Inferential Clustering Approach for Microarray Experiments with Replicated Measurements

Cluster analysis has proven to be a useful tool for investigating the association structure among genes in a microarray data set. There is a rich literature on cluster analysis and various techniques have been developed. Such analyses heavily depend on an appropriate (dis)similarity measure. In this paper, we introduce a general clustering approach based on the confidence interval inferential methodology, which is applied to gene expression data of microarray experiments. Emphasis is placed on data with low replication (three or five replicates). The proposed method makes more efficient use of the measured data and avoids the subjective choice of a dissimilarity measure. This new methodology, when applied to real data, provides an easy-to-use bioinformatics solution for the cluster analysis of microarray experiments with replicates (see the Appendix). Even though the method is presented under the framework of microarray experiments, it is a general algorithm that can be used to identify clusters in any situation. The method's performance is evaluated using simulated and publicly available data set. Our results also clearly show that our method is not an extension of the conventional clustering method based on correlation or euclidean distance.     

Gene Features Selection for Three-Class Disease Classification via Multiple Orthogonal Partial Least Square Discriminant Analysis and S-Plot Using Microarray Data

Motivation

DNA microarray analysis is characterized by obtaining a large number of gene variables from a small number of observations. Cluster analysis is widely used to analyze DNA microarray data to make classification and diagnosis of disease. Because there are so many irrelevant and insignificant genes in a dataset, a feature selection approach must be employed in data analysis. The performance of cluster analysis of this high-throughput data depends on whether the feature selection approach chooses the most relevant genes associated with disease classes.

Results

Here we proposed a new method using multiple Orthogonal Partial Least Squares-Discriminant Analysis (mOPLS-DA) models and S-plots to select the most relevant genes to conduct three-class disease classification and prediction. We tested our method using Golub’s leukemia microarray data. For three classes with subtypes, we proposed hierarchical orthogonal partial least squares-discriminant analysis (OPLS-DA) models and S-plots to select features for two main classes and their subtypes. For three classes in parallel, we employed three OPLS-DA models and S-plots to choose marker genes for each class. The power of feature selection to classify and predict three-class disease was evaluated using cluster analysis. Further, the general performance of our method was tested using four public datasets and compared with those of four other feature selection methods. The results revealed that our method effectively selected the most relevant features for disease classification and prediction, and its performance was better than that of the other methods.     

Using formal concept analysis for microarray data comparison

Microarray technologies, which can measure tens of thousands of gene expression values simultaneously in a single experiment, have become a common research method for biomedical researchers. Computational tools to analyze microarray data for biological discovery are needed. In this paper, we investigate the feasibility of using formal concept analysis (FCA) as a tool for microarray data analysis. The method of FCA builds a (concept) lattice from the experimental data together with additional biological information. For microarray data, each vertex of the lattice corresponds to a subset of genes that are grouped together according to their expression values and some biological information related to gene function. The lattice structure of these gene sets might reflect biological relationships in the dataset. Similarities and differences between experiments can then be investigated by comparing their corresponding lattices according to various graph measures. We apply our method to microarray data derived from influenza-infected mouse lung tissue and healthy controls. Our preliminary results show the promise of our method as a tool for microarray data analysis.     

Integrated analysis of gene expression and copy number data on gene shaving using independent component analysis

DNA microarray gene expression and microarray-based comparative genomic hybridization (aCGH) have been widely used for biomedical discovery. Because of the large number of genes and the complex nature of biological networks, various analysis methods have been proposed. One such method is "gene shaving," a procedure which identifies subsets of the genes with coherent expression patterns and large variation across samples. Since combining genomic information from multiple sources can improve classification and prediction of diseases, in this paper we proposed a new method, "ICA gene shaving" (ICA, independent component analysis), for jointly analyzing gene expression and copy number data. First we used ICA to analyze joint measurements, gene expression and copy number, of a biological system and project the data onto statistically independent biological processes. Next, we used these results to identify patterns of variation in the data and then applied an iterative shaving method. We investigated the properties of our proposed method by analyzing both simulated and real data. We demonstrated that the robustness of our method to noise using simulated data. Using breast cancer data, we showed that our method is superior to the Generalized Singular Value Decomposition (GSVD) gene shaving method for identifying genes associated with breast cancer.     

AGGRESCAN: a server for the prediction and evaluation of "hot spots" of aggregation in polypeptides

Background

A tremendous amount of efforts have been devoted to identifying genes for diagnosis and prognosis of diseases using microarray gene expression data. It has been demonstrated that gene expression data have cluster structure, where the clusters consist of co-regulated genes which tend to have coordinated functions. However, most available statistical methods for gene selection do not take into consideration the cluster structure.

Results

We propose a supervised group Lasso approach that takes into account the cluster structure in gene expression data for gene selection and predictive model building. For gene expression data without biological cluster information, we first divide genes into clusters using the K-means approach and determine the optimal number of clusters using the Gap method. The supervised group Lasso consists of two steps. In the first step, we identify important genes within each cluster using the Lasso method. In the second step, we select important clusters using the group Lasso. Tuning parameters are determined using V-fold cross validation at both steps to allow for further flexibility. Prediction performance is evaluated using leave-one-out cross validation. We apply the proposed method to disease classification and survival analysis with microarray data.

Conclusion

We analyze four microarray data sets using the proposed approach: two cancer data sets with binary cancer occurrence as outcomes and two lymphoma data sets with survival outcomes. The results show that the proposed approach is capable of identifying a small number of influential gene clusters and important genes within those clusters, and has better prediction performance than existing methods.     

Annotating gene function by combining expression data with a modular gene network

MOTIVATION: A promising and reliable approach to annotate gene function is clustering genes not only by using gene expression data but also literature information, especially gene networks. RESULTS: We present a systematic method for gene clustering by combining these totally different two types of data, particularly focusing on network modularity, a global feature of gene networks. Our method is based on learning a probabilistic model, which we call a hidden modular random field in which the relation between hidden variables directly represents a given gene network. Our learning algorithm which minimizes an energy function considering the network modularity is practically time-efficient, regardless of using the global network property. We evaluated our method by using a metabolic network and microarray expression data, changing with microarray datasets, parameters of our model and gold standard clusters. Experimental results showed that our method outperformed other four competing methods, including k-means and existing graph partitioning methods, being statistically significant in all cases. Further detailed analysis showed that our method could group a set of genes into a cluster which corresponds to the folate metabolic pathway while other methods could not. From these results, we can say that our method is highly effective for gene clustering and annotating gene function.     

A network-based gene-weighting approach for pathway analysis

Classical algorithms aiming at identifying biological pathways significantly related to studying conditions frequently reduced pathways to gene sets, with an obvious ignorance of the constitutive non-equivalence of various genes within a defined pathway. We here designed a network-based method to determine such non-equivalence in terms of gene weights. The gene weights determined are biologically consistent and robust to network perturbations. By integrating the gene weights into the classical gene set analysis, with a subsequent correction for the "over-counting" bias associated with multi-subunit proteins, we have developed a novel gene-weighed pathway analysis approach, as implemented in an R package called "Gene Associaqtion Network-based Pathway Analysis" (GANPA). Through analysis of several microarray datasets, including the p53 dataset, asthma dataset and three breast cancer datasets, we demonstrated that our approach is biologically reliable and reproducible, and therefore helpful for microarray data interpretation and hypothesis generation.     

Clustering threshold gradient descent regularization: with applications to microarray studies

MOTIVATION: An important goal of microarray studies is to discover genes that are associated with clinical outcomes, such as disease status and patient survival. While a typical experiment surveys gene expressions on a global scale, there may be only a small number of genes that have significant influence on a clinical outcome. Moreover, expression data have cluster structures and the genes within a cluster have correlated expressions and coordinated functions, but the effects of individual genes in the same cluster may be different. Accordingly, we seek to build statistical models with the following properties. First, the model is sparse in the sense that only a subset of the parameter vector is non-zero. Second, the cluster structures of gene expressions are properly accounted for. RESULTS: For gene expression data without pathway information, we divide genes into clusters using commonly used methods, such as K-means or hierarchical approaches. The optimal number of clusters is determined using the Gap statistic. We propose a clustering threshold gradient descent regularization (CTGDR) method, for simultaneous cluster selection and within cluster gene selection. We apply this method to binary classification and censored survival analysis. Compared to the standard TGDR and other regularization methods, the CTGDR takes into account the cluster structure and carries out feature selection at both the cluster level and within-cluster gene level. We demonstrate the CTGDR on two studies of cancer classification and two studies correlating survival of lymphoma patients with microarray expressions. AVAILABILITY: R code is available upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

miRNA regulatory circuits in ES cells differentiation: a chemical kinetics modeling approach

MicroRNAs (miRNAs) play an important role in gene regulation for Embryonic Stem cells (ES cells), where they either down-regulate target mRNA genes by degradation or repress protein expression of these mRNA genes by inhibiting translation. Well known tables TargetScan and miRanda may predict quite long lists of potential miRNAs inhibitors for each mRNA gene, and one of our goals was to strongly narrow down the list of mRNA targets potentially repressed by a known large list of 400 miRNAs. Our paper focuses on algorithmic analysis of ES cells microarray data to reliably detect repressive interactions between miRNAs and mRNAs. We model, by chemical kinetics equations, the interaction architectures implementing the two basic silencing processes of miRNAs, namely "direct degradation" or "translation inhibition" of targeted mRNAs. For each pair (M,G) of potentially interacting miRMA gene M and mRNA gene G, we parameterize our associated kinetic equations by optimizing their fit with microarray data. When this fit is high enough, we validate the pair (M,G) as a highly probable repressive interaction. This approach leads to the computation of a highly selective and drastically reduced list of repressive pairs (M,G) involved in ES cells differentiation.     

Identifying Gene Interaction Enrichment for Gene Expression Data

Gene set analysis allows the inclusion of knowledge from established gene sets, such as gene pathways, and potentially improves the power of detecting differentially expressed genes. However, conventional methods of gene set analysis focus on gene marginal effects in a gene set, and ignore gene interactions which may contribute to complex human diseases. In this study, we propose a method of gene interaction enrichment analysis, which incorporates knowledge of predefined gene sets (e.g. gene pathways) to identify enriched gene interaction effects on a phenotype of interest. In our proposed method, we also discuss the reduction of irrelevant genes and the extraction of a core set of gene interactions for an identified gene set, which contribute to the statistical variation of a phenotype of interest. The utility of our method is demonstrated through analyses on two publicly available microarray datasets. The results show that our method can identify gene sets that show strong gene interaction enrichments. The enriched gene interactions identified by our method may provide clues to new gene regulation mechanisms related to the studied phenotypes. In summary, our method offers a powerful tool for researchers to exhaustively examine the large numbers of gene interactions associated with complex human diseases, and can be a useful complement to classical gene set analyses which only considers single genes in a gene set.     

Microarray data integration for genome-wide analysis of human tissue-selective gene expression

Background

Microarray gene expression data are accumulating in public databases. The expression profiles contain valuable information for understanding human gene expression patterns. However, the effective use of public microarray data requires integrating the expression profiles from heterogeneous sources.

Results

In this study, we have compiled a compendium of microarray expression profiles of various human tissue samples. The microarray raw data generated in different research laboratories have been obtained and combined into a single dataset after data normalization and transformation. To demonstrate the usefulness of the integrated microarray data for studying human gene expression patterns, we have analyzed the dataset to identify potential tissue-selective genes. A new method has been proposed for genome-wide identification of tissue-selective gene targets using both microarray intensity values and detection calls. The candidate genes for brain, liver and testis-selective expression have been examined, and the results suggest that our approach can select some interesting gene targets for further experimental studies.

Conclusion

A computational approach has been developed in this study for combining microarray expression profiles from heterogeneous sources. The integrated microarray data can be used to investigate tissue-selective expression patterns of human genes.

     

Graph-based consensus clustering for class discovery from gene expression data

MOTIVATION: Consensus clustering, also known as cluster ensemble, is one of the important techniques for microarray data analysis, and is particularly useful for class discovery from microarray data. Compared with traditional clustering algorithms, consensus clustering approaches have the ability to integrate multiple partitions from different cluster solutions to improve the robustness, stability, scalability and parallelization of the clustering algorithms. By consensus clustering, one can discover the underlying classes of the samples in gene expression data. RESULTS: In addition to exploring a graph-based consensus clustering (GCC) algorithm to estimate the underlying classes of the samples in microarray data, we also design a new validation index to determine the number of classes in microarray data. To our knowledge, this is the first time in which GCC is applied to class discovery for microarray data. Given a pre specified maximum number of classes (denoted as K(max) in this article), our algorithm can discover the true number of classes for the samples in microarray data according to a new cluster validation index called the Modified Rand Index. Experiments on gene expression data indicate that our new algorithm can (i) outperform most of the existing algorithms, (ii) identify the number of classes correctly in real cancer datasets, and (iii) discover the classes of samples with biological meaning. AVAILABILITY: Matlab source code for the GCC algorithm is available upon request from Zhiwen Yu.     

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.     

A hidden Markov model-based approach for identifying timing differences in gene expression under different experimental factors

MOTIVATION: Time series experiments of cDNA microarrays have been commonly used in various biological studies and conducted under a lot of experimental factors. A popular approach of time series microarray analysis is to compare one gene with another in their expression profiles, and clustering expression sequences is a typical example. On the other hand, a practically important issue in gene expression is to identify the general timing difference that is caused by experimental factors. This type of difference can be extracted by comparing a set of time series expression profiles under a factor with those under another factor, and so it would be difficult to tackle this issue by using only a current approach for time series microarray analysis. RESULTS: We have developed a systematic method to capture the timing difference in gene expression under different experimental factors, based on hidden Markov models. Our model outputs a real-valued vector at each state and has a unique state transition diagram. The parameters of our model are trained from a given set of pairwise (generally multiplewise) expression sequences. We evaluated our model using synthetic as well as real microarray datasets. The results of our experiment indicate that our method worked favourably to identify the timing ordering under different experimental factors, such as that gene expression under heat shock tended to start earlier than that under oxidative stress. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Adding confidence to gene expression clustering

It has been well established that gene expression data contain large amounts of random variation that affects both the analysis and the results of microarray experiments. Typically, microarray data are either tested for differential expression between conditions or grouped on the basis of profiles that are assessed temporally or across genetic or environmental conditions. While testing differential expression relies on levels of certainty to evaluate the relative worth of various analyses, cluster analysis is exploratory in nature and has not had the benefit of any judgment of statistical inference. By using a novel dissimilarity function to ascertain gene expression clusters and conditional randomization of the data space to illuminate distinctions between statistically significant clusters of gene expression patterns, we aim to provide a level of confidence to inferred clusters of gene expression data. We apply both permutation and convex hull approaches for randomization of the data space and show that both methods can provide an effective assessment of gene expression profiles whose coregulation is statistically different from that expected by random chance alone.     

The clustering of regression models method with applications in gene expression data

Identification of differentially expressed genes and clustering of genes are two important and complementary objectives addressed with gene expression data. For the differential expression question, many "per-gene" analytic methods have been proposed. These methods can generally be characterized as using a regression function to independently model the observations for each gene; various adjustments for multiplicity are then used to interpret the statistical significance of these per-gene regression models over the collection of genes analyzed. Motivated by this common structure of per-gene models, we proposed a new model-based clustering method--the clustering of regression models method, which groups genes that share a similar relationship to the covariate(s). This method provides a unified approach for a family of clustering procedures and can be applied for data collected with various experimental designs. In addition, when combined with per-gene methods for assessing differential expression that employ the same regression modeling structure, an integrated framework for the analysis of microarray data is obtained. The proposed methodology was applied to two microarray data sets, one from a breast cancer study and the other from a yeast cell cycle study.