Microarray learning with ABC

Standard clustering algorithms when applied to DNA microarray data often tend to produce erroneous clusters. A major contributor to this divergence is the feature characteristic of microarray data sets that the number of predictors (genes) in such data far exceeds the number of samples by many orders of magnitude, with only a small percentage of predictors being truly informative with regards to the clustering while the rest merely add noise. An additional complication is that the predictors exhibit an unknown complex correlational configuration embedded in a small subspace of the entire predictor space. Under these conditions, standard clustering algorithms fail to find the true clusters even when applied in tandem with some sort of gene filtering or dimension reduction to reduce the number of predictors. We propose, as an alternative, a novel method for unsupervised classification of DNA microarray data. The method, which is based on the idea of aggregating results obtained from an ensemble of randomly resampled data (where both samples and genes are resampled), introduces a way of tilting the procedure so that the ensemble includes minimal representation from less important areas of the gene predictor space. The method produces a measure of dissimilarity between each pair of samples that can be used in conjunction with (a) a method like Ward's procedure to generate a cluster analysis and (b) multidimensional scaling to generate useful visualizations of the data. We call the dissimilarity measures ABC dissimilarities since they are obtained by aggregating bundles of clusters. An extensive comparison of several clustering methods using actual DNA microarray data convincingly demonstrates that classification using ABC dissimilarities offers significantly superior performance.     

Evaluation and optimization of clustering in gene expression data analysis

MOTIVATION: A measurement of cluster quality is needed to choose potential clusters of genes that contain biologically relevant patterns of gene expression. This is strongly desirable when a large number of gene expression profiles have to be analyzed and proper clusters of genes need to be identified for further analysis, such as the search for meaningful patterns, identification of gene functions or gene response analysis. RESULTS: We propose a new cluster quality method, called stability, by which unsupervised learning of gene expression data can be performed efficiently. The method takes into account a cluster's stability on partition. We evaluate this method and demonstrate its performance using four independent, real gene expression and three simulated datasets. We demonstrate that our method outperforms other techniques listed in the literature. The method has applications in evaluating clustering validity as well as identifying stable clusters. AVAILABILITY: Please contact the first author.     

Analysis of breast cancer progression using principal component analysis and clustering

We develop a new technique to analyse microarray data which uses a combination of principal components analysis and consensus ensemble k-clustering to find robust clusters and gene markers in the data. We apply our method to a public microarray breast cancer dataset which has expression levels of genes in normal samples as well as in three pathological stages of disease; namely, atypical ductal hyperplasia or ADH, ductal carcinoma in situ or DCIS and invasive ductal carcinoma or IDC. Our method averages over clustering techniques and data perturbation to find stable, robust clusters and gene markers. We identify the clusters and their pathways with distinct subtypes of breast cancer (Luminal,Basal and Her2+). We confirm that the cancer phenotype develops early (in early hyperplasia or ADH stage) and find from our analysis that each subtype progresses from ADH to DCIS to IDC along its own specific pathway, as if each was a distinct disease.     

The computational analysis of scientific literature to define and recognize gene expression clusters

A limitation of many gene expression analytic approaches is that they do not incorporate comprehensive background knowledge about the genes into the analysis. We present a computational method that leverages the peer-reviewed literature in the automatic analysis of gene expression data sets. Including the literature in the analysis of gene expression data offers an opportunity to incorporate functional information about the genes when defining expression clusters. We have created a method that associates gene expression profiles with known biological functions. Our method has two steps. First, we apply hierarchical clustering to the given gene expression data set. Secondly, we use text from abstracts about genes to (i) resolve hierarchical cluster boundaries to optimize the functional coherence of the clusters and (ii) recognize those clusters that are most functionally coherent. In the case where a gene has not been investigated and therefore lacks primary literature, articles about well-studied homologous genes are added as references. We apply our method to two large gene expression data sets with different properties. The first contains measurements for a subset of well-studied Saccharomyces cerevisiae genes with multiple literature references, and the second contains newly discovered genes in Drosophila melanogaster; many have no literature references at all. In both cases, we are able to rapidly define and identify the biologically relevant gene expression profiles without manual intervention. In both cases, we identified novel clusters that were not noted by the original investigators.     

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.     

Dimension reduction strategies for analyzing global gene expression data with a response

The analysis of global gene expression data from microarrays is breaking new ground in genetics research, while confronting modelers and statisticians with many critical issues. In this paper, we consider data sets in which a categorical or continuous response is recorded, along with gene expression, on a given number of experimental samples. Data of this type are usually employed to create a prediction mechanism for the response based on gene expression, and to identify a subset of relevant genes. This defines a regression setting characterized by a dramatic under-resolution with respect to the predictors (genes), whose number exceeds by orders of magnitude the number of available observations (samples). We present a dimension reduction strategy that, under appropriate assumptions, allows us to restrict attention to a few linear combinations of the original expression profiles, and thus to overcome under-resolution. These linear combinations can then be used to build and validate a regression model with standard techniques. Moreover, they can be used to rank original predictors, and ultimately to select a subset of them through comparison with a background 'chance scenario' based on a number of independent randomizations. We apply this strategy to publicly available data on leukemia classification.     

Supervised harvesting of expression trees

Background

We propose a new method for supervised learning from gene expression data. We call it 'tree harvesting'. This technique starts with a hierarchical clustering of genes, then models the outcome variable as a sum of the average expression profiles of chosen clusters and their products. It can be applied to many different kinds of outcome measures such as censored survival times, or a response falling in two or more classes (for example, cancer classes). The method can discover genes that have strong effects on their own, and genes that interact with other genes.

Results

We illustrate the method on data from a lymphoma study, and on a dataset containing samples from eight different cancers. It identified some potentially interesting gene clusters. In simulation studies we found that the procedure may require a large number of experimental samples to successfully discover interactions.

Conclusions

Tree harvesting is a potentially useful tool for exploration of gene expression data and identification of interesting clusters of genes worthy of further investigation.     

Assessing reliability of gene clusters from gene expression data

The rapid development of microarray technologies has raised many challenging problems in experiment design and data analysis. Although many numerical algorithms have been successfully applied to analyze gene expression data, the effects of variations and uncertainties in measured gene expression levels across samples and experiments have been largely ignored in the literature. In this article, in the context of hierarchical clustering algorithms, we introduce a statistical resampling method to assess the reliability of gene clusters identified from any hierarchical clustering method. Using the clustering trees constructed from the resampled data, we can evaluate the confidence value for each node in the observed clustering tree. A majority-rule consensus tree can be obtained, showing clusters that only occur in a majority of the resampled trees. We illustrate our proposed methods with applications to two published data sets. Although the methods are discussed in the context of hierarchical clustering methods, they can be applied with other cluster-identification methods for gene expression data to assess the reliability of any gene cluster of interest. Electronic Publication     

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.     

Bivariate microarray analysis: statistical interpretation of two-channel functional genomics data

Conventional statistical methods for interpreting microarray data require large numbers of replicates in order to provide sufficient levels of sensitivity. We recently described a method for identifying differentially-expressed genes in one-channel microarray data 1. Based on the idea that the variance structure of microarray data can itself be a reliable measure of noise, this method allows statistically sound interpretation of as few as two replicates per treatment condition. Unlike the one-channel array, the two-channel platform simultaneously compares gene expression in two RNA samples. This leads to covariation of the measured signals. Hence, by accounting for covariation in the variance model, we can significantly increase the power of the statistical test. We believe that this approach has the potential to overcome limitations of existing methods. We present here a novel approach for the analysis of microarray data that involves modeling the variance structure of paired expression data in the context of a Bayesian framework. We also describe a novel statistical test that can be used to identify differentially-expressed genes. This method, bivariate microarray analysis (BMA), demonstrates dramatically improved sensitivity over existing approaches. We show that with only two array replicates, it is possible to detect gene expression changes that are at best detected with six array replicates by other methods. Further, we show that combining results from BMA with Gene Ontology annotation yields biologically significant results in a ligand-treated macrophage cell system.     

Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters

MOTIVATION: Cluster analysis of genome-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and samples. In the present paper, we focus on several important issues related to clustering algorithms that have not yet been fully studied. RESULTS: We describe a simple and robust algorithm for the clustering of temporal gene expression profiles that is based on the simulated annealing procedure. In general, this algorithm guarantees to eventually find the globally optimal distribution of genes over clusters. We introduce an iterative scheme that serves to evaluate quantitatively the optimal number of clusters for each specific data set. The scheme is based on standard approaches used in regular statistical tests. The basic idea is to organize the search of the optimal number of clusters simultaneously with the optimization of the distribution of genes over clusters. The efficiency of the proposed algorithm has been evaluated by means of a reverse engineering experiment, that is, a situation in which the correct distribution of genes over clusters is known a priori. The employment of this statistically rigorous test has shown that our algorithm places greater than 90% genes into correct clusters. Finally, the algorithm has been tested on real gene expression data (expression changes during yeast cell cycle) for which the fundamental patterns of gene expression and the assignment of genes to clusters are well understood from numerous previous studies.     

Bayesian infinite mixture model based clustering of gene expression profiles

MOTIVATION: The biologic significance of results obtained through cluster analyses of gene expression data generated in microarray experiments have been demonstrated in many studies. In this article we focus on the development of a clustering procedure based on the concept of Bayesian model-averaging and a precise statistical model of expression data. RESULTS: We developed a clustering procedure based on the Bayesian infinite mixture model and applied it to clustering gene expression profiles. Clusters of genes with similar expression patterns are identified from the posterior distribution of clusterings defined implicitly by the stochastic data-generation model. The posterior distribution of clusterings is estimated by a Gibbs sampler. We summarized the posterior distribution of clusterings by calculating posterior pairwise probabilities of co-expression and used the complete linkage principle to create clusters. This approach has several advantages over usual clustering procedures. The analysis allows for incorporation of a reasonable probabilistic model for generating data. The method does not require specifying the number of clusters and resulting optimal clustering is obtained by averaging over models with all possible numbers of clusters. Expression profiles that are not similar to any other profile are automatically detected, the method incorporates experimental replicates, and it can be extended to accommodate missing data. This approach represents a qualitative shift in the model-based cluster analysis of expression data because it allows for incorporation of uncertainties involved in the model selection in the final assessment of confidence in similarities of expression profiles. We also demonstrated the importance of incorporating the information on experimental variability into the clustering model. AVAILABILITY: The MS Windows(TM) based program implementing the Gibbs sampler and supplemental material is available at http://homepages.uc.edu/~medvedm/BioinformaticsSupplement.htm CONTACT: medvedm@email.uc.edu     

Model-based clustering and data transformations for gene expression data.

MOTIVATION: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications. RESULTS: We benchmarked the performance of model-based clustering on several synthetic and real gene expression data sets for which external evaluation criteria were available. The model-based approach has superior performance on our synthetic data sets, consistently selecting the correct model and the number of clusters. On real expression data, the model-based approach produced clusters of quality comparable to a leading heuristic clustering algorithm, but with the key advantage of suggesting the number of clusters and an appropriate model. We also explored the validity of the Gaussian mixture assumption on different transformations of real data. We also assessed the degree to which these real gene expression data sets fit multivariate Gaussian distributions both before and after subjecting them to commonly used data transformations. Suitably chosen transformations seem to result in reasonable fits. AVAILABILITY: MCLUST is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. CONTACT: kayee@cs.washington.edu. SUPPLEMENTARY INFORMATION: http://www.cs.washington.edu/homes/kayee/model.