Improve survival prediction using principal components of gene expression data

The purpose of many microarray studies is to find the association between gene expression and sample characteristics such as treatment type or sample phenotype. There has been a surge of efforts developing different methods for delineating the association. Aside from the high dimensionality of microarray data, one well recognized challenge is the fact that genes could be complicatedly inter-related, thus making many statistical methods inappropriate to use directly on the expression data. Multivariate methods such as principal component analysis （PCA） and clustering are often used as a part of the effort to capture the gene correlation, and the derived components or clusters are used to describe the association between gene expression and sample phenotype. We propose a method for patient population dichotomization using maximally selected test statistics in combination with the PCA method, which shows favorable results. The proposed method is compared with a currently well-recognized method.     

Insights from the clustering of microarray data associated with the heart disease

Heart failure (HF) is the major of cause of mortality and morbidity in the developed world. Gene expression profiles of animal model of heart failure have been used in number of studies to understand human cardiac disease. In this study, statistical methods of analysing microarray data on cardiac tissues from dogs with pacing induced HF were used to identify differentially expressed genes between normal and two abnormal tissues. The unsupervised techniques principal component analysis (PCA) and cluster analysis were explored to distinguish between three different groups of 12 arrays and to separate the genes which are up regulated in different conditions among 23912 genes in heart failure canines'' microarray data. It was found that out of 23912 genes, 1802 genes were differentially expressed in the three groups at 5% level of significance and 496 genes were differentially expressed at 1% level of significance using one way analysis of variance (ANOVA). The genes clustered using PCA and clustering analysis were explored in the paper to understand HF and a small number of differentially expressed genes related to HF were identified.     

Rejoinder to Use of Principal Component Analysis and the GE -Biplot for the Graphical Exploration of Gene Expression Data

Summary This note is in response to Wouters et al. (2003, Biometrics 59, 1131–1139) who compared three methods for exploring gene expression data. Contrary to their summary that principal component analysis is not very informative, we show that it is possible to determine principal component analyses that are useful for exploratory analysis of microarray data. We also present another biplot representation, the GE‐biplot (Gene Expression biplot), that is a useful method for exploring gene expression data with the major advantage of being able to aid interpretation of both the samples and the genes relative to each other.     

Discriminant analysis to evaluate clustering of gene expression data

In this work we present a procedure that combines classical statistical methods to assess the confidence of gene clusters identified by hierarchical clustering of expression data. This approach was applied to a publicly released Drosophila metamorphosis data set [White et al., Science 286 (1999) 2179-2184]. We have been able to produce reliable classifications of gene groups and genes within the groups by applying unsupervised (cluster analysis), dimension reduction (principal component analysis) and supervised methods (linear discriminant analysis) in a sequential form. This procedure provides a means to select relevant information from microarray data, reducing the number of genes and clusters that require further biological analysis.     

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.     

Permutation-validated principal components analysis of microarray data

Background  

In microarray data analysis, the comparison of gene-expression profiles with respect to different conditions and the selection of biologically interesting genes are crucial tasks. Multivariate statistical methods have been applied to analyze these large datasets. Less work has been published concerning the assessment of the reliability of gene-selection procedures. Here we describe a method to assess reliability in multivariate microarray data analysis using permutation-validated principal components analysis (PCA). The approach is designed for microarray data with a group structure.     

Characteristic gene selection via weighting principal components by singular values

Conventional gene selection methods based on principal component analysis (PCA) use only the first principal component (PC) of PCA or sparse PCA to select characteristic genes. These methods indeed assume that the first PC plays a dominant role in gene selection. However, in a number of cases this assumption is not satisfied, so the conventional PCA-based methods usually provide poor selection results. In order to improve the performance of the PCA-based gene selection method, we put forward the gene selection method via weighting PCs by singular values (WPCS). Because different PCs have different importance, the singular values are exploited as the weights to represent the influence on gene selection of different PCs. The ROC curves and AUC statistics on artificial data show that our method outperforms the state-of-the-art methods. Moreover, experimental results on real gene expression data sets show that our method can extract more characteristic genes in response to abiotic stresses than conventional gene selection methods.     

A DSRPCL-SVM approach to informative gene analysis

Microarray data based tumor diagnosis is a very interesting topic in bioinformatics. One of the key problems is the discovery and analysis of informative genes of a tumor. Although there are many elaborate approaches to this problem, it is still difficult to select a reasonable set of informative genes for tumor diagnosis only with microarray data. In this paper, we classify the genes expressed through microarray data into a number of clusters via the distance sensitive rival penalized competitive learning （DSRPCL） algorithm and then detect the informative gene cluster or set with the help of support vector machine （SVM）. Moreover, the critical or powerful informative genes can be found through further classifications and detections on the obtained informative gene clusters. It is well demonstrated by experiments on the colon, leukemia, and breast cancer datasets that our proposed DSRPCL-SVM approach leads to a reasonable selection of informative genes for tumor diagnosis.     

Applications of support vector machines to cancer classification with microarray data

Microarray gene expression data usually have a large number of dimensions, e.g., over ten thousand genes, and a small number of samples, e.g., a few tens of patients. In this paper, we use the support vector machine (SVM) for cancer classification with microarray data. Dimensionality reduction methods, such as principal components analysis (PCA), class-separability measure, Fisher ratio, and t-test, are used for gene selection. A voting scheme is then employed to do multi-group classification by k(k - 1) binary SVMs. We are able to obtain the same classification accuracy but with much fewer features compared to other published results.     

Tumor classification by partial least squares using microarray gene expression data

MOTIVATION: One important application of gene expression microarray data is classification of samples into categories, such as the type of tumor. The use of microarrays allows simultaneous monitoring of thousands of genes expressions per sample. This ability to measure gene expression en masse has resulted in data with the number of variables p(genes) far exceeding the number of samples N. Standard statistical methodologies in classification and prediction do not work well or even at all when N < p. Modification of existing statistical methodologies or development of new methodologies is needed for the analysis of microarray data. RESULTS: We propose a novel analysis procedure for classifying (predicting) human tumor samples based on microarray gene expressions. This procedure involves dimension reduction using Partial Least Squares (PLS) and classification using Logistic Discrimination (LD) and Quadratic Discriminant Analysis (QDA). We compare PLS to the well known dimension reduction method of Principal Components Analysis (PCA). Under many circumstances PLS proves superior; we illustrate a condition when PCA particularly fails to predict well relative to PLS. The proposed methods were applied to five different microarray data sets involving various human tumor samples: (1) normal versus ovarian tumor; (2) Acute Myeloid Leukemia (AML) versus Acute Lymphoblastic Leukemia (ALL); (3) Diffuse Large B-cell Lymphoma (DLBCLL) versus B-cell Chronic Lymphocytic Leukemia (BCLL); (4) normal versus colon tumor; and (5) Non-Small-Cell-Lung-Carcinoma (NSCLC) versus renal samples. Stability of classification results and methods were further assessed by re-randomization studies.     

A simple and robust algorithm for microarray data clustering based on gene population-variance ratio metric

With the advent of the microarray technology, the field of life science has been greatly revolutionized, since this technique allows the simultaneous monitoring of the expression levels of thousands of genes in a particular organism. However, the statistical analysis of expression data has its own challenges, primarily because of the huge amount of data that is to be dealt with, and also because of the presence of noise, which is almost an inherent characteristic of microarray data. Clustering is one tool used to mine meaningful patterns from microarray data. In this paper, we present a novel method of clustering yeast microarray data, which is robust and yet simple to implement. It identifies the best clusters from a given dataset on the basis of the population of the clusters as well as the variance of the feature values of the members from the cluster-center. It has been found to yield satisfactory results even in the presence of noisy data.     

Principal component analysis for clustering gene expression data

MOTIVATION: There is a great need to develop analytical methodology to analyze and to exploit the information contained in gene expression data. Because of the large number of genes and the complexity of biological networks, clustering is a useful exploratory technique for analysis of gene expression data. Other classical techniques, such as principal component analysis (PCA), have also been applied to analyze gene expression data. Using different data analysis techniques and different clustering algorithms to analyze the same data set can lead to very different conclusions. Our goal is to study the effectiveness of principal components (PCs) in capturing cluster structure. Specifically, using both real and synthetic gene expression data sets, we compared the quality of clusters obtained from the original data to the quality of clusters obtained after projecting onto subsets of the principal component axes. RESULTS: Our empirical study showed that clustering with the PCs instead of the original variables does not necessarily improve, and often degrades, cluster quality. In particular, the first few PCs (which contain most of the variation in the data) do not necessarily capture most of the cluster structure. We also showed that clustering with PCs has different impact on different algorithms and different similarity metrics. Overall, we would not recommend PCA before clustering except in special circumstances.     

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.     

Analysis of the real EADGENE data set: Multivariate approaches and post analysis (Open Access publication)

The aim of this paper was to describe, and when possible compare, the multivariate methods used by the participants in the EADGENE WP1.4 workshop. The first approach was for class discovery and class prediction using evidence from the data at hand. Several teams used hierarchical clustering (HC) or principal component analysis (PCA) to identify groups of differentially expressed genes with a similar expression pattern over time points and infective agent (E. coli or S. aureus). The main result from these analyses was that HC and PCA were able to separate tissue samples taken at 24 h following E. coli infection from the other samples. The second approach identified groups of differentially co-expressed genes, by identifying clusters of genes highly correlated when animals were infected with E. coli but not correlated more than expected by chance when the infective pathogen was S. aureus. The third approach looked at differential expression of predefined gene sets. Gene sets were defined based on information retrieved from biological databases such as Gene Ontology. Based on these annotation sources the teams used either the GlobalTest or the Fisher exact test to identify differentially expressed gene sets. The main result from these analyses was that gene sets involved in immune defence responses were differentially expressed.     

CIT: identification of differentially expressed clusters of genes from microarray data

Cluster Identification Tool (CIT) is a microarray analysis program that identifies differentially expressed genes. Following division of experimental samples based on a parameter of interest, CIT uses a statistical discrimination metric and permutation analysis to identify clusters of genes or individual genes that best differentiate between the experimental groups. CIT integrates with the freely available CLUSTER and TREEVIEW programs to form a more complete microarray analysis package.     

Robust prostate cancer marker genes emerge from direct integration of inter-study microarray data

MOTIVATION: DNA microarray data analysis has been used previously to identify marker genes which discriminate cancer from normal samples. However, due to the limited sample size of each study, there are few common markers among different studies of the same cancer. With the rapid accumulation of microarray data, it is of great interest to integrate inter-study microarray data to increase sample size, which could lead to the discovery of more reliable markers. RESULTS: We present a novel, simple method of integrating different microarray datasets to identify marker genes and apply the method to prostate cancer datasets. In this study, by applying a new statistical method, referred to as the top-scoring pair (TSP) classifier, we have identified a pair of robust marker genes (HPN and STAT6) by integrating microarray datasets from three different prostate cancer studies. Cross-platform validation shows that the TSP classifier built from the marker gene pair, which simply compares relative expression values, achieves high accuracy, sensitivity and specificity on independent datasets generated using various array platforms. Our findings suggest a new model for the discovery of marker genes from accumulated microarray data and demonstrate how the great wealth of microarray data can be exploited to increase the power of statistical analysis. CONTACT: leixu@jhu.edu.     

Assessment of Heavy Metal Contamination in the Sediments of the Shuangtaizi Estuary Using Multivariate Statistical Techniques

In order to assess heavy metal pollution of sediment samples collected from Shuangtaizi estuary, contamination factor (CF) and multivariate statistical analyses, including principal component analysis (PCA), cluster analysis (CA) and correlation analysis, are carried out in this paper. CF confirms that Pb, Cu and Hg concentrations are very low and all fall within the range of background, while Zn and Cd demonstrate moderate contamination (in A10, A13, A15, A16 and A17 sites) and very high contamination (in A10, A13, A15 and A17 sites), respectively. The PCA indicates that four significant principal components (PCs) are extracted, explaining 88.959% of total variance, which suggests that Pb, Cu and Zn are mainly associated with organic carbon (OC). The result from CA is consistent with that obtained from PCA, classifying that the heavy metals in two clusters derive from different sources. Correlation analysis supports the conclusions from PCA and CA, elucidating the relationships between heavy metals and particle sizes of the sediments.     

How many differentially expressed genes: A perspective from the comparison of genotypic and phenotypic distances

Identifying differentially expressed genes is critical in microarray data analysis. Many methods have been developed by combining p-value, fold-change, and various statistical models to determine these genes. When using these methods, it is necessary to set up various pre-determined cutoff values. However, many of these cutoff values are somewhat arbitrary and may not have clear connections to biology. In this study, a genetic distance method based on gene expression level was developed to analyze eight sets of microarray data extracted from the GEO database. Since the genes used in distance calculation have been ranked by fold-change, the genetic distance becomes more stable when adding more genes in the calculation, indicating there is an optimal set of genes which are sufficient to characterize the stable difference between samples. This set of genes is differentially expressed genes representing both the genotypic and phenotypic differences between samples.