Gene selection: a Bayesian variable selection approach

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

Missing-value estimation using linear and non-linear regression with Bayesian gene selection

MOTIVATION: Data from microarray experiments are usually in the form of large matrices of expression levels of genes under different experimental conditions. Owing to various reasons, there are frequently missing values. Estimating these missing values is important because they affect downstream analysis, such as clustering, classification and network design. Several methods of missing-value estimation are in use. The problem has two parts: (1) selection of genes for estimation and (2) design of an estimation rule. RESULTS: We propose Bayesian variable selection to obtain genes to be used for estimation, and employ both linear and nonlinear regression for the estimation rule itself. Fast implementation issues for these methods are discussed, including the use of QR decomposition for parameter estimation. The proposed methods are tested on data sets arising from hereditary breast cancer and small round blue-cell tumors. The results compare very favorably with currently used methods based on the normalized root-mean-square error. AVAILABILITY: The appendix is available from http://gspsnap.tamu.edu/gspweb/zxb/missing_zxb/ (user: gspweb; passwd: gsplab).     

LS Bound based gene selection for DNA microarray data

MOTIVATION: One problem with discriminant analysis of DNA microarray data is that each sample is represented by quite a large number of genes, and many of them are irrelevant, insignificant or redundant to the discriminant problem at hand. Methods for selecting important genes are, therefore, of much significance in microarray data analysis. In the present study, a new criterion, called LS Bound measure, is proposed to address the gene selection problem. The LS Bound measure is derived from leave-one-out procedure of LS-SVMs (least squares support vector machines), and as the upper bound for leave-one-out classification results it reflects to some extent the generalization performance of gene subsets. RESULTS: We applied this LS Bound measure for gene selection on two benchmark microarray datasets: colon cancer and leukemia. We also compared the LS Bound measure with other evaluation criteria, including the well-known Fisher's ratio and Mahalanobis class separability measure, and other published gene selection algorithms, including Weighting factor and SVM Recursive Feature Elimination. The strength of the LS Bound measure is that it provides gene subsets leading to more accurate classification results than the filter method while its computational complexity is at the level of the filter method. AVAILABILITY: A companion website can be accessed at http://www.ntu.edu.sg/home5/pg02776030/lsbound/. The website contains: (1) the source code of the gene selection algorithm; (2) the complete set of tables and figures regarding the experimental study; (3) proof of the inequality (9). CONTACT: ekzmao@ntu.edu.sg.     

Bayesian variable selection for the analysis of microarray data with censored outcomes

MOTIVATION: A common task in microarray data analysis consists of identifying genes associated with a phenotype. When the outcomes of interest are censored time-to-event data, standard approaches assess the effect of genes by fitting univariate survival models. In this paper, we propose a Bayesian variable selection approach, which allows the identification of relevant markers by jointly assessing sets of genes. We consider accelerated failure time (AFT) models with log-normal and log-t distributional assumptions. A data augmentation approach is used to impute the failure times of censored observations and mixture priors are used for the regression coefficients to identify promising subsets of variables. The proposed method provides a unified procedure for the selection of relevant genes and the prediction of survivor functions. RESULTS: We demonstrate the performance of the method on simulated examples and on several microarray datasets. For the simulation study, we consider scenarios with large number of noisy variables and different degrees of correlation between the relevant and non-relevant (noisy) variables. We are able to identify the correct covariates and obtain good prediction of the survivor functions. For the microarray applications, some of our selected genes are known to be related to the diseases under study and a few are in agreement with findings from other researchers. AVAILABILITY: The Matlab code for implementing the Bayesian variable selection method may be obtained from the corresponding author. CONTACT: mvannucci@stat.tamu.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Bayesian automatic relevance determination algorithms for classifying gene expression data

MOTIVATION: We investigate two new Bayesian classification algorithms incorporating feature selection. These algorithms are applied to the classification of gene expression data derived from cDNA microarrays. RESULTS: We demonstrate the effectiveness of the algorithms on three gene expression datasets for cancer, showing they compare well with alternative kernel-based techniques. By automatically incorporating feature selection, accurate classifiers can be constructed utilizing very few features and with minimal hand-tuning. We argue that the feature selection is meaningful and some of the highlighted genes appear to be medically important.     

Multi-class cancer classification using multinomial probit regression with Bayesian gene selection

We consider the problems of multi-class cancer classification from gene expression data. After discussing the multinomial probit regression model with Bayesian gene selection, we propose two Bayesian gene selection schemes: one employs different strongest genes for different probit regressions; the other employs the same strongest genes for all regressions. Some fast implementation issues for Bayesian gene selection are discussed, including preselection of the strongest genes and recursive computation of the estimation errors using QR decomposition. The proposed gene selection techniques are applied to analyse real breast cancer data, small round blue-cell tumours, the national cancer institute's anti-cancer drug-screen data and acute leukaemia data. Compared with existing multi-class cancer classifications, our proposed methods can find which genes are the most important genes affecting which kind of cancer. Also, the strongest genes selected using our methods are consistent with the biological significance. The recognition accuracies are very high using our proposed methods.     

Gene selection using support vector machines with non-convex penalty

MOTIVATION: With the development of DNA microarray technology, scientists can now measure the expression levels of thousands of genes simultaneously in one single experiment. One current difficulty in interpreting microarray data comes from their innate nature of 'high-dimensional low sample size'. Therefore, robust and accurate gene selection methods are required to identify differentially expressed group of genes across different samples, e.g. between cancerous and normal cells. Successful gene selection will help to classify different cancer types, lead to a better understanding of genetic signatures in cancers and improve treatment strategies. Although gene selection and cancer classification are two closely related problems, most existing approaches handle them separately by selecting genes prior to classification. We provide a unified procedure for simultaneous gene selection and cancer classification, achieving high accuracy in both aspects. RESULTS: In this paper we develop a novel type of regularization in support vector machines (SVMs) to identify important genes for cancer classification. A special nonconvex penalty, called the smoothly clipped absolute deviation penalty, is imposed on the hinge loss function in the SVM. By systematically thresholding small estimates to zeros, the new procedure eliminates redundant genes automatically and yields a compact and accurate classifier. A successive quadratic algorithm is proposed to convert the non-differentiable and non-convex optimization problem into easily solved linear equation systems. The method is applied to two real datasets and has produced very promising results. AVAILABILITY: MATLAB codes are available upon request from the authors.     

Selecting a minimal number of relevant genes from microarray data to design accurate tissue classifiers

It is essential to select a minimal number of relevant genes from microarray data while maximizing classification accuracy for the development of inexpensive diagnostic tests. However, it is intractable to simultaneously optimize gene selection and classification accuracy that is a large parameter optimization problem. We propose an efficient evolutionary approach to gene selection from microarray data which can be combined with the optimal design of various multiclass classifiers. The proposed method (named GeneSelect) consists of three parts which are fully cooperated: an efficient encoding scheme of candidate solutions, a generalized fitness function, and an intelligent genetic algorithm (IGA). An existing hybrid approach based on genetic algorithm and maximum likelihood classification (GA/MLHD) is proposed to select a small number of relevant genes for accurate classification of samples. To evaluate the performance of GeneSelect, the gene selection is combined with the same maximum likelihood classification (named IGA/MLHD) for convenient comparisons. The performance of IGA/MLHD is applied to 11 cancer-related human gene expression datasets. The simulation results show that IGA/MLHD is superior to GA/MLHD in terms of the number of selected genes, classification accuracy, and robustness of selected genes and accuracy.     

Between-group analysis of microarray data

MOTIVATION: Most supervised classification methods are limited by the requirement for more cases than variables. In microarray data the number of variables (genes) far exceeds the number of cases (arrays), and thus filtering and pre-selection of genes is required. We describe the application of Between Group Analysis (BGA) to the analysis of microarray data. A feature of BGA is that it can be used when the number of variables (genes) exceeds the number of cases (arrays). BGA is based on carrying out an ordination of groups of samples, using a standard method such as Correspondence Analysis (COA), rather than an ordination of the individual microarray samples. As such, it can be viewed as a method of carrying out COA with grouped data. RESULTS: We illustrate the power of the method using two cancer data sets. In both cases, we can quickly and accurately classify test samples from any number of specified a priori groups and identify the genes which characterize these groups. We obtained very high rates of correct classification, as determined by jack-knife or validation experiments with training and test sets. The results are comparable to those from other methods in terms of accuracy but the power and flexibility of BGA make it an especially attractive method for the analysis of microarray cancer data.     

Regional insertional mutagenesis of specific genes on the CIC5F11/CIC2B9 locus of Arabidopsis thaliana chromosome 5 using the Ac/Ds transposon in combination with the cDNA scanning method.

We have recently developed a novel cDNA selection method (the cDNA scanning method) to select cDNAs for expressed genes in specific regions of the genome [Hayashida et al. (1995) Gene 165: 155, Seki et al. (1997) Plant J. 12: 481]. The gene Ds is known to transpose mainly in its neighborhood. By combining the cDNA scanning method with this trait of Ds, we started functional analysis of region-specific expressed genes on the Arabidopsis thaliana genome. DNA fragments of yeast artificial chromosome (YAC) clones CIC5F11 and CIC2B9 on A. thaliana chromosome 5 were used for the selection of region-specific cDNAs. In total, 50 and 68 cDNA clones were selected from CIC5F11 and CIC2B9, respectively. In parallel, we transposed Ds from a donor T-DNA line, which was mapped on the CIC5F11/CIC2B9 locus of chromosome 5, and obtained Ds-transposed lines. To isolate Ds insertion mutants in the 10 specific genes identified by the cDNA scanning method, we carried out PCR-based screening of 100 Ds-transposed lines and found that 2 lines contain Ds mutations in the genes isolated. We also isolated Ds-flanking genomic DNAs by thermal asymmetric interlaced PCR (TAIL-PCR) in 153 Ds transposon-tagged lines. Southern blot analysis showed that 14% of the lines contained the transposed Ds in the CIC5F11/2B9 region. This suggests that this Ac/Ds transposon system is effective for region-specific insertional mutagenesis.     

Sorting points into neighborhoods (SPIN): data analysis and visualization by ordering distance matrices

SUMMARY: We introduce a novel unsupervised approach for the organization and visualization of multidimensional data. At the heart of the method is a presentation of the full pairwise distance matrix of the data points, viewed in pseudocolor. The ordering of points is iteratively permuted in search of a linear ordering, which can be used to study embedded shapes. Several examples indicate how the shapes of certain structures in the data (elongated, circular and compact) manifest themselves visually in our permuted distance matrix. It is important to identify the elongated objects since they are often associated with a set of hidden variables, underlying continuous variation in the data. The problem of determining an optimal linear ordering is shown to be NP-Complete, and therefore an iterative search algorithm with O(n3) step-complexity is suggested. By using sorting points into neighborhoods, i.e. SPIN to analyze colon cancer expression data we were able to address the serious problem of sample heterogeneity, which hinders identification of metastasis related genes in our data. Our methodology brings to light the continuous variation of heterogeneity--starting with homogeneous tumor samples and gradually increasing the amount of another tissue. Ordering the samples according to their degree of contamination by unrelated tissue allows the separation of genes associated with irrelevant contamination from those related to cancer progression. AVAILABILITY: Software package will be available for academic users upon request.     

Outcome signature genes in breast cancer: is there a unique set?

MOTIVATION: Predicting the metastatic potential of primary malignant tissues has direct bearing on the choice of therapy. Several microarray studies yielded gene sets whose expression profiles successfully predicted survival. Nevertheless, the overlap between these gene sets is almost zero. Such small overlaps were observed also in other complex diseases, and the variables that could account for the differences had evoked a wide interest. One of the main open questions in this context is whether the disparity can be attributed only to trivial reasons such as different technologies, different patients and different types of analyses. RESULTS: To answer this question, we concentrated on a single breast cancer dataset, and analyzed it by a single method, the one which was used by van't Veer et al. to produce a set of outcome-predictive genes. We showed that, in fact, the resulting set of genes is not unique; it is strongly influenced by the subset of patients used for gene selection. Many equally predictive lists could have been produced from the same analysis. Three main properties of the data explain this sensitivity: (1) many genes are correlated with survival; (2) the differences between these correlations are small; (3) the correlations fluctuate strongly when measured over different subsets of patients. A possible biological explanation for these properties is discussed. CONTACT: eytan.domany@weizmann.ac.il SUPPLEMENTARY INFORMATION: http://www.weizmann.ac.il/physics/complex/compphys/downloads/liate/     

Genetic algorithm optimization for pre-processing and variable selection of spectroscopic data

MOTIVATION: The major difficulties relating to mathematical modelling of spectroscopic data are inconsistencies in spectral reproducibility and the black box nature of the modelling techniques. For the analysis of biological samples the first problem is due to biological, experimental and machine variability which can lead to sample size differences and unavoidable baseline shifts. Consequently, there is often a requirement for mathematical correction(s) to be made to the raw data if the best possible model is to be formed. The second problem prevents interpretation of the results since the variables that most contribute to the analysis are not easily revealed; as a result, the opportunity to obtain new knowledge from such data is lost. METHODS: We used genetic algorithms (GAs) to select spectral pre-processing steps for Fourier transform infrared (FT-IR) spectroscopic data. We demonstrate a novel approach for the selection of important discriminatory variables by GA from FT-IR spectra for multi-class identification by discriminant function analysis (DFA). RESULTS: The GA selects sensible pre-processing steps from a total of approximately 10(10) possible mathematical transformations. Application of these algorithms results in a 16% reduction in the model error when compared against the raw data model. GA-DFA recovers six variables from the full set of 882 spectral variables against which a satisfactory DFA model can be formed; thus inferences can be made as to the biochemical differences that are reflected by these spectral bands.     

Analysis of recursive gene selection approaches from microarray data

MOTIVATION: Finding a small subset of most predictive genes from microarray for disease prediction is a challenging problem. Support vector machines (SVMs) have been found to be successful with a recursive procedure in selecting important genes for cancer prediction. However, it is not well understood how much of the success depends on the choice of the specific classifier and how much on the recursive procedure. We answer this question by examining multiple classifers [SVM, ridge regression (RR) and Rocchio] with feature selection in recursive and non-recursive settings on three DNA microarray datasets (ALL-AML Leukemia data, Breast Cancer data and GCM data). RESULTS: We found recursive RR most effective. On the AML-ALL dataset, it achieved zero error rate on the test set using only three genes (selected from over 7000), which is more encouraging than the best published result (zero error rate using 8 genes by recursive SVM). On the Breast Cancer dataset and the two largest categories of the GCM dataset, the results achieved by recursive RR are also very encouraging. A further analysis of the experimental results shows that different classifiers penalize redundant features to different extent and this property plays an important role in the recursive feature selection process. RR classifier tends to penalize redundant features to a much larger extent than the SVM does. This may be the reason why recursive RR has a better performance in selecting genes.     

MSVM-RFE: extensions of SVM-RFE for multiclass gene selection on DNA microarray data

MOTIVATION: Given the thousands of genes and the small number of samples, gene selection has emerged as an important research problem in microarray data analysis. Support Vector Machine-Recursive Feature Elimination (SVM-RFE) is one of a group of recently described algorithms which represent the stat-of-the-art for gene selection. Just like SVM itself, SVM-RFE was originally designed to solve binary gene selection problems. Several groups have extended SVM-RFE to solve multiclass problems using one-versus-all techniques. However, the genes selected from one binary gene selection problem may reduce the classification performance in other binary problems. RESULTS: In the present study, we propose a family of four extensions to SVM-RFE (called MSVM-RFE) to solve the multiclass gene selection problem, based on different frameworks of multiclass SVMs. By simultaneously considering all classes during the gene selection stages, our proposed extensions identify genes leading to more accurate classification.     

Expression cloning of cDNAs that render cancer cells resistant to Pseudomonas and diphtheria toxin and immunotoxins.

BACKGROUND: Several immunotoxins in which antibodies are coupled to plant or bacterial toxins are now in clinical trials for the treatment of cancer. One of these is B3-LysPE38 in which MAb B3 which reacts with many human cancers, is coupled with a genetically modified form of Pseudomonas exotoxin (PE). MATERIALS AND METHODS: To investigate how cells can become resistant to PE-derived immunotoxins, we constructed an immunotoxin-sensitive MCF-7 breast cancer cell line that contains SV40 T antigen and allows episomal replication of SV40 origin containing plasmids. We transfected a pCDM8/HeLa cDNA expression library into these cells, thereby causing over-expression of the plasmid-encoded genes. The transfected cells were treated with immunotoxin to select for resistance-mediating plasmids, which were reisolated from these cells and amplified in Escherichia coli. The resulting plasmid pool was transfected into cells for two further rounds of selection and plasmid reisolation. RESULTS: Several plasmids that caused immunotoxin resistance were enriched by this selection procedure. Four plasmids were stably transfected into MCF-7 cells and found to increase their resistance to PE-derived immunotoxins by 5- to 20-fold. These plasmids also confer resistance to native PE and to diphtheria toxin but not to ricin or cycloheximide. Thus, they appear to specifically interfere with the action of ADP-ribosylating toxins. CONCLUSION: Cancer cells can become resistant to immunotoxins by deregulated expression of normal genes. The clinical significance of this type of resistance will be evaluated in clinical trials.     

Feature selection environment for genomic applications

Background  

Feature selection is a pattern recognition approach to choose important variables according to some criteria in order to distinguish or explain certain phenomena (i.e., for dimensionality reduction). There are many genomic and proteomic applications that rely on feature selection to answer questions such as selecting signature genes which are informative about some biological state, e.g., normal tissues and several types of cancer; or inferring a prediction network among elements such as genes, proteins and external stimuli. In these applications, a recurrent problem is the lack of samples to perform an adequate estimate of the joint probabilities between element states. A myriad of feature selection algorithms and criterion functions have been proposed, although it is difficult to point the best solution for each application.     

Molecular dissection of a cosmid from a gene-rich region in 17q21 and characterization of a candidate gene for α-N-acetylglucosaminidase with two cDNA isoforms

A cosmid mapped to human Chromosome (Chr) 17q21, c140c10, was found to contain a CpG island. We completed the sequence analysis of c140c10 because of two considerations: the cosmid contained an STS from the 17-β-hydroxysteroid dehydrogenase gene (17-HSD), which was believed to be a neighbor of the breast cancer susceptibility gene, BRCA1; CpG islands are usually associated downstream and/or upstream of human genes. Computer-based exon trapping of the cosmid sequence revealed putative additional exons. With two of those exons used as a probe to screen human placental cDNA libraries, two cDNA isoforms for a novel gene, designated as ufHSD, were isolated. The amino acid sequence of the open reading frames of the cDNA showed no significant homology to any protein in the data base. However, it is possible that our cDNAs are from the gene for α-acetylglucosaminidase, which has recently been localized to the same region. Northern analyses show that the major isoform is expressed in all tissues tested, with the highest expression in blood leukocytes and lowest in brain. Finally, our study has shown that the 46.7-kb cosmid c140c10 encompasses loci for five genes and pseudo-genes: ΨPTP4A, ufHSD, 17-HSDI, 17-HSDII, and 22A1. Received: 19 February 1996 / Accepted: 1 May 1996