Evaluation of statistical correlation and validation methods for construction of gene co-expression networks

High-throughput technologies such as microarrays have led to the rapid accumulation of large scale genomic data providing opportunities to systematically infer gene function and co-expression networks. Typical steps of co-expression network analysis using microarray data consist of estimation of pair-wise gene co-expression using some similarity measure, construction of co-expression networks, identification of clusters of co-expressed genes and post-cluster analyses such as cluster validation. This dissertation is primarily concerned with development and evaluation of approaches for the first and the last steps – estimation of gene co-expression matrices and validation of network clusters. Since clustering methods are not a focus, only a paraclique clustering algorithm will be used in this evaluation. First, a novel Bayesian approach is presented for combining the Pearson correlation with prior biological information from Gene Ontology, yielding a biologically relevant estimate of gene co-expression. The addition of biological information by the Bayesian approach reduced noise in the paraclique gene clusters as indicated by high silhouette and increased homogeneity of clusters in terms of molecular function. Standard similarity measures including correlation coefficients from Pearson, Spearman, Kendall’s Tau, Shrinkage, Partial, and Mutual information, and Euclidean and Manhattan distance measures were evaluated. Based on quality metrics such as cluster homogeneity and stability with respect to ontological categories, clusters resulting from partial correlation and mutual information were more biologically relevant than those from any other correlation measures. Second, statistical quality of clusters was evaluated using approaches based on permutation tests and Mantel correlation to identify significant and informative clusters that capture most of the covariance in the dataset. Third, the utility of statistical contrasts was studied for classification of temporal patterns of gene expression. Specifically, polynomial and Helmert contrast analyses were shown to provide a means of labeling the co-expressed gene sets because they showed similar temporal profiles

Supervised group Lasso with applications to microarray data analysis

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

Clustering Gene Expression Data Based on Predicted Differential Effects of GV Interaction

Microarray has become a popular biotechnology in biological and medical research. However, systematic and stochastic variabilities in microarray data are expected and unavoidable, resulting in the problem that the raw measurements have inherent “noise” within microarray experiments. Currently, logarithmic ratios are usually analyzed by various clustering methods directly, which may introduce bias interpretation in identifying groups of genes or samples. In this paper, a statistical method based on mixed model approaches was proposed for microarray data cluster analysis. The underlying rationale of this method is to partition the observed total gene expression level into various variations caused by different factors using an ANOVA model, and to predict the differential effects of GV (gene by variety) interaction using the adjusted unbiased prediction (AUP) method. The predicted GV interaction effects can then be used as the inputs of cluster analysis. We illustrated the application of our method with a gene expression dataset and elucidated the utility of our approach using an external validation

Validation of Gene Expression Profiles in Genomic Data through Complementary Use of Cluster Analysis and PCA-Related Biplots

High-throughput genomic assays are used in molecular biology to explore patterns of joint expression of thousands of genes. These methodologies had relevant developments in the last decade, and concurrently there was a need for appropriate methods for analyzing the massive data generated. Identifying sets of genes and samples characterized by similar values of expression and validating these results are two critical issues related to these investigations because of their clinical implication. From a statistical perspective, unsupervised class discovery methods like Cluster Analysis are generally adopted. However, the use of Cluster Analysis mainly relies on the use of hierarchical techniques without considering possible use of other methods. This is partially due to software availability and to easiness of representation of results through a heatmap, which allows to simultaneously visualize clusterization of genes and samples on the same graphical device. One drawback of this strategy is that clusters' stability is often neglected, thus leading to over-interpretation of results. Moreover, validation of results using external datasets is still subject of discussion, since it is well known that batch effects may condition gene expression results even after normalization. In this paper we compared several clustering algorithms (hierarchical, k-means, model-based, Affinity Propagation) and stability indices to discover common patterns of expression and to assess clustering reliability, and propose a rank-based passive projection of Principal Components for validation purposes. Results from a study involving 23 tumor cell lines and 76 genes related to a specific biological pathway and derived from a publicly available dataset, are presented

Partial mixture model for tight clustering of gene expression time-course

Background: Tight clustering arose recently from a desire to obtain tighter and potentially more informative clusters in gene expression studies. Scattered genes with relatively loose correlations should be excluded from the clusters. However, in the literature there is little work dedicated to this area of research. On the other hand, there has been extensive use of maximum likelihood techniques for model parameter estimation. By contrast, the minimum distance estimator has been largely ignored. Results: In this paper we show the inherent robustness of the minimum distance estimator that makes it a powerful tool for parameter estimation in model-based time-course clustering. To apply minimum distance estimation, a partial mixture model that can naturally incorporate replicate information and allow scattered genes is formulated. We provide experimental results of simulated data fitting, where the minimum distance estimator demonstrates superior performance to the maximum likelihood estimator. Both biological and statistical validations are conducted on a simulated dataset and two real gene expression datasets. Our proposed partial regression clustering algorithm scores top in Gene Ontology driven evaluation, in comparison with four other popular clustering algorithms. Conclusion: For the first time partial mixture model is successfully extended to time-course data analysis. The robustness of our partial regression clustering algorithm proves the suitability of the ombination of both partial mixture model and minimum distance estimator in this field. We show that tight clustering not only is capable to generate more profound understanding of the dataset under study well in accordance to established biological knowledge, but also presents interesting new hypotheses during interpretation of clustering results. In particular, we provide biological evidences that scattered genes can be relevant and are interesting subjects for study, in contrast to prevailing opinion

Consensus clustering and functional interpretation of gene-expression data

Microarray analysis using clustering algorithms can suffer from lack of inter-method consistency in assigning related gene-expression profiles to clusters. Obtaining a consensus set of clusters from a number of clustering methods should improve confidence in gene-expression analysis. Here we introduce consensus clustering, which provides such an advantage. When coupled with a statistically based gene functional analysis, our method allowed the identification of novel genes regulated by NFκB and the unfolded protein response in certain B-cell lymphomas

Techniques for clustering gene expression data

Many clustering techniques have been proposed for the analysis of gene expression data obtained from microarray experiments. However, choice of suitable method(s) for a given experimental dataset is not straightforward. Common approaches do not translate well and fail to take account of the data profile. This review paper surveys state of the art applications which recognises these limitations and implements procedures to overcome them. It provides a framework for the evaluation of clustering in gene expression analyses. The nature of microarray data is discussed briefly. Selected examples are presented for the clustering methods considered

clValid: An R Package for Cluster Validation

The R package clValid contains functions for validating the results of a clustering analysis. There are three main types of cluster validation measures available, "internal", "stability", and "biological". The user can choose from nine clustering algorithms in existing R packages, including hierarchical, K-means, self-organizing maps (SOM), and model-based clustering. In addition, we provide a function to perform the self-organizing tree algorithm (SOTA) method of clustering. Any combination of validation measures and clustering methods can be requested in a single function call. This allows the user to simultaneously evaluate several clustering algorithms while varying the number of clusters, to help determine the most appropriate method and number of clusters for the dataset of interest. Additionally, the package can automatically make use of the biological information contained in the Gene Ontology (GO) database to calculate the biological validation measures, via the annotation packages available in Bioconductor. The function returns an object of S4 class "clValid", which has summary, plot, print, and additional methods which allow the user to display the optimal validation scores and extract clustering results.

Towards knowledge-based gene expression data mining

The field of gene expression data analysis has grown in the past few years from being purely data-centric to integrative, aiming at complementing microarray analysis with data and knowledge from diverse available sources. In this review, we report on the plethora of gene expression data mining techniques and focus on their evolution toward knowledge-based data analysis approaches. In particular, we discuss recent developments in gene expression-based analysis methods used in association and classification studies, phenotyping and reverse engineering of gene networks