A statistical framework for testing functional categories in microarray data

Ready access to emerging databases of gene annotation and functional pathways has shifted assessments of differential expression in DNA microarray studies from single genes to groups of genes with shared biological function. This paper takes a critical look at existing methods for assessing the differential expression of a group of genes (functional category), and provides some suggestions for improved performance. We begin by presenting a general framework, in which the set of genes in a functional category is compared to the complementary set of genes on the array. The framework includes tests for overrepresentation of a category within a list of significant genes, and methods that consider continuous measures of differential expression. Existing tests are divided into two classes. Class 1 tests assume gene-specific measures of differential expression are independent, despite overwhelming evidence of positive correlation. Analytic and simulated results are presented that demonstrate Class 1 tests are strongly anti-conservative in practice. Class 2 tests account for gene correlation, typically through array permutation that by construction has proper Type I error control for the induced null. However, both Class 1 and Class 2 tests use a null hypothesis that all genes have the same degree of differential expression. We introduce a more sensible and general (Class 3) null under which the profile of differential expression is the same within the category and complement. Under this broader null, Class 2 tests are shown to be conservative. We propose standard bootstrap methods for testing against the Class 3 null and demonstrate they provide valid Type I error control and more power than array permutation in simulated datasets and real microarray experiments.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS146 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rank discriminants for predicting phenotypes from RNA expression

Statistical methods for analyzing large-scale biomolecular data are commonplace in computational biology. A notable example is phenotype prediction from gene expression data, for instance, detecting human cancers, differentiating subtypes and predicting clinical outcomes. Still, clinical applications remain scarce. One reason is that the complexity of the decision rules that emerge from standard statistical learning impedes biological understanding, in particular, any mechanistic interpretation. Here we explore decision rules for binary classification utilizing only the ordering of expression among several genes; the basic building blocks are then two-gene expression comparisons. The simplest example, just one comparison, is the TSP classifier, which has appeared in a variety of cancer-related discovery studies. Decision rules based on multiple comparisons can better accommodate class heterogeneity, and thereby increase accuracy, and might provide a link with biological mechanism. We consider a general framework ("rank-in-context") for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context"). We then specialize to two examples: voting among several pairs and comparing the median expression in two groups of genes. Comprehensive experiments assess accuracy relative to other, more complex, methods, and reinforce earlier observations that simple classifiers are competitive.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS738 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Automated data integration for developmental biological research

In an era exploding with genome-scale data, a major challenge for developmental biologists is how to extract significant clues from these publicly available data to benefit our studies of individual genes, and how to use them to improve our understanding of development at a systems level. Several studies have successfully demonstrated new approaches to classic developmental questions by computationally integrating various genome-wide data sets. Such computational approaches have shown great potential for facilitating research: instead of testing 20,000 genes, researchers might test 200 to the same effect. We discuss the nature and state of this art as it applies to developmental research

Estimating genomic coexpression networks using first-order conditional independence

We describe a computationally efficient statistical framework for estimating networks of coexpressed genes. This framework exploits first-order conditional independence relationships among gene-expression measurements to estimate patterns of association. We use this approach to estimate a coexpression network from microarray gene-expression measurements from Saccharomyces cerevisiae. We demonstrate the biological utility of this approach by showing that a large number of metabolic pathways are coherently represented in the estimated network. We describe a complementary unsupervised graph search algorithm for discovering locally distinct subgraphs of a large weighted graph. We apply this algorithm to our coexpression network model and show that subgraphs found using this approach correspond to particular biological processes or contain representatives of distinct gene families

Bayesian meta-analysis for identifying periodically expressed genes in fission yeast cell cycle

The effort to identify genes with periodic expression during the cell cycle from genome-wide microarray time series data has been ongoing for a decade. However, the lack of rigorous modeling of periodic expression as well as the lack of a comprehensive model for integrating information across genes and experiments has impaired the effort for the accurate identification of periodically expressed genes. To address the problem, we introduce a Bayesian model to integrate multiple independent microarray data sets from three recent genome-wide cell cycle studies on fission yeast. A hierarchical model was used for data integration. In order to facilitate an efficient Monte Carlo sampling from the joint posterior distribution, we develop a novel Metropolis--Hastings group move. A surprising finding from our integrated analysis is that more than 40% of the genes in fission yeast are significantly periodically expressed, greatly enhancing the reported 10--15% of the genes in the current literature. It calls for a reconsideration of the periodically expressed gene detection problem.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS300 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effects of dependence in high-dimensional multiple testing problems

<p>Abstract</p> <p>Background</p> <p>We consider effects of dependence among variables of high-dimensional data in multiple hypothesis testing problems, in particular the False Discovery Rate (FDR) control procedures. Recent simulation studies consider only simple correlation structures among variables, which is hardly inspired by real data features. Our aim is to systematically study effects of several network features like sparsity and correlation strength by imposing dependence structures among variables using random correlation matrices.</p> <p>Results</p> <p>We study the robustness against dependence of several FDR procedures that are popular in microarray studies, such as Benjamin-Hochberg FDR, Storey's q-value, SAM and resampling based FDR procedures. False Non-discovery Rates and estimates of the number of null hypotheses are computed from those methods and compared. Our simulation study shows that methods such as SAM and the q-value do not adequately control the FDR to the level claimed under dependence conditions. On the other hand, the adaptive Benjamini-Hochberg procedure seems to be most robust while remaining conservative. Finally, the estimates of the number of true null hypotheses under various dependence conditions are variable.</p> <p>Conclusion</p> <p>We discuss a new method for efficient guided simulation of dependent data, which satisfy imposed network constraints as conditional independence structures. Our simulation set-up allows for a structural study of the effect of dependencies on multiple testing criterions and is useful for testing a potentially new method on <it>π</it>₀or FDR estimation in a dependency context.</p

Post hoc pattern matching: assigning significance to statistically defined expression patterns in single channel microarray data

<p>Abstract</p> <p>Background</p> <p>Researchers using RNA expression microarrays in experimental designs with more than two treatment groups often identify statistically significant genes with ANOVA approaches. However, the ANOVA test does not discriminate which of the multiple treatment groups differ from one another. Thus, <it>post hoc </it>tests, such as linear contrasts, template correlations, and pairwise comparisons are used. Linear contrasts and template correlations work extremely well, especially when the researcher has <it>a priori </it>information pointing to a particular pattern/template among the different treatment groups. Further, all pairwise comparisons can be used to identify particular, treatment group-dependent patterns of gene expression. However, these approaches are biased by the researcher's assumptions, and some treatment-based patterns may fail to be detected using these approaches. Finally, different patterns may have different probabilities of occurring by chance, importantly influencing researchers' conclusions about a pattern and its constituent genes.</p> <p>Results</p> <p>We developed a four step, <it>post hoc </it>pattern matching (PPM) algorithm to automate single channel gene expression pattern identification/significance. First, 1-Way Analysis of Variance (ANOVA), coupled with <it>post hoc </it>'all pairwise' comparisons are calculated for all genes. Second, for each ANOVA-significant gene, all pairwise contrast results are encoded to create unique pattern ID numbers. The # genes found in each pattern in the data is identified as that pattern's 'actual' frequency. Third, using Monte Carlo simulations, those patterns' frequencies are estimated in random data ('random' gene pattern frequency). Fourth, a Z-score for overrepresentation of the pattern is calculated ('actual' against 'random' gene pattern frequencies). We wrote a Visual Basic program (StatiGen) that automates PPM procedure, constructs an Excel workbook with standardized graphs of overrepresented patterns, and lists of the genes comprising each pattern. The visual basic code, installation files for StatiGen, and sample data are available as supplementary material.</p> <p>Conclusion</p> <p>The PPM procedure is designed to augment current microarray analysis procedures by allowing researchers to incorporate all of the information from post hoc tests to establish unique, overarching gene expression patterns in which there is no overlap in gene membership. In our hands, PPM works well for studies using from three to six treatment groups in which the researcher is interested in treatment-related patterns of gene expression. Hardware/software limitations and extreme number of theoretical expression patterns limit utility for larger numbers of treatment groups. Applied to a published microarray experiment, the StatiGen program successfully flagged patterns that had been manually assigned in prior work, and further identified other gene expression patterns that may be of interest. Thus, over a moderate range of treatment groups, PPM appears to work well. It allows researchers to assign statistical probabilities to patterns of gene expression that fit <it>a priori </it>expectations/hypotheses, it preserves the data's ability to show the researcher interesting, yet unanticipated gene expression patterns, and assigns the majority of ANOVA-significant genes to non-overlapping patterns.</p

Sources of variation in Affymetrix microarray experiments

BACKGROUND: A typical microarray experiment has many sources of variation which can be attributed to biological and technical causes. Identifying sources of variation and assessing their magnitude, among other factors, are important for optimal experimental design. The objectives of this study were: (1) to estimate relative magnitudes of different sources of variation and (2) to evaluate agreement between biological and technical replicates. RESULTS: We performed a microarray experiment using a total of 24 Affymetrix GeneChip(® )arrays. The study included 4(th )mammary gland samples from eight 21-day-old Sprague Dawley CD female rats exposed to genistein (soy isoflavone). RNA samples from each rat were split to assess variation arising at labeling and hybridization steps. A general linear model was used to estimate variance components. Pearson correlations were computed to evaluate agreement between technical and biological replicates. CONCLUSION: The greatest source of variation was biological variation, followed by residual error, and finally variation due to labeling when *.cel files were processed with dChip and RMA image processing algorithms. When MAS 5.0 or GCRMA-EB were used, the greatest source of variation was residual error, followed by biology and labeling. Correlations between technical replicates were consistently higher than between biological replicates

Feature selection when there are many influential features

Recent discussion of the success of feature selection methods has argued that focusing on a relatively small number of features has been counterproductive. Instead, it is suggested, the number of significant features can be in the thousands or tens of thousands, rather than (as is commonly supposed at present) approximately in the range from five to fifty. This change, in orders of magnitude, in the number of influential features, necessitates alterations to the way in which we choose features and to the manner in which the success of feature selection is assessed. In this paper, we suggest a general approach that is suited to cases where the number of relevant features is very large, and we consider particular versions of the approach in detail. We propose ways of measuring performance, and we study both theoretical and numerical properties of the proposed methodology.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ536 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm