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.     

Regularization network-based gene selection for microarray data analysis

Microarray data contains a large number of genes (usually more than 1000) and a relatively small number of samples (usually fewer than 100). This presents problems to discriminant analysis of microarray data. One way to alleviate the problem is to reduce dimensionality of data by selecting important genes to the discriminant problem. Gene selection can be cast as a feature selection problem in the context of pattern classification. Feature selection approaches are broadly grouped into filter methods and wrapper methods. The wrapper method outperforms the filter method but at the cost of more intensive computation. In the present study, we proposed a wrapper-like gene selection algorithm based on the Regularization Network. Compared with classical wrapper method, the computational costs in our gene selection algorithm is significantly reduced, because the evaluation criterion we proposed does not demand repeated training in the leave-one-out procedure.     

Feature Selection for high Dimensional DNA Microarray data using hybrid approaches

Feature selection from DNA microarray data is a major challenge due to high dimensionality in expression data. The number of samples in the microarray data set is much smaller compared to the number of genes. Hence the data is improper to be used as the training set of a classifier. Therefore it is important to select features prior to training the classifier. It should be noted that only a small subset of genes from the data set exhibits a strong correlation with the class. This is because finding the relevant genes from the data set is often non-trivial. Thus there is a need to develop robust yet reliable methods for gene finding in expression data. We describe the use of several hybrid feature selection approaches for gene finding in expression data. These approaches include filtering (filter out the best genes from the data set) and wrapper (best subset of genes from the data set) phases. The methods use information gain (IG) and Pearson Product Moment Correlation (PPMC) as the filtering parameters and biogeography based optimization (BBO) as the wrapper approach. K nearest neighbour algorithm (KNN) and back propagation neural network are used for evaluating the fitness of gene subsets during feature selection. Our analysis shows that an impressive performance is provided by the IG-BBO-KNN combination in different data sets with high accuracy (>90%) and low error rate.     

Randomized probe selection algorithm for microarray design

DNA microarray technology, originally developed to measure the level of gene expression, has become one of the most widely used tools in genomic study. The crux of microarray design lies in how to select a unique probe that distinguishes a given genomic sequence from other sequences. Due to its significance, probe selection attracts a lot of attention. Various probe selection algorithms have been developed in recent years. Good probe selection algorithms should produce a small number of candidate probes. Efficiency is also crucial because the data involved are usually huge. Most existing algorithms are usually not sufficiently selective and quite a large number of probes are returned. We propose a new direction to tackle the problem and give an efficient algorithm based on randomization to select a small set of probes and demonstrate that such a small set of probes is sufficient to distinguish each sequence from all the other sequences. Based on the algorithm, we have developed probe selection software RandPS, which runs efficiently in practice. The software is available on our website (http://www.csc.liv.ac.uk/ approximately cindy/RandPS/RandPS.htm). We test our algorithm via experiments on different genomes (Escherichia coli, Saccharamyces cerevisiae, etc.) and our algorithm is able to output unique probes for most of the genes efficiently. The other genes can be identified by a combination of at most two probes.     

Gene Selection for Multiclass Prediction by Weighted Fisher Criterion

Gene expression profiling has been widely used to study molecular signatures of many diseases and to develop molecular diagnostics for disease prediction. Gene selection, as an important step for improved diagnostics, screens tens of thousands of genes and identifies a small subset that discriminates between disease types. A two-step gene selection method is proposed to identify informative gene subsets for accurate classification of multiclass phenotypes. In the first step, individually discriminatory genes (IDGs) are identified by using one-dimensional weighted Fisher criterion (wFC). In the second step, jointly discriminatory genes (JDGs) are selected by sequential search methods, based on their joint class separability measured by multidimensional weighted Fisher criterion (wFC). The performance of the selected gene subsets for multiclass prediction is evaluated by artificial neural networks (ANNs) and/or support vector machines (SVMs). By applying the proposed IDG/JDG approach to two microarray studies, that is, small round blue cell tumors (SRBCTs) and muscular dystrophies (MDs), we successfully identified a much smaller yet efficient set of JDGs for diagnosing SRBCTs and MDs with high prediction accuracies (96.9% for SRBCTs and 92.3% for MDs, resp.). These experimental results demonstrated that the two-step gene selection method is able to identify a subset of highly discriminative genes for improved multiclass prediction.     

A simple procedure for estimating the false discovery rate

MOTIVATION: The most used criterion in microarray data analysis is nowadays the false discovery rate (FDR). In the framework of estimating procedures based on the marginal distribution of the P-values without any assumption on gene expression changes, estimators of the FDR are necessarily conservatively biased. Indeed, only an upper bound estimate can be obtained for the key quantity pi0, which is the probability for a gene to be unmodified. In this paper, we propose a novel family of estimators for pi0 that allows the calculation of FDR. RESULTS: The very simple method for estimating pi0 called LBE (Location Based Estimator) is presented together with results on its variability. Simulation results indicate that the proposed estimator performs well in finite sample and has the best mean square error in most of the cases as compared with the procedures QVALUE, BUM and SPLOSH. The different procedures are then applied to real datasets. AVAILABILITY: The R function LBE is available at http://ifr69.vjf.inserm.fr/lbe CONTACT: broet@vjf.inserm.fr.     

New gene selection method for classification of cancer subtypes considering within-class variation

In this work we propose a new method for finding gene subsets of microarray data that effectively discriminates subtypes of disease. We developed a new criterion for measuring the relevance of individual genes by using mean and standard deviation of distances from each sample to the class centroid in order to treat the well-known problem of gene selection, large within-class variation. Also this approach has the advantage that it is applicable not only to binary classification but also to multiple classification problems. We demonstrated the performance of the method by applying it to the publicly available microarray datasets, leukemia (two classes) and small round blue cell tumors (four classes). The proposed method provides a very small number of genes compared with the previous methods without loss of discriminating power and thus it can effectively facilitate further biological and clinical researches.     

Gene clustering based on clusterwide mutual information.

Cluster analysis of gene-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and constructing gene regulatory networks. The motivation for considering mutual information is its capacity to measure a general dependence among gene random variables. We propose a novel clustering strategy based on minimizing mutual information among gene clusters. Simulated annealing is employed to solve the optimization problem. Bootstrap techniques are employed to get more accurate estimates of mutual information when the data sample size is small. Moreover, we propose to combine the mutual information criterion and traditional distance criteria such as the Euclidean distance and the fuzzy membership metric in designing the clustering algorithm. The performances of the new clustering methods are compared with those of some existing methods, using both synthesized data and experimental data. It is seen that the clustering algorithm based on a combined metric of mutual information and fuzzy membership achieves the best performance. The supplemental material is available at www.gspsnap.tamu.edu/gspweb/zxb/glioma_zxb.     

Variable selection for logistic regression using a prediction-focused information criterion

In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the focused information criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the mean squared error of the estimator of the quantity of interest in the selected model. In this article, we propose more general versions of the FIC, allowing other risk measures such as the one based on L(p) error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy.     

A variational Bayesian mixture modelling framework for cluster analysis of gene-expression data

MOTIVATION: Accurate subcategorization of tumour types through gene-expression profiling requires analytical techniques that estimate the number of categories or clusters rigorously and reliably. Parametric mixture modelling provides a natural setting to address this problem. RESULTS: We compare a criterion for model selection that is derived from a variational Bayesian framework with a popular alternative based on the Bayesian information criterion. Using simulated data, we show that the variational Bayesian method is more accurate in finding the true number of clusters in situations that are relevant to current and future microarray studies. We also compare the two criteria using freely available tumour microarray datasets and show that the variational Bayesian method is more sensitive to capturing biologically relevant structure.     

Predicting survival from microarray data--a comparative study

MOTIVATION: Survival prediction from gene expression data and other high-dimensional genomic data has been subject to much research during the last years. These kinds of data are associated with the methodological problem of having many more gene expression values than individuals. In addition, the responses are censored survival times. Most of the proposed methods handle this by using Cox's proportional hazards model and obtain parameter estimates by some dimension reduction or parameter shrinkage estimation technique. Using three well-known microarray gene expression data sets, we compare the prediction performance of seven such methods: univariate selection, forward stepwise selection, principal components regression (PCR), supervised principal components regression, partial least squares regression (PLS), ridge regression and the lasso. RESULTS: Statistical learning from subsets should be repeated several times in order to get a fair comparison between methods. Methods using coefficient shrinkage or linear combinations of the gene expression values have much better performance than the simple variable selection methods. For our data sets, ridge regression has the overall best performance. AVAILABILITY: Matlab and R code for the prediction methods are available at http://www.med.uio.no/imb/stat/bmms/software/microsurv/.     

Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network

We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. Selecting the optimal graph, which gives the best representation of the system among genes, is still a problem to be solved. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes.     

On the probability of correct selection for large k populations, with application to microarray data

One frontier of modern statistical research is the problems arising from data sets with extremely large k (>1000) populations, e.g. microarray and neuroimaging data. For many such problems the focus shifts from testing for significance to selecting, filtering, or screening. Classical Ranking and Selection Methodology (RSM) studied the probability of correct selection (PCS). PCS is the probability that the "best" (t = 1) of k populations is truly selected, according to some specified criteria of best. This paper extends and adapts two selection goals from the RSM literature that are suitable for large k problems (d-best and G-best selection). It is then shown how estimation of PCS for selecting multiple (t > 1) populations with d-best and G-best selection can be implemented to provide a useful measure of the quality of a given selection. A simulation study and the application of the proposed method to a benchmark microarray data set show it is an effective and versatile tool for assessing the probability that a particular gene selection or gene filtering step truly obtains the best genes. Moreover, the proposed method is fully general and may be applied to any such extremely large k problem.     

Extreme value distribution based gene selection criteria for discriminant microarray data analysis using logistic regression.

One important issue commonly encountered in the analysis of microarray data is to decide which and how many genes should be selected for further studies. For discriminant microarray data analyses based on statistical models, such as the logistic regression models, gene selection can be accomplished by a comparison of the maximum likelihood of the model given the real data, L(D|M), and the expected maximum likelihood of the model given an ensemble of surrogate data with randomly permuted label, L(D(0)|M). Typically, the computational burden for obtaining L(D(0)M) is immense, often exceeding the limits of available computing resources by orders of magnitude. Here, we propose an approach that circumvents such heavy computations by mapping the simulation problem to an extreme-value problem. We present the derivation of an asymptotic distribution of the extreme-value as well as its mean, median, and variance. Using this distribution, we propose two gene selection criteria, and we apply them to two microarray datasets and three classification tasks for illustration.     

Highly resistant regression and object matching

In many disciplines, it is of great importance to match objects. Procrustes analysis is a popular method for comparing labeled point configurations based on a least squares criterion. We consider alternative procedures that are highly resistant to outlier points, and we describe an application in electrophoretic gel matching. We consider procedures based on S estimators, least median of squares, and least quartile difference estimators. Practical implementation issues are discussed, including random subset selection and intelligent subset selection (where subsets with small size or near collinear subsets are ignored). The relative performances of the resistant and Procrustes methods are examined in a simulation study.     

Characteristics of predictor sets found using differential prioritization

Background  

Feature selection plays an undeniably important role in classification problems involving high dimensional datasets such as microarray datasets. For filter-based feature selection, two well-known criteria used in forming predictor sets are relevance and redundancy. However, there is a third criterion which is at least as important as the other two in affecting the efficacy of the resulting predictor sets. This criterion is the degree of differential prioritization (DDP), which varies the emphases on relevance and redundancy depending on the value of the DDP. Previous empirical works on publicly available microarray datasets have confirmed the effectiveness of the DDP in molecular classification. We now propose to establish the fundamental strengths and merits of the DDP-based feature selection technique. This is to be done through a simulation study which involves vigorous analyses of the characteristics of predictor sets found using different values of the DDP from toy datasets designed to mimic real-life microarray datasets.     

Empirical Bayes estimation of gene-specific effects in micro-array research

Micro-array technology allows investigators the opportunity to measure expression levels of thousands of genes simultaneously. However, investigators are also faced with the challenge of simultaneous estimation of gene expression differences for thousands of genes with very small sample sizes. Traditional estimators of differences between treatment means (ordinary least squares estimators or OLS) are not the best estimators if interest is in estimation of gene expression differences for an ensemble of genes. In the case that gene expression differences are regarded as exchangeable samples from a common population, estimators are available that result in much smaller average mean-square error across the population of gene expression difference estimates. We have simulated the application of such an estimator, namely an empirical Bayes (EB) estimator of random effects in a hierarchical linear model (normal-normal). Simulation results revealed mean-square error as low as 0.05 times the mean-square error of OLS estimators (i.e., the difference between treatment means). We applied the analysis to an example dataset as a demonstration of the shrinkage of EB estimators and of the reduction in mean-square error, i.e., increase in precision, associated with EB estimators in this analysis. The method described here is available in software that is available at .     

Corrected small-sample estimation of the Bayes error

MOTIVATION: A major problem of pattern classification is estimation of the Bayes error when only small samples are available. One way to estimate the Bayes error is to design a classifier based on some classification rule applied to sample data, estimate the error of the designed classifier, and then use this estimate as an estimate of the Bayes error. Relative to the Bayes error, the expected error of the designed classifier is biased high, and this bias can be severe with small samples. RESULTS: This paper provides a correction for the bias by subtracting a term derived from the representation of the estimation error. It does so for Boolean classifiers, these being defined on binary features. Although the general theory applies to any Boolean classifier, a model is introduced to reduce the number of parameters. A key point is that the expected correction is conservative. Properties of the corrected estimate are studied via simulation. The correction applies to binary predictors because they are mathematically identical to Boolean classifiers. In this context the correction is adapted to the coefficient of determination, which has been used to measure nonlinear multivariate relations between genes and design genetic regulatory networks. An application using gene-expression data from a microarray experiment is provided on the website http://gspsnap.tamu.edu/smallsample/ (user:'smallsample', password:'smallsample)').     

A mathematical model for the validation of gene selection methods

Gene selection methods aim at determining biologically relevant subsets of genes in DNA microarray experiments. However, their assessment and validation represent a major difficulty since the subset of biologically relevant genes is usually unknown. To solve this problem a novel procedure for generating biologically plausible synthetic gene expression data is proposed. It is based on a proper mathematical model representing gene expression signatures and expression profiles through Boolean threshold functions. The results show that the proposed procedure can be successfully adopted to analyze the quality of statistical and machine learning-based gene selection algorithms.