Small sample issues for microarray-based classification

In order to study the molecular biological differences between normal and diseased tissues, it is desirable to perform classification among diseases and stages of disease using microarray-based gene-expression values. Owing to the limited number of microarrays typically used in these studies, serious issues arise with respect to the design, performance and analysis of classifiers based on microarray data. This paper reviews some fundamental issues facing small-sample classification: classification rules, constrained classifiers, error estimation and feature selection. It discusses both unconstrained and constrained classifier design from sample data, and the contributions to classifier error from constrained optimization and lack of optimality owing to design from sample data. The difficulty with estimating classifier error when confined to small samples is addressed, particularly estimating the error from training data. The impact of small samples on the ability to include more than a few variables as classifier features is explained.     

Classification using partial least squares with penalized logistic regression

MOTIVATION: One important aspect of data-mining of microarray data is to discover the molecular variation among cancers. In microarray studies, the number n of samples is relatively small compared to the number p of genes per sample (usually in thousands). It is known that standard statistical methods in classification are efficient (i.e. in the present case, yield successful classifiers) particularly when n is (far) larger than p. This naturally calls for the use of a dimension reduction procedure together with the classification one. RESULTS: In this paper, the question of classification in such a high-dimensional setting is addressed. We view the classification problem as a regression one with few observations and many predictor variables. We propose a new method combining partial least squares (PLS) and Ridge penalized logistic regression. We review the existing methods based on PLS and/or penalized likelihood techniques, outline their interest in some cases and theoretically explain their sometimes poor behavior. Our procedure is compared with these other classifiers. The predictive performance of the resulting classification rule is illustrated on three data sets: Leukemia, Colon and Prostate.     

An adaptive optimal ensemble classifier via bagging and rank aggregation with applications to high dimensional data

Background  

Generally speaking, different classifiers tend to work well for certain types of data and conversely, it is usually not known a priori which algorithm will be optimal in any given classification application. In addition, for most classification problems, selecting the best performing classification algorithm amongst a number of competing algorithms is a difficult task for various reasons. As for example, the order of performance may depend on the performance measure employed for such a comparison. In this work, we present a novel adaptive ensemble classifier constructed by combining bagging and rank aggregation that is capable of adaptively changing its performance depending on the type of data that is being classified. The attractive feature of the proposed classifier is its multi-objective nature where the classification results can be simultaneously optimized with respect to several performance measures, for example, accuracy, sensitivity and specificity. We also show that our somewhat complex strategy has better predictive performance as judged on test samples than a more naive approach that attempts to directly identify the optimal classifier based on the training data performances of the individual classifiers.     

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.     

Feature Selection and Classification of MAQC-II Breast Cancer and Multiple Myeloma Microarray Gene Expression Data

Microarray data has a high dimension of variables but available datasets usually have only a small number of samples, thereby making the study of such datasets interesting and challenging. In the task of analyzing microarray data for the purpose of, e.g., predicting gene-disease association, feature selection is very important because it provides a way to handle the high dimensionality by exploiting information redundancy induced by associations among genetic markers. Judicious feature selection in microarray data analysis can result in significant reduction of cost while maintaining or improving the classification or prediction accuracy of learning machines that are employed to sort out the datasets. In this paper, we propose a gene selection method called Recursive Feature Addition (RFA), which combines supervised learning and statistical similarity measures. We compare our method with the following gene selection methods:

• Support Vector Machine Recursive Feature Elimination (SVMRFE)
• Leave-One-Out Calculation Sequential Forward Selection (LOOCSFS)
• Gradient based Leave-one-out Gene Selection (GLGS)

To evaluate the performance of these gene selection methods, we employ several popular learning classifiers on the MicroArray Quality Control phase II on predictive modeling (MAQC-II) breast cancer dataset and the MAQC-II multiple myeloma dataset. Experimental results show that gene selection is strictly paired with learning classifier. Overall, our approach outperforms other compared methods. The biological functional analysis based on the MAQC-II breast cancer dataset convinced us to apply our method for phenotype prediction. Additionally, learning classifiers also play important roles in the classification of microarray data and our experimental results indicate that the Nearest Mean Scale Classifier (NMSC) is a good choice due to its prediction reliability and its stability across the three performance measurements: Testing accuracy, MCC values, and AUC errors.     

Multi-TGDR: A Regularization Method for Multi-Class Classification in Microarray Experiments

Background

As microarray technology has become mature and popular, the selection and use of a small number of relevant genes for accurate classification of samples has arisen as a hot topic in the circles of biostatistics and bioinformatics. However, most of the developed algorithms lack the ability to handle multiple classes, arguably a common application. Here, we propose an extension to an existing regularization algorithm, called Threshold Gradient Descent Regularization (TGDR), to specifically tackle multi-class classification of microarray data. When there are several microarray experiments addressing the same/similar objectives, one option is to use a meta-analysis version of TGDR (Meta-TGDR), which considers the classification task as a combination of classifiers with the same structure/model while allowing the parameters to vary across studies. However, the original Meta-TGDR extension did not offer a solution to the prediction on independent samples. Here, we propose an explicit method to estimate the overall coefficients of the biomarkers selected by Meta-TGDR. This extension permits broader applicability and allows a comparison between the predictive performance of Meta-TGDR and TGDR using an independent testing set.

Results

Using real-world applications, we demonstrated the proposed multi-TGDR framework works well and the number of selected genes is less than the sum of all individualized binary TGDRs. Additionally, Meta-TGDR and TGDR on the batch-effect adjusted pooled data approximately provided same results. By adding Bagging procedure in each application, the stability and good predictive performance are warranted.

Conclusions

Compared with Meta-TGDR, TGDR is less computing time intensive, and requires no samples of all classes in each study. On the adjusted data, it has approximate same predictive performance with Meta-TGDR. Thus, it is highly recommended.     

An evolutionary approach for gene selection and classification of microarray data based on SVM error-bound theories

Microarrays have thousands to tens-of-thousands of gene features, but only a few hundred patient samples are available. The fundamental problem in microarray data analysis is identifying genes whose disruption causes congenital or acquired disease in humans. In this paper, we propose a new evolutionary method that can efficiently select a subset of potentially informative genes for support vector machine (SVM) classifiers. The proposed evolutionary method uses SVM with a given subset of gene features to evaluate the fitness function, and new subsets of features are selected based on the estimates of generalization error of SVMs and frequency of occurrence of the features in the evolutionary approach. Thus, in theory, selected genes reflect to some extent the generalization performance of SVM classifiers. We compare our proposed method with several existing methods and find that the proposed method can obtain better classification accuracy with a smaller number of selected genes than the existing methods.     

Evaluation of Gene Expression Classification Studies: Factors Associated with Classification Performance

Classification methods used in microarray studies for gene expression are diverse in the way they deal with the underlying complexity of the data, as well as in the technique used to build the classification model. The MAQC II study on cancer classification problems has found that performance was affected by factors such as the classification algorithm, cross validation method, number of genes, and gene selection method. In this paper, we study the hypothesis that the disease under study significantly determines which method is optimal, and that additionally sample size, class imbalance, type of medical question (diagnostic, prognostic or treatment response), and microarray platform are potentially influential. A systematic literature review was used to extract the information from 48 published articles on non-cancer microarray classification studies. The impact of the various factors on the reported classification accuracy was analyzed through random-intercept logistic regression. The type of medical question and method of cross validation dominated the explained variation in accuracy among studies, followed by disease category and microarray platform. In total, 42% of the between study variation was explained by all the study specific and problem specific factors that we studied together.     

Class prediction and discovery using gene microarray and proteomics mass spectroscopy data: curses,caveats, cautions

MOTIVATION: Two practical realities constrain the analysis of microarray data, mass spectra from proteomics, and biomedical infrared or magnetic resonance spectra. One is the 'curse of dimensionality': the number of features characterizing these data is in the thousands or tens of thousands. The other is the 'curse of dataset sparsity': the number of samples is limited. The consequences of these two curses are far-reaching when such data are used to classify the presence or absence of disease. RESULTS: Using very simple classifiers, we show for several publicly available microarray and proteomics datasets how these curses influence classification outcomes. In particular, even if the sample per feature ratio is increased to the recommended 5-10 by feature extraction/reduction methods, dataset sparsity can render any classification result statistically suspect. In addition, several 'optimal' feature sets are typically identifiable for sparse datasets, all producing perfect classification results, both for the training and independent validation sets. This non-uniqueness leads to interpretational difficulties and casts doubt on the biological relevance of any of these 'optimal' feature sets. We suggest an approach to assess the relative quality of apparently equally good classifiers.     

A blocking strategy to improve gene selection for classification of gene expression data

Because of high dimensionality, machine learning algorithms typically rely on feature selection techniques in order to perform effective classification in microarray gene expression data sets. However, the large number of features compared to the number of samples makes the task of feature selection computationally hard and prone to errors. This paper interprets feature selection as a task of stochastic optimization, where the goal is to select among an exponential number of alternative gene subsets the one expected to return the highest generalization in classification. Blocking is an experimental design strategy which produces similar experimental conditions to compare alternative stochastic configurations in order to be confident that observed differences in accuracy are due to actual differences rather than to fluctuations and noise effects. We propose an original blocking strategy for improving feature selection which aggregates in a paired way the validation outcomes of several learning algorithms to assess a gene subset and compare it to others. This is a novelty with respect to conventional wrappers, which commonly adopt a sole learning algorithm to evaluate the relevance of a given set of variables. The rationale of the approach is that, by increasing the amount of experimental conditions under which we validate a feature subset, we can lessen the problems related to the scarcity of samples and consequently come up with a better selection. The paper shows that the blocking strategy significantly improves the performance of a conventional forward selection for a set of 16 publicly available cancer expression data sets. The experiments involve six different classifiers and show that improvements take place independent of the classification algorithm used after the selection step. Two further validations based on available biological annotation support the claim that blocking strategies in feature selection may improve the accuracy and the quality of the solution. The first validation is based on retrieving PubMEd abstracts associated to the selected genes and matching them to regular expressions describing the biological phenomenon underlying the expression data sets. The biological validation that follows is based on the use of the Bioconductor package GoStats in order to perform Gene Ontology statistical analysis.     

Avoiding model selection bias in small-sample genomic datasets

MOTIVATION: Genomic datasets generated by high-throughput technologies are typically characterized by a moderate number of samples and a large number of measurements per sample. As a consequence, classification models are commonly compared based on resampling techniques. This investigation discusses the conceptual difficulties involved in comparative classification studies. Conclusions derived from such studies are often optimistically biased, because the apparent differences in performance are usually not controlled in a statistically stringent framework taking into account the adopted sampling strategy. We investigate this problem by means of a comparison of various classifiers in the context of multiclass microarray data. RESULTS: Commonly used accuracy-based performance values, with or without confidence intervals, are inadequate for comparing classifiers for small-sample data. We present a statistical methodology that avoids bias in cross-validated model selection in the context of small-sample scenarios. This methodology is valid for both k-fold cross-validation and repeated random sampling.     

Improved Microarray-Based Decision Support with Graph Encoded Interactome Data

In the past, microarray studies have been criticized due to noise and the limited overlap between gene signatures. Prior biological knowledge should therefore be incorporated as side information in models based on gene expression data to improve the accuracy of diagnosis and prognosis in cancer. As prior knowledge, we investigated interaction and pathway information from the human interactome on different aspects of biological systems. By exploiting the properties of kernel methods, relations between genes with similar functions but active in alternative pathways could be incorporated in a support vector machine classifier based on spectral graph theory. Using 10 microarray data sets, we first reduced the number of data sources relevant for multiple cancer types and outcomes. Three sources on metabolic pathway information (KEGG), protein-protein interactions (OPHID) and miRNA-gene targeting (microRNA.org) outperformed the other sources with regard to the considered class of models. Both fixed and adaptive approaches were subsequently considered to combine the three corresponding classifiers. Averaging the predictions of these classifiers performed best and was significantly better than the model based on microarray data only. These results were confirmed on 6 validation microarray sets, with a significantly improved performance in 4 of them. Integrating interactome data thus improves classification of cancer outcome for the investigated microarray technologies and cancer types. Moreover, this strategy can be incorporated in any kernel method or non-linear version of a non-kernel method.     

Bayesian hierarchical error model for analysis of gene expression data

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.     

A comparative study of feature selection and multiclass classification methods for tissue classification based on gene expression

This paper studies the problem of building multiclass classifiers for tissue classification based on gene expression. The recent development of microarray technologies has enabled biologists to quantify gene expression of tens of thousands of genes in a single experiment. Biologists have begun collecting gene expression for a large number of samples. One of the urgent issues in the use of microarray data is to develop methods for characterizing samples based on their gene expression. The most basic step in the research direction is binary sample classification, which has been studied extensively over the past few years. This paper investigates the next step-multiclass classification of samples based on gene expression. The characteristics of expression data (e.g. large number of genes with small sample size) makes the classification problem more challenging. The process of building multiclass classifiers is divided into two components: (i) selection of the features (i.e. genes) to be used for training and testing and (ii) selection of the classification method. This paper compares various feature selection methods as well as various state-of-the-art classification methods on various multiclass gene expression datasets. Our study indicates that multiclass classification problem is much more difficult than the binary one for the gene expression datasets. The difficulty lies in the fact that the data are of high dimensionality and that the sample size is small. The classification accuracy appears to degrade very rapidly as the number of classes increases. In particular, the accuracy was very low regardless of the choices of the methods for large-class datasets (e.g. NCI60 and GCM). While increasing the number of samples is a plausible solution to the problem of accuracy degradation, it is important to develop algorithms that are able to analyze effectively multiple-class expression data for these special datasets.     

Interpretable gene expression classifier with an accurate and compact fuzzy rule base for microarray data analysis

An accurate classifier with linguistic interpretability using a small number of relevant genes is beneficial to microarray data analysis and development of inexpensive diagnostic tests. Several frequently used techniques for designing classifiers of microarray data, such as support vector machine, neural networks, k-nearest neighbor, and logistic regression model, suffer from low interpretabilities. This paper proposes an interpretable gene expression classifier (named iGEC) with an accurate and compact fuzzy rule base for microarray data analysis. The design of iGEC has three objectives to be simultaneously optimized: maximal classification accuracy, minimal number of rules, and minimal number of used genes. An "intelligent" genetic algorithm IGA is used to efficiently solve the design problem with a large number of tuning parameters. The performance of iGEC is evaluated using eight commonly-used data sets. It is shown that iGEC has an accurate, concise, and interpretable rule base (1.1 rules per class) on average in terms of test classification accuracy (87.9%), rule number (3.9), and used gene number (5.0). Moreover, iGEC not only has better performance than the existing fuzzy rule-based classifier in terms of the above-mentioned objectives, but also is more accurate than some existing non-rule-based classifiers.     

Developing optimal prediction models for cancer classification using gene expression data

Microarrays can provide genome-wide expression patterns for various cancers, especially for tumor sub-types that may exhibit substantially different patient prognosis. Using such gene expression data, several approaches have been proposed to classify tumor sub-types accurately. These classification methods are not robust, and often dependent on a particular training sample for modelling, which raises issues in utilizing these methods to administer proper treatment for a future patient. We propose to construct an optimal, robust prediction model for classifying cancer sub-types using gene expression data. Our model is constructed in a step-wise fashion implementing cross-validated quadratic discriminant analysis. At each step, all identified models are validated by an independent sample of patients to develop a robust model for future data. We apply the proposed methods to two microarray data sets of cancer: the acute leukemia data by Golub et al. and the colon cancer data by Alon et al. We have found that the dimensionality of our optimal prediction models is relatively small for these cases and that our prediction models with one or two gene factors outperforms or has competing performance, especially for independent samples, to other methods based on 50 or more predictive gene factors. The methodology is implemented and developed by the procedures in R and Splus. The source code can be obtained at http://hesweb1.med.virginia.edu/bioinformatics.     

Regularized ROC method for disease classification and biomarker selection with microarray data

MOTIVATION: An important application of microarrays is to discover genomic biomarkers, among tens of thousands of genes assayed, for disease classification. Thus there is a need for developing statistical methods that can efficiently use such high-throughput genomic data, select biomarkers with discriminant power and construct classification rules. The ROC (receiver operator characteristic) technique has been widely used in disease classification with low-dimensional biomarkers because (1) it does not assume a parametric form of the class probability as required for example in the logistic regression method; (2) it accommodates case-control designs and (3) it allows treating false positives and false negatives differently. However, due to computational difficulties, the ROC-based classification has not been used with microarray data. Moreover, the standard ROC technique does not incorporate built-in biomarker selection. RESULTS: We propose a novel method for biomarker selection and classification using the ROC technique for microarray data. The proposed method uses a sigmoid approximation to the area under the ROC curve as the objective function for classification and the threshold gradient descent regularization method for estimation and biomarker selection. Tuning parameter selection based on the V-fold cross validation and predictive performance evaluation are also investigated. The proposed approach is demonstrated with a simulation study, the Colon data and the Estrogen data. The proposed approach yields parsimonious models with excellent classification performance.     

M@CBETH: a microarray classification benchmarking tool

Microarray classification can be useful to support clinical management decisions for individual patients in, for example, oncology. However, comparing classifiers and selecting the best for each microarray dataset can be a tedious and non-straightforward task. The M@CBETH (a MicroArray Classification BEnchmarking Tool on a Host server) web service offers the microarray community a simple tool for making optimal two-class predictions. M@CBETH aims at finding the best prediction among different classification methods by using randomizations of the benchmarking dataset. The M@CBETH web service intends to introduce an optimal use of clinical microarray data classification.     

A critical evaluation of network and pathway-based classifiers for outcome prediction in breast cancer

Recently, several classifiers that combine primary tumor data, like gene expression data, and secondary data sources, such as protein-protein interaction networks, have been proposed for predicting outcome in breast cancer. In these approaches, new composite features are typically constructed by aggregating the expression levels of several genes. The secondary data sources are employed to guide this aggregation. Although many studies claim that these approaches improve classification performance over single genes classifiers, the gain in performance is difficult to assess. This stems mainly from the fact that different breast cancer data sets and validation procedures are employed to assess the performance. Here we address these issues by employing a large cohort of six breast cancer data sets as benchmark set and by performing an unbiased evaluation of the classification accuracies of the different approaches. Contrary to previous claims, we find that composite feature classifiers do not outperform simple single genes classifiers. We investigate the effect of (1) the number of selected features; (2) the specific gene set from which features are selected; (3) the size of the training set and (4) the heterogeneity of the data set on the performance of composite feature and single genes classifiers. Strikingly, we find that randomization of secondary data sources, which destroys all biological information in these sources, does not result in a deterioration in performance of composite feature classifiers. Finally, we show that when a proper correction for gene set size is performed, the stability of single genes sets is similar to the stability of composite feature sets. Based on these results there is currently no reason to prefer prognostic classifiers based on composite features over single genes classifiers for predicting outcome in breast cancer.     

Exploring metabolic pathway disruption in the subchronic phencyclidine model of schizophrenia with the Generalized Singular Value Decomposition

Background

One of the major goals in gene and protein expression profiling of cancer is to identify biomarkers and build classification models for prediction of disease prognosis or treatment response. Many traditional statistical methods, based on microarray gene expression data alone and individual genes' discriminatory power, often fail to identify biologically meaningful biomarkers thus resulting in poor prediction performance across data sets. Nonetheless, the variables in multivariable classifiers should synergistically interact to produce more effective classifiers than individual biomarkers.

Results

We developed an integrated approach, namely network-constrained support vector machine (netSVM), for cancer biomarker identification with an improved prediction performance. The netSVM approach is specifically designed for network biomarker identification by integrating gene expression data and protein-protein interaction data. We first evaluated the effectiveness of netSVM using simulation studies, demonstrating its improved performance over state-of-the-art network-based methods and gene-based methods for network biomarker identification. We then applied the netSVM approach to two breast cancer data sets to identify prognostic signatures for prediction of breast cancer metastasis. The experimental results show that: (1) network biomarkers identified by netSVM are highly enriched in biological pathways associated with cancer progression; (2) prediction performance is much improved when tested across different data sets. Specifically, many genes related to apoptosis, cell cycle, and cell proliferation, which are hallmark signatures of breast cancer metastasis, were identified by the netSVM approach. More importantly, several novel hub genes, biologically important with many interactions in PPI network but often showing little change in expression as compared with their downstream genes, were also identified as network biomarkers; the genes were enriched in signaling pathways such as TGF-beta signaling pathway, MAPK signaling pathway, and JAK-STAT signaling pathway. These signaling pathways may provide new insight to the underlying mechanism of breast cancer metastasis.

Conclusions

We have developed a network-based approach for cancer biomarker identification, netSVM, resulting in an improved prediction performance with network biomarkers. We have applied the netSVM approach to breast cancer gene expression data to predict metastasis in patients. Network biomarkers identified by netSVM reveal potential signaling pathways associated with breast cancer metastasis, and help improve the prediction performance across independent data sets.