SVM based models yield prediction accuracy rates in the range of approximately 90% on validation data, when antigen set sizes are between 25 and 50. These results strongly indicate that the top-ranked antigens can be considered high-priority candidates for diagnostic development. AVAILABILITY: All software programs are written in R and available at http://www.igb.uci.edu/index.php?page=tools and at http://www.r-project.org. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Statistically Consistent Identification of Differentially Expressed Genes in DNA Chip Data Over the Whole Expression Range

BACKGROUND: It is a well known problem that standard techniques for analysing DNA chip data misspecify genes. In particular, genes that are confirmed to be active, often do not show up as potential candidates. This is possibly due to non-homogeneous distributions of expression levels over the whole expression range. METHODS: We introduce a method that allows the detection of genes based on a self-adaptive threshold. The threshold is determined for equally-populated expression bands by assuming a normal distribution of logarithms of expression level ratios. By specifying a significance level, the threshold is set according to 'local' expression statistics within a band. We call this method the relative variance method (RVM). We derive a test statistic for the RVM and compare it with other methods. On this statistical basis, we show that RVM is a complementary approach to the t-test, significance analysis of microarrays (SAM) or empirical Bayes analysis of microarrays (EBAM). The RVM should be particularly useful for experiments with small sample size. RESULTS: Using a clinical dataset, we demonstrate that the RVM can correctly identify known marker genes, which are not found by the t-test, SAM or EBAM. CONCLUSION: In situations with limited sample material and small number of replicates, as is often the case in clinical datasets, use of the proposed RVM provides a higher reliability of potential candidate genes.     

A practical false discovery rate approach to identifying patterns of differential expression in microarray data

SUMMARY: Searching for differentially expressed genes is one of the most common applications for microarrays, yet statistically there are difficult hurdles to achieving adequate rigor and practicality. False discovery rate (FDR) approaches have become relatively standard; however, how to define and control the FDR has been hotly debated. Permutation estimation approaches such as SAM and PaGE can be effective; however, they leave much room for improvement. We pursue the permutation estimation method and describe a convenient definition for the FDR that can be estimated in a straightforward manner. We then discuss issues regarding the choice of statistic and data transformation. It is impossible to optimize the power of any statistic for thousands of genes simultaneously, and we look at the practical consequences of this. For example, the log transform can both help and hurt at the same time, depending on the gene. We examine issues surrounding the SAM 'fudge factor' parameter, and how to handle these issues by optimizing with respect to power.     

A hierarchical unsupervised growing neural network for clustering gene expression patterns

MOTIVATION: We describe a new approach to the analysis of gene expression data coming from DNA array experiments, using an unsupervised neural network. DNA array technologies allow monitoring thousands of genes rapidly and efficiently. One of the interests of these studies is the search for correlated gene expression patterns, and this is usually achieved by clustering them. The Self-Organising Tree Algorithm, (SOTA) (Dopazo,J. and Carazo,J.M. (1997) J. Mol. Evol., 44, 226-233), is a neural network that grows adopting the topology of a binary tree. The result of the algorithm is a hierarchical cluster obtained with the accuracy and robustness of a neural network. RESULTS: SOTA clustering confers several advantages over classical hierarchical clustering methods. SOTA is a divisive method: the clustering process is performed from top to bottom, i.e. the highest hierarchical levels are resolved before going to the details of the lowest levels. The growing can be stopped at the desired hierarchical level. Moreover, a criterion to stop the growing of the tree, based on the approximate distribution of probability obtained by randomisation of the original data set, is provided. By means of this criterion, a statistical support for the definition of clusters is proposed. In addition, obtaining average gene expression patterns is a built-in feature of the algorithm. Different neurons defining the different hierarchical levels represent the averages of the gene expression patterns contained in the clusters. Since SOTA runtimes are approximately linear with the number of items to be classified, it is especially suitable for dealing with huge amounts of data. The method proposed is very general and applies to any data providing that they can be coded as a series of numbers and that a computable measure of similarity between data items can be used. AVAILABILITY: A server running the program can be found at: http://bioinfo.cnio.es/sotarray.     

The Use of Background Signal in the Transformation of cDNA-Microarray Measurements

As the application field of microarrays grows, so does the need for appropriate statistical tools to analyse the signal intensity measurements. Normalisation procedures are required to make the signals from different channels and arrays comparable. One objective, which is also the focus of this report, is to remove the curvature seen on plots of the log ratio versus the mean log intensity values of two channels.A number of methods already exist that are based on the assumption of a shift between the measurements of the two channels. In this article, we explore the use of background measurements to estimate and correct for the shift. We compare our proposal with some well known methods by applying them to microarrays from two studies. These two studies investigate the effect of vegetable diets on the gene expression in colon and lung tissue of mice.Graphical illustrations and a robust summary statistic show that all transformations are an improvement to the raw data. Overall, the best results are obtained with our proposed transformation that takes the background measurements into account.