Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data

Identification of full and partial class relevant genes

Multiclass cancer classification on microarray data has provided the feasibility of cancer diagnosis across all of the common malignancies in parallel. Using multiclass cancer feature selection approaches, it is now possible to identify genes relevant to a set of cancer types. However, besides identifying the relevant genes for the set of all cancer types, it is deemed to be more informative to biologists if the relevance of each gene to specific cancer or subset of cancer types could be revealed or pinpointed. In this paper, we introduce two new definitions of multiclass relevancy features, i.e., full class relevant (FCR) and partial class relevant (PCR) features. Particularly, FCR denotes genes that serve as candidate biomarkers for discriminating all cancer types. PCR, on the other hand, are genes that distinguish subsets of cancer types. Subsequently, a Markov blanket embedded memetic algorithm is proposed for the simultaneous identification of both FCR and PCR genes. Results obtained on commonly used synthetic and real-world microarray data sets show that the proposed approach converges to valid FCR and PCR genes that would assist biologists in their research work. The identification of both FCR and PCR genes is found to generate improvement in classification accuracy on many microarray data sets. Further comparison study to existing state-of-the-art feature selection algorithms also reveals the effectiveness and efficiency of the proposed approach.

Microrna profiling analysis of differences between the melanoma of young adults and older adults

BACKGROUND

This study represents the first attempt to perform a profiling analysis of the intergenerational differences in the microRNAs (miRNAs) of primary cutaneous melanocytic neoplasms in young adult and older age groups. The data emphasize the importance of these master regulators in the transcriptional machinery of melanocytic neoplasms and suggest that differential levels of expressions of these miRs may contribute to differences in phenotypic and pathologic presentation of melanocytic neoplasms at different ages.

METHODS

An exploratory miRNA analysis of 666 miRs by low density microRNA arrays was conducted on formalin fixed and paraffin embedded tissues (FFPE) from 10 older adults and 10 young adults including conventional melanoma and melanocytic neoplasms of uncertain biological significance. Age-matched benign melanocytic nevi were used as controls.

RESULTS

Primary melanoma in patients greater than 60 years old was characterized by the increased expression of miRs regulating TLR-MyD88-NF-kappaB pathway (hsa-miR-199a), RAS/RAB22A pathway (hsa-miR-204); growth differentiation and migration (hsa-miR337), epithelial mesenchymal transition (EMT) (let-7b, hsa-miR-10b/10b*), invasion and metastasis (hsa-miR-10b/10b*), hsa-miR-30a/e*, hsa-miR-29c*; cellular matrix components (hsa-miR-29c*); invasion-cytokinesis (hsa-miR-99b*) compared to melanoma of younger patients. MiR-211 was dramatically downregulated compared to nevi controls, decreased with increasing age and was among the miRs linked to metastatic processes. Melanoma in young adult patients had increased expression of hsa-miR-449a and decreased expression of hsa-miR-146b, hsa-miR-214*. MiR-30a* in clinical stages I-II adult and pediatric melanoma could predict classification of melanoma tissue in the two extremes of age groups. Although the number of cases is small, positive lymph node status in the two age groups was characterized by the statistically significant expression of hsa-miR-30a* and hsa-miR-204 (F-test, p-value < 0.001).

CONCLUSIONS

Our findings, although preliminary, support the notion that the differential biology of melanoma at the extremes of age is driven, in part, by deregulation of microRNA expression and by fine tuning of miRs that are already known to regulate cell cycle, inflammation, Epithelial-Mesenchymal Transition (EMT)/stroma and more specifically genes known to be altered in melanoma. Our analysis reveals that miR expression differences create unique patterns of frequently affected biological processes that clearly distinguish old age from young age melanomas. This is a novel characterization of the miRnomes of melanocytic neoplasms at two extremes of age and identifies potential diagnostic and clinico-pathologic biomarkers that may serve as novel miR-based targeted modalities in melanoma diagnosis and treatment.

Learning curves in classification with microarray data

The performance of many repeated tasks improves with experience and practice. This improvement tends to be rapid initially and then decreases. The term "learning curve" is often used to describe the phenomenon. In supervised machine learning, the performance of classification algorithms often increases with the number of observations used to train the algorithm. We use progressively larger samples of observations to train the algorithm and then plot performance against the number of training observations. This yields the familiar negatively accelerating learning curve. To quantify the learning curve, we fit inverse power law models to the progressively sampled data. We fit such learning curves to four large clinical cancer genomic datasets, using three classifiers (diagonal linear discriminant analysis, K-nearest-neighbor with three neighbors, and support vector machines) and four values for the number of top genes included (5, 50, 500, 5,000). The inverse power law models fit the progressively sampled data reasonably well and showed considerable diversity when multiple classifiers are applied to the same data. Some classifiers showed rapid and continued increase in performance as the number of training samples increased, while others showed little if any improvement. Assessing classifier efficiency is particularly important in genomic studies since samples are so expensive to obtain. It is important to employ an algorithm that uses the predictive information efficiently, but with a modest number of training samples (>50), learning curves can be used to assess the predictive efficiency of classification algorithms.

Molecular sampling of prostate cancer: a dilemma for predicting disease progression

BACKGROUND

Current prostate cancer prognostic models are based on pre-treatment prostate specific antigen (PSA) levels, biopsy Gleason score, and clinical staging but in practice are inadequate to accurately predict disease progression. Hence, we sought to develop a molecular panel for prostate cancer progression by reasoning that molecular profiles might further improve current clinical models.

METHODS

We analyzed a Swedish Watchful Waiting cohort with up to 30 years of clinical follow up using a novel method for gene expression profiling. This cDNA-mediated annealing, selection, ligation, and extension (DASL) method enabled the use of formalin-fixed paraffin-embedded transurethral resection of prostate (TURP) samples taken at the time of the initial diagnosis. We determined the expression profiles of 6100 genes for 281 men divided in two extreme groups: men who died of prostate cancer and men who survived more than 10 years without metastases (lethals and indolents, respectively). Several statistical and machine learning models using clinical and molecular features were evaluated for their ability to distinguish lethal from indolent cases.

RESULTS

Surprisingly, none of the predictive models using molecular profiles significantly improved over models using clinical variables only. Additional computational analysis confirmed that molecular heterogeneity within both the lethal and indolent classes is widespread in prostate cancer as compared to other types of tumors.

CONCLUSIONS

The determination of the molecularly dominant tumor nodule may be limited by sampling at time of initial diagnosis, may not be present at time of initial diagnosis, or may occur as the disease progresses making the development of molecular biomarkers for prostate cancer progression challenging.

Comparison of two output-coding strategies for multi-class tumor classification using gene expression data and Latent Variable Model as binary classifier

Multi-class cancer classification based on microarray data is described. A generalized output-coding scheme based on One Versus One (OVO) combined with Latent Variable Model (LVM) is used. Results from the proposed One Versus One (OVO) outputcoding strategy is compared with the results obtained from the generalized One Versus All (OVA) method and their efficiencies of using them for multi-class tumor classification have been studied. This comparative study was done using two microarray gene expression data: Global Cancer Map (GCM) dataset and brain cancer (BC) dataset. Primary feature selection was based on fold change and penalized t-statistics. Evaluation was conducted with varying feature numbers. The OVO coding strategy worked quite well with the BC data, while both OVO and OVA results seemed to be similar for the GCM data. The selection of output coding methods for combining binary classifiers for multi-class tumor classification depends on the number of tumor types considered, the discrepancies between the tumor samples used for training as well as the heterogeneity of expression within the cancer subtypes used as training data.

Shrinkage-based diagonal discriminant analysis and its applications in high-dimensional data

High-dimensional data such as microarrays have brought us new statistical challenges. For example, using a large number of genes to classify samples based on a small number of microarrays remains a difficult problem. Diagonal discriminant analysis, support vector machines, and k-nearest neighbor have been suggested as among the best methods for small sample size situations, but none was found to be superior to others. In this article, we propose an improved diagonal discriminant approach through shrinkage and regularization of the variances. The performance of our new approach along with the existing methods is studied through simulations and applications to real data. These studies show that the proposed shrinkage-based and regularization diagonal discriminant methods have lower misclassification rates than existing methods in many cases.

Pathway-BasedFeature Selection Algorithm for Cancer Microarray Data

Classification of cancers based on gene expressions produces better accuracy when compared to that of the clinical markers. Feature selection improves the accuracy of these classification algorithms by reducing the chance of overfitting that happens due to large number of features. We develop a new feature selection method called Biological Pathway-based Feature Selection (BPFS) for microarray data. Unlike most of the existing methods, our method integrates signaling and gene regulatory pathways with gene expression data to minimize the chance of overfitting of the method and to improve the test accuracy. Thus, BPFS selects a biologically meaningful feature set that is minimally redundant. Our experiments on published breast cancer datasets demonstrate that all of the top 20 genes found by our method are associated with cancer. Furthermore, the classification accuracy of our signature is up to 18% better than that of vant Veers 70 gene signature, and it is up to 8% better accuracy than the best published feature selection method, I-RELIEF.

A composite transcriptional signature differentiates responses towards closely related herbicides in Arabidopsis thaliana and Brassica napus

In this study, genome-wide expression profiling based on Affymetrix ATH1 arrays was used to identify discriminating responses of Arabidopsis thaliana to five herbicides, which contain active ingredients targeting two different branches of amino acid biosynthesis. One herbicide contained glyphosate, which targets 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS), while the other four herbicides contain different acetolactate synthase (ALS) inhibiting compounds. In contrast to the herbicide containing glyphosate, which affected only a few transcripts, many effects of the ALS inhibiting herbicides were revealed based on transcriptional changes related to ribosome biogenesis and translation, secondary metabolism, cell wall modification and growth. The expression pattern of a set of 101 genes provided a specific, composite signature that was distinct from other major stress responses and differentiated among herbicides targeting the same enzyme (ALS) or containing the same chemical class of active ingredient (sulfonylurea). A set of homologous genes could be identified in Brassica napus that exhibited a similar expression pattern and correctly distinguished exposure to the five herbicides. Our results show the ability of a limited number of genes to classify and differentiate responses to closely related herbicides in A. thaliana and B. napus and the transferability of a complex transcriptional signature across species.

Weighted Distance Weighted Discrimination and Its Asymptotic Properties

While Distance Weighted Discrimination (DWD) is an appealing approach to classification in high dimensions, it was designed for balanced datasets. In the case of unequal costs, biased sampling, or unbalanced data, there are major improvements available, using appropriately weighted versions of DWD (wDWD). A major contribution of this paper is the development of optimal weighting schemes for various nonstandard classification problems. In addition, we discuss several alternative criteria and propose an adaptive weighting scheme (awDWD) and demonstrate its advantages over nonadaptive weighting schemes under some situations. The second major contribution is a theoretical study of weighted DWD. Both high-dimensional low sample-size asymptotics and Fisher consistency of DWD are studied. The performance of weighted DWD is evaluated using simulated examples and two real data examples. The theoretical results are also confirmed by simulations.

Use of DNA-damaging agents and RNA pooling to assess expression profiles associated with BRCA1 and BRCA2 mutation status in familial breast cancer patients

A large number of rare sequence variants of unknown clinical significance have been identified in the breast cancer susceptibility genes, BRCA1 and BRCA2. Laboratory-based methods that can distinguish between carriers of pathogenic mutations and non-carriers are likely to have utility for the classification of these sequence variants. To identify predictors of pathogenic mutation status in familial breast cancer patients, we explored the use of gene expression arrays to assess the effect of two DNA–damaging agents (irradiation and mitomycin C) on cellular response in relation to BRCA1 and BRCA2 mutation status. A range of regimes was used to treat 27 lymphoblastoid cell-lines (LCLs) derived from affected women in high-risk breast cancer families (nine BRCA1, nine BRCA2, and nine non-BRCA1/2 or BRCAX individuals) and nine LCLs from healthy individuals. Using an RNA–pooling strategy, we found that treating LCLs with 1.2 µM mitomycin C and measuring the gene expression profiles 1 hour post-treatment had the greatest potential to discriminate BRCA1, BRCA2, and BRCAX mutation status. A classifier was built using the expression profile of nine QRT–PCR validated genes that were associated with BRCA1, BRCA2, and BRCAX status in RNA pools. These nine genes could distinguish BRCA1 from BRCA2 carriers with 83% accuracy in individual samples, but three-way analysis for BRCA1, BRCA2, and BRCAX had a maximum of 59% prediction accuracy. Our results suggest that, compared to BRCA1 and BRCA2 mutation carriers, non-BRCA1/2 (BRCAX) individuals are genetically heterogeneous. This study also demonstrates the effectiveness of RNA pools to compare the expression profiles of cell-lines from BRCA1, BRCA2, and BRCAX cases after treatment with irradiation and mitomycin C as a method to prioritize treatment regimes for detailed downstream expression analysis.

A large number of rare sequence variants of unknown clinical significance have been identified in the breast cancer susceptibility genes, BRCA1 and BRCA2. Laboratory methods to identify which of these variants are mutations would have utility for counseling and clinical decision making when identified in patients with a family history of breast cancer. We used DNA–damaging agents to disturb gene expression profiles of cell-lines derived from blood of patients, and we compared patterns from women with BRCA1 and BRCA2 mutations to women familial breast cancer families without such mutations. Using a pooling strategy, which allowed us to compare several treatments at one time, we identified which treatment caused the greatest difference in gene-expression changes between patient groups and used this treatment method for further study. We were able to accurately classify BRCA1 and BRCA2 samples, and our results supported other reported findings that suggested familial breast cancer patients without BRCA1/2 mutations are genetically heterogeneous. We demonstrate a useful strategy to identify treatments that induce gene expression differences associated with BRCA1/2 mutation status. This strategy may aid the development of a molecular-based tool to screen individuals from multi-case breast cancer families for the presence of pathogenic mutations.

Time-series nasal epithelial transcriptomics during natural pollen exposure in healthy subjects and allergic patients

BACKGROUND

The role of epithelium has recently awakened interest in the studies of type I hypersensitivity.

OBJECTIVE

We analysed the nasal transcriptomics epithelial response to natural birch pollen exposure in a time series manner.

METHODS

Human nasal epithelial cell swabs were collected from birch pollen allergic patients and healthy controls in winter season. In addition, four specimens at weekly intervals were collected from the same subjects during natural birch pollen exposure in spring and transcriptomic analyses were performed.

RESULTS

The nasal epithelium of healthy subjects responded vigorously to allergen exposure. The immune response was a dominating category of this response. Notably, the healthy subjects did not display any clinical symptoms regardless of this response detected by transcriptomic analysis. Concomitantly, the epithelium of allergic subjects responded also, but with a different set of responders. In allergic patients the regulation of dyneins, the molecular motors of intracellular transport dominated. This further supports our previous hypothesis that the birch pollen exposure results in an active uptake of allergen into the epithelium only in allergic subjects but not in healthy controls.

CONCLUSION

We showed that birch pollen allergen causes a defence response in healthy subjects, but not in allergic subjects. Instead, allergic patients actively transport pollen allergen through the epithelium to tissue mast cells. Our study showed that new hypotheses can arise from the application of discovery driven methodologies. To understand complex multifactorial diseases, such as type I hypersensitivity, this kind of hypotheses might be worth further analyses.

Validation of differential gene expression algorithms: application comparing fold-change estimation to hypothesis testing

BACKGROUND

Sustained research on the problem of determining which genes are differentially expressed on the basis of microarray data has yielded a plethora of statistical algorithms, each justified by theory, simulation, or ad hoc validation and yet differing in practical results from equally justified algorithms. Recently, a concordance method that measures agreement among gene lists have been introduced to assess various aspects of differential gene expression detection. This method has the advantage of basing its assessment solely on the results of real data analyses, but as it requires examining gene lists of given sizes, it may be unstable.

RESULTS

Two methodologies for assessing predictive error are described: a cross-validation method and a posterior predictive method. As a nonparametric method of estimating prediction error from observed expression levels, cross validation provides an empirical approach to assessing algorithms for detecting differential gene expression that is fully justified for large numbers of biological replicates. Because it leverages the knowledge that only a small portion of genes are differentially expressed, the posterior predictive method is expected to provide more reliable estimates of algorithm performance, allaying concerns about limited biological replication. In practice, the posterior predictive method can assess when its approximations are valid and when they are inaccurate. Under conditions in which its approximations are valid, it corroborates the results of cross validation. Both comparison methodologies are applicable to both single-channel and dual-channel microarrays. For the data sets considered, estimating prediction error by cross validation demonstrates that empirical Bayes methods based on hierarchical models tend to outperform algorithms based on selecting genes by their fold changes or by non-hierarchical model-selection criteria. (The latter two approaches have comparable performance.) The posterior predictive assessment corroborates these findings.

CONCLUSIONS

Algorithms for detecting differential gene expression may be compared by estimating each algorithm's error in predicting expression ratios, whether such ratios are defined across microarray channels or between two independent groups.According to two distinct estimators of prediction error, algorithms using hierarchical models outperform the other algorithms of the study. The fact that fold-change shrinkage performed as well as conventional model selection criteria calls for investigating algorithms that combine the strengths of significance testing and fold-change estimation.

Identification of S100A8-correlated genes for prediction of disease progression in non-muscle invasive bladder cancer

Background

S100 calcium binding protein A8 (S100A8) has been implicated as a prognostic indicator in several types of cancer. However, previous studies are limited in their ability to predict the clinical behavior of the cancer. Here, we sought to identify a molecular signature based on S100A8 expression and to assess its usefulness as a prognostic indicator of disease progression in non-muscle invasive bladder cancer (NMIBC).

Methods

We used 103 primary NMIBC specimens for microarray gene expression profiling. The median follow-up period for all patients was 57.6 months (range: 3.2 to 137.0 months). Various statistical methods, including the leave-one-out cross validation method, were applied to identify a gene expression signature able to predict the likelihood of progression. The prognostic value of the gene expression signature was validated in an independent cohort (n = 302).

Results

Kaplan-Meier estimates revealed significant differences in disease progression associated with the expression signature of S100A8-correlated genes (log-rank test, P < 0.001). Multivariate Cox regression analysis revealed that the expression signature of S100A8-correlated genes was a strong predictor of disease progression (hazard ratio = 15.225, 95% confidence interval = 1.746 to 133.52, P = 0.014). We validated our results in an independent cohort and confirmed that this signature produced consistent prediction patterns. Finally, gene network analyses of the signature revealed that S100A8, IL1B, and S100A9 could be important mediators of the progression of NMIBC.

Conclusions

The prognostic molecular signature defined by S100A8-correlated genes represents a promising diagnostic tool for the identification of NMIBC patients that have a high risk of progression to muscle invasive bladder cancer.

Dual KS: Defining Gene Sets with Tissue Set Enrichment Analysis

BACKGROUND

Gene set enrichment analysis (GSEA) is an analytic approach which simultaneously reduces the dimensionality of microarray data and enables ready inference of the biological meaning of observed gene expression patterns. Here we invert the GSEA process to identify class-specific gene signatures. Because our approach uses the Kolmogorov-Smirnov approach both to define class specific signatures and to classify samples using those signatures, we have termed this methodology "Dual-KS" (DKS).

RESULTS

The optimum gene signature identified by the DKS algorithm was smaller than other methods to which it was compared in 5 out of 10 datasets. The estimated error rate of DKS using the optimum gene signature was smaller than the estimated error rate of the random forest method in 4 out of the 10 datasets, and was equivalent in two additional datasets. DKS performance relative to other benchmarked algorithms was similar to its performance relative to random forests.

CONCLUSIONS

DKS is an efficient analytic methodology that can identify highly parsimonious gene signatures useful for classification in the context of microarray studies. The algorithm is available as the dualKS package for R as part of the bioconductor project.

A multi-filter enhanced genetic ensemble system for gene selection and sample classification of microarray data

Background

Feature selection techniques are critical to the analysis of high dimensional datasets. This is especially true in gene selection from microarray data which are commonly with extremely high feature-to-sample ratio. In addition to the essential objectives such as to reduce data noise, to reduce data redundancy, to improve sample classification accuracy, and to improve model generalization property, feature selection also helps biologists to focus on the selected genes to further validate their biological hypotheses.

Results

In this paper we describe an improved hybrid system for gene selection. It is based on a recently proposed genetic ensemble (GE) system. To enhance the generalization property of the selected genes or gene subsets and to overcome the overfitting problem of the GE system, we devised a mapping strategy to fuse the goodness information of each gene provided by multiple filtering algorithms. This information is then used for initialization and mutation operation of the genetic ensemble system.

Conclusion

We used four benchmark microarray datasets (including both binary-class and multi-class classification problems) for concept proving and model evaluation. The experimental results indicate that the proposed multi-filter enhanced genetic ensemble (MF-GE) system is able to improve sample classification accuracy, generate more compact gene subset, and converge to the selection results more quickly. The MF-GE system is very flexible as various combinations of multiple filters and classifiers can be incorporated based on the data characteristics and the user preferences.

Robust depth-based tools for the analysis of gene expression data

Microarray experiments provide data on the expression levels of thousands of genes and, therefore, statistical methods applicable to the analysis of such high-dimensional data are needed. In this paper, we propose robust nonparametric tools for the description and analysis of microarray data based on the concept of functional depth, which measures the centrality of an observation within a sample. We show that this concept can be easily adapted to high-dimensional observations and, in particular, to gene expression data. This allows the development of the following depth-based inference tools: (1) a scale curve for measuring and visualizing the dispersion of a set of points, (2) a rank test for deciding if 2 groups of multidimensional observations come from the same population, and (3) supervised classification techniques for assigning a new sample to one of G given groups. We apply these methods to microarray data, and to simulated data including contaminated models, and show that they are robust, efficient, and competitive with other procedures proposed in the literature, outperforming them in some situations.

Effect of training-sample size and classification difficulty on the accuracy of genomic predictors

Introduction

As part of the MicroArray Quality Control (MAQC)-II project, this analysis examines how the choice of univariate feature-selection methods and classification algorithms may influence the performance of genomic predictors under varying degrees of prediction difficulty represented by three clinically relevant endpoints.

Methods

We used gene-expression data from 230 breast cancers (grouped into training and independent validation sets), and we examined 40 predictors (five univariate feature-selection methods combined with eight different classifiers) for each of the three endpoints. Their classification performance was estimated on the training set by using two different resampling methods and compared with the accuracy observed in the independent validation set.

Results

A ranking of the three classification problems was obtained, and the performance of 120 models was estimated and assessed on an independent validation set. The bootstrapping estimates were closer to the validation performance than were the cross-validation estimates. The required sample size for each endpoint was estimated, and both gene-level and pathway-level analyses were performed on the obtained models.

Conclusions

We showed that genomic predictor accuracy is determined largely by an interplay between sample size and classification difficulty. Variations on univariate feature-selection methods and choice of classification algorithm have only a modest impact on predictor performance, and several statistically equally good predictors can be developed for any given classification problem.

ANMM4CBR: a case-based reasoning method for gene expression data classification

BACKGROUND

Accurate classification of microarray data is critical for successful clinical diagnosis and treatment. The "curse of dimensionality" problem and noise in the data, however, undermines the performance of many algorithms.

METHOD

In order to obtain a robust classifier, a novel Additive Nonparametric Margin Maximum for Case-Based Reasoning (ANMM4CBR) method is proposed in this article. ANMM4CBR employs a case-based reasoning (CBR) method for classification. CBR is a suitable paradigm for microarray analysis, where the rules that define the domain knowledge are difficult to obtain because usually only a small number of training samples are available. Moreover, in order to select the most informative genes, we propose to perform feature selection via additively optimizing a nonparametric margin maximum criterion, which is defined based on gene pre-selection and sample clustering. Our feature selection method is very robust to noise in the data.

RESULTS

The effectiveness of our method is demonstrated on both simulated and real data sets. We show that the ANMM4CBR method performs better than some state-of-the-art methods such as support vector machine (SVM) and k nearest neighbor (kNN), especially when the data contains a high level of noise.

AVAILABILITY

The source code is attached as an additional file of this paper.

Functional embedding for the classification of gene expression profiles

MOTIVATION

Low sample size n high-dimensional large p data with n<<p are commonly encountered in genomics and statistical genetics. Ill-conditioning of the variance-covariance matrix for such data renders the traditional multivariate data analytical approaches unattractive. On the other side, functional data analysis (FDA) approaches are designed for infinite-dimensional data and therefore may have potential for the analysis of large p data. We herein propose a functional embedding (FEM) technique, which exploits the interface between multivariate and functional data, aiming at borrowing strength across the sample through FDA techniques in order to resolve the difficulties caused by the high dimension p.

RESULTS

Using pairwise dissimilarities among predictor variables, one obtains a univariate configuration of these covariates. This is interpreted as variable ordination that defines the domain of a suitable function space, thus leading to the FEM of the high-dimensional data. The embedding may then be followed by functional logistic regression for the classification of high-dimensional multivariate data as an example for downstream analysis. The resulting functional classification is evaluated on several published gene expression array datasets and a mass spectrometric data, and is shown to compare favorably with various methods that have been employed previously for the classification of these high-dimensional gene expression profiles.

Feature selection for gene expression using model-based entropy

Gene expression data usually contain a large number of genes but a small number of samples. Feature selection for gene expression data aims at finding a set of genes that best discriminate biological samples of different types. Using machine learning techniques, traditional gene selection based on empirical mutual information suffers the data sparseness issue due to the small number of samples. To overcome the sparseness issue, we propose a model-based approach to estimate the entropy of class variables on the model, instead of on the data themselves. Here, we use multivariate normal distributions to fit the data, because multivariate normal distributions have maximum entropy among all real-valued distributions with a specified mean and standard deviation and are widely used to approximate various distributions. Given that the data follow a multivariate normal distribution, since the conditional distribution of class variables given the selected features is a normal distribution, its entropy can be computed with the log-determinant of its covariance matrix. Because of the large number of genes, the computation of all possible log-determinants is not efficient. We propose several algorithms to largely reduce the computational cost. The experiments on seven gene data sets and the comparison with other five approaches show the accuracy of the multivariate Gaussian generative model for feature selection, and the efficiency of our algorithms.

Linear Programming Approaches for Multiple-Class Discriminant and Classification Analysis

New linear programming approaches are proposed as nonparametric procedures for multiple-class discriminant and classification analysis. A new MSD model minimizing the sum of the classification errors is formulated to construct discriminant functions. This model has desirable properties because it is versatile and is immune to the pathologies of some of the earlier mathematical programming models for two-class classification. It is also purely systematic and algorithmic and no user ad hoc and trial judgment is required. Furthermore, it can be used as the basis to develop other models, such as a multiple-class support vector machine and a mixed integer programming model, for discrimination and classification. A MMD model minimizing the maximum of the classification errors, although with very limited use, is also studied. These models may also be considered as generalizations of mathematical programming formulations for two-class classification. By the same approach, other mathematical programming formulations for two-class classification can be easily generalized to multiple-class formulations. Results on standard as well as randomly generated test datasets show that the MSD model is very effective in generating powerful discriminant functions.

Introduction to the development and validation of predictive biomarker models from high-throughput data sets

High-throughput technologies can routinely assay biological or clinical samples and produce wide data sets where each sample is associated with tens of thousands of measurements. Such data sets can be mined to discover biomarkers and develop statistical models capable of predicting an endpoint of interest from data measured in the samples. The field of biomarker model development combines methods from statistics and machine learning to develop and evaluate predictive biomarker models. In this chapter, we discuss the computational steps involved in the development of biomarker models designed to predict information about individual samples and review approaches often used to implement each step. A practical example of biomarker model development in a large gene expression data set is presented. This example leverages BDVal, a suite of biomarker model development programs developed as an open-source project (see http://bdval.org /).

Chemometric brains for artificial tongues

The last years showed a significant trend toward the exploitation of rapid and economic analytical devices able to provide multiple information about samples. Among these, the so-called artificial tongues represent effective tools which allow a global sample characterization comparable to a fingerprint. Born as taste sensors for food evaluation, such devices proved to be useful for a wider number of purposes. In this review, a critical overview of artificial tongue applications over the last decade is outlined. In particular, the focus is centered on the chemometric techniques, which allow the extraction of valuable information from nonspecific data. The basic steps of signal processing and pattern recognition are discussed and the principal chemometric techniques are described in detail, highlighting benefits and drawbacks of each one. Furthermore, some novel methods recently introduced and particularly suitable for artificial tongue data are presented.

Optimal classifier selection and negative bias in error rate estimation: an empirical study on high-dimensional prediction

BACKGROUND

In biometric practice, researchers often apply a large number of different methods in a "trial-and-error" strategy to get as much as possible out of their data and, due to publication pressure or pressure from the consulting customer, present only the most favorable results. This strategy may induce a substantial optimistic bias in prediction error estimation, which is quantitatively assessed in the present manuscript. The focus of our work is on class prediction based on high-dimensional data (e.g. microarray data), since such analyses are particularly exposed to this kind of bias.

METHODS

In our study we consider a total of 124 variants of classifiers (possibly including variable selection or tuning steps) within a cross-validation evaluation scheme. The classifiers are applied to original and modified real microarray data sets, some of which are obtained by randomly permuting the class labels to mimic non-informative predictors while preserving their correlation structure.

RESULTS

We assess the minimal misclassification rate over the different variants of classifiers in order to quantify the bias arising when the optimal classifier is selected a posteriori in a data-driven manner. The bias resulting from the parameter tuning (including gene selection parameters as a special case) and the bias resulting from the choice of the classification method are examined both separately and jointly.

CONCLUSIONS

The median minimal error rate over the investigated classifiers was as low as 31% and 41% based on permuted uninformative predictors from studies on colon cancer and prostate cancer, respectively. We conclude that the strategy to present only the optimal result is not acceptable because it yields a substantial bias in error rate estimation, and suggest alternative approaches for properly reporting classification accuracy.

Comparison of linear discriminant analysis methods for the classification of cancer based on gene expression data

Background

More studies based on gene expression data have been reported in great detail, however, one major challenge for the methodologists is the choice of classification methods. The main purpose of this research was to compare the performance of linear discriminant analysis (LDA) and its modification methods for the classification of cancer based on gene expression data.

Methods

The classification performance of linear discriminant analysis (LDA) and its modification methods was evaluated by applying these methods to six public cancer gene expression datasets. These methods included linear discriminant analysis (LDA), prediction analysis for microarrays (PAM), shrinkage centroid regularized discriminant analysis (SCRDA), shrinkage linear discriminant analysis (SLDA) and shrinkage diagonal discriminant analysis (SDDA). The procedures were performed by software R 2.80.

Results

PAM picked out fewer feature genes than other methods from most datasets except from Brain dataset. For the two methods of shrinkage discriminant analysis, SLDA selected more genes than SDDA from most datasets except from 2-class lung cancer dataset. When comparing SLDA with SCRDA, SLDA selected more genes than SCRDA from 2-class lung cancer, SRBCT and Brain dataset, the result was opposite for the rest datasets. The average test error of LDA modification methods was lower than LDA method.

Conclusions

The classification performance of LDA modification methods was superior to that of traditional LDA with respect to the average error and there was no significant difference between theses modification methods.

SPRED: A machine learning approach for the identification of classical and non-classical secretory proteins in mammalian genomes

Eukaryotic protein secretion generally occurs via the classical secretory pathway that traverses the ER and Golgi apparatus. Secreted proteins usually contain a signal sequence with all the essential information required to target them for secretion. However, some proteins like fibroblast growth factors (FGF-1, FGF-2), interleukins (IL-1 alpha, IL-1 beta), galectins and thioredoxin are exported by an alternative pathway. This is known as leaderless or non-classical secretion and works without a signal sequence. Most computational methods for the identification of secretory proteins use the signal peptide as indicator and are therefore not able to identify substrates of non-classical secretion. In this work, we report a random forest method, SPRED, to identify secretory proteins from protein sequences irrespective of N-terminal signal peptides, thus allowing also correct classification of non-classical secretory proteins. Training was performed on a dataset containing 600 extracellular proteins and 600 cytoplasmic and/or nuclear proteins. The algorithm was tested on 180 extracellular proteins and 1380 cytoplasmic and/or nuclear proteins. We obtained 85.92% accuracy from training and 82.18% accuracy from testing. Since SPRED does not use N-terminal signals, it can detect non-classical secreted proteins by filtering those secreted proteins with an N-terminal signal by using SignalP. SPRED predicted 15 out of 19 experimentally verified non-classical secretory proteins. By scanning the entire human proteome we identified 566 protein sequences potentially undergoing non-classical secretion. The dataset and standalone version of the SPRED software is available at http://www.inb.uni-luebeck.de/tools-demos/spred/spred.

A comprehensive sensitivity analysis of microarray breast cancer classification under feature variability

BACKGROUND

Large discrepancies in signature composition and outcome concordance have been observed between different microarray breast cancer expression profiling studies. This is often ascribed to differences in array platform as well as biological variability. We conjecture that other reasons for the observed discrepancies are the measurement error associated with each feature and the choice of preprocessing method. Microarray data are known to be subject to technical variation and the confidence intervals around individual point estimates of expression levels can be wide. Furthermore, the estimated expression values also vary depending on the selected preprocessing scheme. In microarray breast cancer classification studies, however, these two forms of feature variability are almost always ignored and hence their exact role is unclear.

RESULTS

We have performed a comprehensive sensitivity analysis of microarray breast cancer classification under the two types of feature variability mentioned above. We used data from six state of the art preprocessing methods, using a compendium consisting of eight different datasets, involving 1131 hybridizations, containing data from both one and two-color array technology. For a wide range of classifiers, we performed a joint study on performance, concordance and stability. In the stability analysis we explicitly tested classifiers for their noise tolerance by using perturbed expression profiles that are based on uncertainty information directly related to the preprocessing methods. Our results indicate that signature composition is strongly influenced by feature variability, even if the array platform and the stratification of patient samples are identical. In addition, we show that there is often a high level of discordance between individual class assignments for signatures constructed on data coming from different preprocessing schemes, even if the actual signature composition is identical.

CONCLUSION

Feature variability can have a strong impact on breast cancer signature composition, as well as the classification of individual patient samples. We therefore strongly recommend that feature variability is considered in analyzing data from microarray breast cancer expression profiling experiments.

Using the ratio of means as the effect size measure in combining results of microarray experiments

Background

Development of efficient analytic methodologies for combining microarray results is a major challenge in gene expression analysis. The widely used effect size models are thought to provide an efficient modeling framework for this purpose, where the measures of association for each study and each gene are combined, weighted by the standard errors. A significant disadvantage of this strategy is that the quality of different data sets may be highly variable, but this information is usually neglected during the integration. Moreover, it is widely known that the estimated standard deviations are probably unstable in the commonly used effect size measures (such as standardized mean difference) when sample sizes in each group are small.

Results

We propose a re-parameterization of the traditional mean difference based effect measure by using the log ratio of means as an effect size measure for each gene in each study. The estimated effect sizes for all studies were then combined under two modeling frameworks: the quality-unweighted random effects models and the quality-weighted random effects models. We defined the quality measure as a function of the detection p-value, which indicates whether a transcript is reliably detected or not on the Affymetrix gene chip. The new effect size measure is evaluated and compared under the quality-weighted and quality-unweighted data integration frameworks using simulated data sets, and also in several data sets of prostate cancer patients and controls. We focus on identifying differentially expressed biomarkers for prediction of cancer outcomes.

Conclusion

Our results show that the proposed effect size measure (log ratio of means) has better power to identify differentially expressed genes, and that the detected genes have better performance in predicting cancer outcomes than the commonly used effect size measure, the standardized mean difference (SMD), under both quality-weighted and quality-unweighted data integration frameworks. The new effect size measure and the quality-weighted microarray data integration framework provide efficient ways to combine microarray results.

Tailored aggregation for classification

Compression and variable selection are two classical strategies to deal with large-dimension data sets in classification. We propose an alternative strategy, called aggregation, which consists of a clustering step of redundant variables and a compression step within each group. We develop a statistical framework to define tailored aggregation methods that can be combined with selection methods to build reliable classifiers that benefit from the information contained in redundant variables. Two algorithms are proposed for ordered and nonordered variables, respectively. Applications to the kNN and CART algorithms are presented.

Analysis of DNA microarray expression data

DNA microarrays are powerful tools for studying biological mechanisms and for developing prognostic and predictive classifiers for identifying the patients who require treatment and are best candidates for specific treatments. Because microarrays produce so much data from each specimen, they offer great opportunities for discovery and great dangers or producing misleading claims. Microarray based studies require clear objectives for selecting cases and appropriate analysis methods. Effective analysis of microarray data, where the number of measured variables is orders of magnitude greater than the number of cases, requires specialized statistical methods which have recently been developed. Recent literature reviews indicate that serious problems of analysis exist a substantial proportion of publications. This manuscript attempts to provide a non-technical summary of the key principles of statistical design and analysis for studies that utilize microarray expression profiling.

Correlation between gene expression and clinical data through linear and nonlinear principal components analyses: muscular dystrophies as case studies

The large dimension of microarray data and the complex dependence structure among genes make data analysis extremely challenging. In the last decade several statistical techniques have been proposed to tackle genome-wide expression data; however, clinical and molecular data associated to pathologies have often been considered as separate dimensions of the same phenomenon, especially when clinical variables lie on a multidimensional space. A better comprehension of the relationships between clinical and molecular data can be obtained if both data types are combined and integrated. In this work we adopt a multidimensional correlation strategy together with linear and nonlinear principal component, to integrate genetic and clinical information obtained from two sets of dystrophic patients. With this approach we decompose different aspects of clinical manifestations and correlate these features with the correspondent patterns of differential gene expression.

Graph ranking for exploratory gene data analysis

Background

Microarray technology has made it possible to simultaneously monitor the expression levels of thousands of genes in a single experiment. However, the large number of genes greatly increases the challenges of analyzing, comprehending and interpreting the resulting mass of data. Selecting a subset of important genes is inevitable to address the challenge. Gene selection has been investigated extensively over the last decade. Most selection procedures, however, are not sufficient for accurate inference of underlying biology, because biological significance does not necessarily have to be statistically significant. Additional biological knowledge needs to be integrated into the gene selection procedure.

Results

We propose a general framework for gene ranking. We construct a bipartite graph from the Gene Ontology (GO) and gene expression data. The graph describes the relationship between genes and their associated molecular functions. Under a species condition, edge weights of the graph are assigned to be gene expression level. Such a graph provides a mathematical means to represent both species-independent and species-dependent biological information. We also develop a new ranking algorithm to analyze the weighted graph via a kernelized spatial depth (KSD) approach. Consequently, the importance of gene and molecular function can be simultaneously ranked by a real-valued measure, KSD, which incorporates the global and local structure of the graph. Over-expressed and under-regulated genes also can be separately ranked.

Conclusion

The gene-function bigraph integrates molecular function annotations into gene expression data. The relevance of genes is described in the graph (through a common function). The proposed method provides an exploratory framework for gene data analysis.

From disease association to risk assessment: an optimistic view from genome-wide association studies on type 1 diabetes

Genome-wide association studies (GWAS) have been fruitful in identifying disease susceptibility loci for common and complex diseases. A remaining question is whether we can quantify individual disease risk based on genotype data, in order to facilitate personalized prevention and treatment for complex diseases. Previous studies have typically failed to achieve satisfactory performance, primarily due to the use of only a limited number of confirmed susceptibility loci. Here we propose that sophisticated machine-learning approaches with a large ensemble of markers may improve the performance of disease risk assessment. We applied a Support Vector Machine (SVM) algorithm on a GWAS dataset generated on the Affymetrix genotyping platform for type 1 diabetes (T1D) and optimized a risk assessment model with hundreds of markers. We subsequently tested this model on an independent Illumina-genotyped dataset with imputed genotypes (1,008 cases and 1,000 controls), as well as a separate Affymetrix-genotyped dataset (1,529 cases and 1,458 controls), resulting in area under ROC curve (AUC) of approximately 0.84 in both datasets. In contrast, poor performance was achieved when limited to dozens of known susceptibility loci in the SVM model or logistic regression model. Our study suggests that improved disease risk assessment can be achieved by using algorithms that take into account interactions between a large ensemble of markers. We are optimistic that genotype-based disease risk assessment may be feasible for diseases where a notable proportion of the risk has already been captured by SNP arrays.

Laplacian linear discriminant analysis approach to unsupervised feature selection

Until recently, numerous feature selection techniques have been proposed and found wide applications in genomics and proteomics. For instance, feature/gene selection has proven to be useful for biomarker discovery from microarray and mass spectrometry data. While supervised feature selection has been explored extensively, there are only a few unsupervised methods that can be applied to exploratory data analysis. In this paper, we address the problem of unsupervised feature selection. First, we extend Laplacian linear discriminant analysis (LLDA) to unsupervised cases. Second, we propose a novel algorithm for computing LLDA, which is efficient in the case of high dimensionality and small sample size as in microarray data. Finally, an unsupervised feature selection method, called LLDA-based Recursive Feature Elimination (LLDA-RFE), is proposed. We apply LLDA-RFE to several public data sets of cancer microarrays and compare its performance with those of Laplacian score and SVD-entropy, two state-of-the-art unsupervised methods, and with that of Fisher score, a supervised filter method. Our results demonstrate that LLDA-RFE outperforms Laplacian score and shows favorable performance against SVD-entropy. It performs even better than Fisher score for some of the data sets, despite the fact that LLDA-RFE is fully unsupervised.

Sparsity optimization method for multivariate feature screening for gene expression analysis

Constructing features from high-dimensional gene expression data is a critically important task for monitoring and predicting patients' diseases, or for knowledge discovery in computational molecular biology. The features need to capture the essential characteristics of the data to be maximally distinguishable. Moreover, the essential features usually lie in small or extremely low-dimensional subspaces, and it is crucial to find them for knowledge discovery and pattern classification. We present a computational method for extracting small or even extremely low-dimensional subspaces for multivariate feature screening and gene expression analysis using sparse optimization techniques. After we transform the feature screening problem into a convex optimization problem, we develop an efficient primal-dual interior-point method expressively for solving large-scale problems. The effectiveness of our method is confirmed by our experimental results. The computer programs will be publicly available.

Gene expression based leukemia sub-classification using committee neural networks

Analysis of gene expression data provides an objective and efficient technique for sub-classification of leukemia. The purpose of the present study was to design a committee neural networks based classification systems to subcategorize leukemia gene expression data. In the study, a binary classification system was considered to differentiate acute lymphoblastic leukemia from acute myeloid leukemia. A ternary classification system which classifies leukemia expression data into three subclasses including B-cell acute lymphoblastic leukemia, T-cell acute lymphoblastic leukemia and acute myeloid leukemia was also developed. In each classification system gene expression profiles of leukemia patients were first subjected to a sequence of simple preprocessing steps. This resulted in filtering out approximately 95 percent of the non-informative genes. The remaining 5 percent of the informative genes were used to train a set of artificial neural networks with different parameters and architectures. The networks that gave the best results during initial testing were recruited into a committee. The committee decision was by majority voting. The committee neural network system was later evaluated using data not used in training. The binary classification system classified microarray gene expression profiles into two categories with 100 percent accuracy and the ternary system correctly predicted the three subclasses of leukemia in over 97 percent of the cases.

Empirical Bayes Estimates for Large-Scale Prediction Problems

Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to large-scale prediction, where the optimum Bayes prediction rule is estimated employing the data from all the predictors. Microarray examples are used to illustrate the method. The results show a close connection with the shrunken centroids algorithm of Tibshirani et al. (2002), a frequentist regularization approach to large-scale prediction, and also with false discovery rate theory.

Adaptive regularization using the entire solution surface

Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L₁- and L_∞-norms, that adapts to a variety of situations including sparseness and nonsparseness, grouping and nongrouping. The proposed penalty performs grouping and adaptive regularization. In addition, we introduce a novel homotopy algorithm utilizing subgradients for developing regularization solution surfaces involving multiple regularizers. This permits efficient computation and adaptive tuning. Numerical experiments are conducted using simulation. In simulated and real examples, the proposed penalty compares well against popular alternatives.