Pathway analysis using random forests classification and regression

MOTIVATION: Although numerous methods have been developed to better capture biological information from microarray data, commonly used single gene-based methods neglect interactions among genes and leave room for other novel approaches. For example, most classification and regression methods for microarray data are based on the whole set of genes and have not made use of pathway information. Pathway-based analysis in microarray studies may lead to more informative and relevant knowledge for biological researchers. RESULTS: In this paper, we describe a pathway-based classification and regression method using Random Forests to analyze gene expression data. The proposed methods allow researchers to rank important pathways from externally available databases, discover important genes, find pathway-based outlying cases and make full use of a continuous outcome variable in the regression setting. We also compared Random Forests with other machine learning methods using several datasets and found that Random Forests classification error rates were either the lowest or the second-lowest. By combining pathway information and novel statistical methods, this procedure represents a promising computational strategy in dissecting pathways and can provide biological insight into the study of microarray data. AVAILABILITY: Source code written in R is available from http://bioinformatics.med.yale.edu/pathway-analysis/rf.htm.     

Weighted set enrichment of gene expression data

Background

Sets of genes that are known to be associated with each other can be used to interpret microarray data. This gene set approach to microarray data analysis can illustrate patterns of gene expression which may be more informative than analyzing the expression of individual genes. Various statistical approaches exist for the analysis of gene sets. There are three main classes of these methods: over-representation analysis, functional class scoring, and pathway topology based methods.

Methods

We propose weighted hypergeometric and weighted chi-squared methods in order to assign a rank to the degree to which each gene participates in the enrichment. Each gene is assigned a weight determined by the absolute value of its log fold change, which is then raised to a certain power. The power value can be adjusted as needed. Datasets from the Gene Expression Omnibus are used to test the method. The significantly enriched pathways are validated through searching the literature in order to determine their relevance to the dataset.

Results

Although these methods detect fewer significantly enriched pathways, they can potentially produce more relevant results. Furthermore, we compare the results of different enrichment methods on a set of microarray studies all containing data from various rodent neuropathic pain models.

Discussion

Our method is able to produce more consistent results than other methods when evaluated on similar datasets. It can also potentially detect relevant pathways that are not identified by the standard methods. However, the lack of biological ground truth makes validating the method difficult.

     

CressExpress: a tool for large-scale mining of expression data from Arabidopsis

CressExpress is a user-friendly, online, coexpression analysis tool for Arabidopsis (Arabidopsis thaliana) microarray expression data that computes patterns of correlated expression between user-entered query genes and the rest of the genes in the genome. Unlike other coexpression tools, CressExpress allows characterization of tissue-specific coexpression networks through user-driven filtering of input data based on sample tissue type. CressExpress also performs pathway-level coexpression analysis on each set of query genes, identifying and ranking genes based on their common connections with two or more query genes. This allows identification of novel candidates for involvement in common processes and functions represented by the query group. Users launch experiments using an easy-to-use Web-based interface and then receive the full complement of results, along with a record of tool settings and parameters, via an e-mail link to the CressExpress Web site. Data sets featured in CressExpress are strictly versioned and include expression data from MAS5, GCRMA, and RMA array processing algorithms. To demonstrate applications for CressExpress, we present coexpression analyses of cellulose synthase genes, indolic glucosinolate biosynthesis, and flowering. We show that subselecting sample types produces a richer network for genes involved in flowering in Arabidopsis. CressExpress provides direct access to expression values via an easy-to-use URL-based Web service, allowing users to determine quickly if their query genes are coexpressed with each other and likely to yield informative pathway-level coexpression results. The tool is available at http://www.cressexpress.org.     

Integrating functional knowledge during sample clustering for microarray data using unsupervised decision trees

Clustering of microarray gene expression data is performed routinely, for genes as well as for samples. Clustering of genes can exhibit functional relationships between genes; clustering of samples on the other hand is important for finding e.g. disease subtypes, relevant patient groups for stratification or related treatments. Usually this is done by first filtering the genes for high-variance under the assumption that they carry most of the information needed for separating different sample groups. If this assumption is violated, important groupings in the data might be lost. Furthermore, classical clustering methods do not facilitate the biological interpretation of the results. Therefore, we propose to methodologically integrate the clustering algorithm with prior biological information. This is different from other approaches as knowledge about classes of genes can be directly used to ease the interpretation of the results and possibly boost clustering performance. Our approach computes dendrograms that resemble decision trees with gene classes used to split the data at each node which can help to find biologically meaningful differences between the sample groups. We have tested the proposed method both on simulated and real data and conclude its usefulness as a complementary method, especially when assumptions of few differentially expressed genes along with an informative mapping of genes to different classes are met.     

Analysis on Differential Gene Expression Data for Prediction of New Biological Features in Permanent Atrial Fibrillation

Permanent Atrial fibrillation (pmAF) has largely remained incurable since the existing information for explaining precise mechanisms underlying pmAF is not sufficient. Microarray analysis offers a broader and unbiased approach to identify and predict new biological features of pmAF. By considering the unbalanced sample numbers in most microarray data of case - control, we designed an asymmetric principal component analysis algorithm and applied it to re - analyze differential gene expression data of pmAF patients and control samples for predicting new biological features. Finally, we identified 51 differentially expressed genes using the proposed method, in which 42 differentially expressed genes are new findings compared with two related works on the same data and the existing studies. The enrichment analysis illustrated the reliability of identified differentially expressed genes. Moreover, we predicted three new pmAF – related signaling pathways using the identified differentially expressed genes via the KO-Based Annotation System. Our analysis and the existing studies supported that the predicted signaling pathways may promote the pmAF progression. The results above are worthy to do further experimental studies. This work provides some new insights into molecular features of pmAF. It has also the potentially important implications for improved understanding of the molecular mechanisms of pmAF.     

Assessment method for a power analysis to identify differentially expressed pathways

Gene expression data can provide a very rich source of information for elucidating the biological function on the pathway level if the experimental design considers the needs of the statistical analysis methods. The purpose of this paper is to provide a comparative analysis of statistical methods for detecting the differentially expression of pathways (DEP). In contrast to many other studies conducted so far, we use three novel simulation types, producing a more realistic correlation structure than previous simulation methods. This includes also the generation of surrogate data from two large-scale microarray experiments from prostate cancer and ALL. As a result from our comprehensive analysis of 41,004 parameter configurations, we find that each method should only be applied if certain conditions of the data from a pathway are met. Further, we provide method-specific estimates for the optimal sample size for microarray experiments aiming to identify DEP in order to avoid an underpowered design. Our study highlights the sensitivity of the studied methods on the parameters of the system.     

Appearance frequency modulated gene set enrichment testing

Background  

Gene set enrichment testing has helped bridge the gap from an individual gene to a systems biology interpretation of microarray data. Although gene sets are defined a priori based on biological knowledge, current methods for gene set enrichment testing treat all genes equal. It is well-known that some genes, such as those responsible for housekeeping functions, appear in many pathways, whereas other genes are more specialized and play a unique role in a single pathway. Drawing inspiration from the field of information retrieval, we have developed and present here an approach to incorporate gene appearance frequency (in KEGG pathways) into two current methods, Gene Set Enrichment Analysis (GSEA) and logistic regression-based LRpath framework, to generate more reproducible and biologically meaningful results.     

The latent process decomposition of cDNA microarray data sets

We present a new computational technique (a software implementation, data sets, and supplementary information are available at http://www.enm.bris.ac.uk/lpd/) which enables the probabilistic analysis of cDNA microarray data and we demonstrate its effectiveness in identifying features of biomedical importance. A hierarchical Bayesian model, called Latent Process Decomposition (LPD), is introduced in which each sample in the data set is represented as a combinatorial mixture over a finite set of latent processes, which are expected to correspond to biological processes. Parameters in the model are estimated using efficient variational methods. This type of probabilistic model is most appropriate for the interpretation of measurement data generated by cDNA microarray technology. For determining informative substructure in such data sets, the proposed model has several important advantages over the standard use of dendrograms. First, the ability to objectively assess the optimal number of sample clusters. Second, the ability to represent samples and gene expression levels using a common set of latent variables (dendrograms cluster samples and gene expression values separately which amounts to two distinct reduced space representations). Third, in constrast to standard cluster models, observations are not assigned to a single cluster and, thus, for example, gene expression levels are modeled via combinations of the latent processes identified by the algorithm. We show this new method compares favorably with alternative cluster analysis methods. To illustrate its potential, we apply the proposed technique to several microarray data sets for cancer. For these data sets it successfully decomposes the data into known subtypes and indicates possible further taxonomic subdivision in addition to highlighting, in a wholly unsupervised manner, the importance of certain genes which are known to be medically significant. To illustrate its wider applicability, we also illustrate its performance on a microarray data set for yeast.     

Bayesian Network Expansion Identifies New ROS and Biofilm Regulators

Signaling and regulatory pathways that guide gene expression have only been partially defined for most organisms. However, given the increasing number of microarray measurements, it may be possible to reconstruct such pathways and uncover missing connections directly from experimental data. Using a compendium of microarray gene expression data obtained from Escherichia coli, we constructed a series of Bayesian network models for the reactive oxygen species (ROS) pathway as defined by EcoCyc. A consensus Bayesian network model was generated using those networks sharing the top recovered score. This microarray-based network only partially agreed with the known ROS pathway curated from the literature and databases. A top network was then expanded to predict genes that could enhance the Bayesian network model using an algorithm we termed ‘BN+1’. This expansion procedure predicted many stress-related genes (e.g., dusB and uspE), and their possible interactions with other ROS pathway genes. A term enrichment method discovered that biofilm-associated microarray data usually contained high expression levels of both uspE and gadX. The predicted involvement of gene uspE in the ROS pathway and interactions between uspE and gadX were confirmed experimentally using E. coli reporter strains. Genes gadX and uspE showed a feedback relationship in regulating each other''s expression. Both genes were verified to regulate biofilm formation through gene knockout experiments. These data suggest that the BN+1 expansion method can faithfully uncover hidden or unknown genes for a selected pathway with significant biological roles. The presently reported BN+1 expansion method is a generalized approach applicable to the characterization and expansion of other biological pathways and living systems.     

Biological pathway selection through nonlinear dimension reduction

In the analysis of high-throughput biological data, it is often believed that the biological units such as genes behave interactively by groups, that is, pathways in our context. It is conceivable that utilization of priorly available pathway knowledge would greatly facilitate both interpretation and estimation in statistical analysis of such high-dimensional biological data. In this article, we propose a 2-step procedure for the purpose of identifying pathways that are related to and influence the clinical phenotype. In the first step, a nonlinear dimension reduction method is proposed, which permits flexible within-pathway gene interactions as well as nonlinear pathway effects on the response. In the second step, a regularized model-based pathway ranking and selection procedure is developed that is built upon the summary features extracted from the first step. Simulations suggest that the new method performs favorably compared to the existing solutions. An analysis of a glioblastoma microarray data finds 4 pathways that have evidence of support from the biological literature.     

Application of independent component analysis to microarrays

We apply linear and nonlinear independent component analysis (ICA) to project microarray data into statistically independent components that correspond to putative biological processes, and to cluster genes according to over- or under-expression in each component. We test the statistical significance of enrichment of gene annotations within clusters. ICA outperforms other leading methods, such as principal component analysis, k-means clustering and the Plaid model, in constructing functionally coherent clusters on microarray datasets from Saccharomyces cerevisiae, Caenorhabditis elegans and human.     

Evaluation of experimental designs for two-color cDNA microarrays.

The major goal of two-color cDNA microarray experiments is to measure the relative gene expression level (i.e., relative amount of mRNA) of each gene between samples in studies of gene expression. More specifically, given an N-sample experiment, we need all N(N - 1)/2 relative expression levels of all sample pairs of each gene for identification of the differentially expressed genes and for clustering of gene expression patterns. However, the intensities observed from two-color cDNA microarray experiments do not simply represent the relative gene expression level. They are composed of signal (gene expression level), noise, and other factors. In discussions on the experimental design of two-color cDNA microarray experiments, little attention has been given to the fact that different combinations of test and control samples will produce microarray intensities data with varying intrinsic composition of factors. As a consequence, not all experimental designs for two-color cDNA microarray experiments are able to provide all possible relative gene expression levels. This phenomenon has never been addressed. To obtain all possible relative gene expression levels, a novel method for two-color cDNA microarray experimental design evaluation is necessary that will allow the making of an accurate choice. In this study, we propose a model-based approach to illustrate how the factor composition of microarray intensities changed with different experimental designs in two-color cDNA microarray experiments. By analyzing 12 experimental designs (including 5 general forms), we demonstrate that not all experimental designs are able to provide all possible relative gene expression levels due to the differences in factor composition. Our results indicate that whether an experimental design can provide all possible relative expression levels of all sample pairs for each gene should be the first criterion to be considered in an evaluation of experimental designs for two-color cDNA microarray experiments.     

Pathway analysis of microarray data via regression.

Pathway analysis of microarray data evaluates gene expression profiles of a priori defined biological pathways in association with a phenotype of interest. We propose a unified pathway-analysis method that can be used for diverse phenotypes including binary, multiclass, continuous, count, rate, and censored survival phenotypes. The proposed method also allows covariate adjustments and correlation in the phenotype variable that is encountered in longitudinal, cluster-sampled, and paired designs. These are accomplished by combining the regression-based test statistic for each individual gene in a pathway of interest into a pathway-level test statistic. Applications of the proposed method are illustrated with two real pathway-analysis examples: one evaluating relapse-associated gene expression involving a matched-pair binary phenotype in children with acute lymphoblastic leukemia; and the other investigating gene expression in breast cancer tissues in relation to patients' survival (a censored survival phenotype). Implementations for various phenotypes are available in R. Additionally, an Excel Add-in for a user-friendly interface is currently being developed.     

Using control genes to correct for unwanted variation in microarray data

Microarray expression studies suffer from the problem of batch effects and other unwanted variation. Many methods have been proposed to adjust microarray data to mitigate the problems of unwanted variation. Several of these methods rely on factor analysis to infer the unwanted variation from the data. A central problem with this approach is the difficulty in discerning the unwanted variation from the biological variation that is of interest to the researcher. We present a new method, intended for use in differential expression studies, that attempts to overcome this problem by restricting the factor analysis to negative control genes. Negative control genes are genes known a priori not to be differentially expressed with respect to the biological factor of interest. Variation in the expression levels of these genes can therefore be assumed to be unwanted variation. We name this method "Remove Unwanted Variation, 2-step" (RUV-2). We discuss various techniques for assessing the performance of an adjustment method and compare the performance of RUV-2 with that of other commonly used adjustment methods such as Combat and Surrogate Variable Analysis (SVA). We present several example studies, each concerning genes differentially expressed with respect to gender in the brain and find that RUV-2 performs as well or better than other methods. Finally, we discuss the possibility of adapting RUV-2 for use in studies not concerned with differential expression and conclude that there may be promise but substantial challenges remain.     

Comparison of algorithms for the analysis of Affymetrix microarray data as evaluated by co-expression of genes in known operons

Oligonucleotide microarrays are an informative tool to elucidate gene regulatory networks. In order for gene expression levels to be comparable across microarrays, normalization procedures have to be invoked. A large number of methods have been described to correct for systematic biases in microarray experiments. The performance of these methods has been tested only to a limited extend. Here, we evaluate two different types of microarray analyses: (i) the same gene in replicate samples and (ii) different, but co-expressed genes in the same sample. The reliability of the latter analysis needs to be determined for the analysis of regulatory networks and our report is the first attempt to evaluate for the accuracy of different microarray normalization methods in this respect. Consistent with previous results we observed a large effect of the normalization method on the outcome of the expression analyses. Our analyses indicate that different normalization methods should be performed depending on whether a study is aiming to detect differential gene expression between independent samples or whether co-expressed genes should be identified. We make recommendations about the most appropriate method to use.