Differential gene expression detection and sample classification using penalized linear regression models

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p > n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.     

Dimension reduction-based penalized logistic regression for cancer classification using microarray data

The use of penalized logistic regression for cancer classification using microarray expression data is presented. Two dimension reduction methods are respectively combined with the penalized logistic regression so that both the classification accuracy and computational speed are enhanced. Two other machine-learning methods, support vector machines and least-squares regression, have been chosen for comparison. It is shown that our methods have achieved at least equal or better results. They also have the advantage that the output probability can be explicitly given and the regression coefficients are easier to interpret. Several other aspects, such as the selection of penalty parameters and components, pertinent to the application of our methods for cancer classification are also discussed.     

Effective dimension reduction methods for tumor classification using gene expression data

MOTIVATION: One particular application of microarray data, is to uncover the molecular variation among cancers. One feature of microarray studies is the fact that the number n of samples collected is relatively small compared to the number p of genes per sample which are usually in the thousands. In statistical terms this very large number of predictors compared to a small number of samples or observations makes the classification problem difficult. An efficient way to solve this problem is by using dimension reduction statistical techniques in conjunction with nonparametric discriminant procedures. RESULTS: We view the classification problem as a regression problem with few observations and many predictor variables. We use an adaptive dimension reduction method for generalized semi-parametric regression models that allows us to solve the 'curse of dimensionality problem' arising in the context of expression data. The predictive performance of the resulting classification rule is illustrated on two well know data sets in the microarray literature: the leukemia data that is known to contain classes that are easy 'separable' and the colon data set.     

Classification of gene microarrays by penalized logistic regression

Classification of patient samples is an important aspect of cancer diagnosis and treatment. The support vector machine (SVM) has been successfully applied to microarray cancer diagnosis problems. However, one weakness of the SVM is that given a tumor sample, it only predicts a cancer class label but does not provide any estimate of the underlying probability. We propose penalized logistic regression (PLR) as an alternative to the SVM for the microarray cancer diagnosis problem. We show that when using the same set of genes, PLR and the SVM perform similarly in cancer classification, but PLR has the advantage of additionally providing an estimate of the underlying probability. Often a primary goal in microarray cancer diagnosis is to identify the genes responsible for the classification, rather than class prediction. We consider two gene selection methods in this paper, univariate ranking (UR) and recursive feature elimination (RFE). Empirical results indicate that PLR combined with RFE tends to select fewer genes than other methods and also performs well in both cross-validation and test samples. A fast algorithm for solving PLR is also described.     

Using rule-based machine learning for candidate disease gene prioritization and sample classification of cancer gene expression data

Microarray data analysis has been shown to provide an effective tool for studying cancer and genetic diseases. Although classical machine learning techniques have successfully been applied to find informative genes and to predict class labels for new samples, common restrictions of microarray analysis such as small sample sizes, a large attribute space and high noise levels still limit its scientific and clinical applications. Increasing the interpretability of prediction models while retaining a high accuracy would help to exploit the information content in microarray data more effectively. For this purpose, we evaluate our rule-based evolutionary machine learning systems, BioHEL and GAssist, on three public microarray cancer datasets, obtaining simple rule-based models for sample classification. A comparison with other benchmark microarray sample classifiers based on three diverse feature selection algorithms suggests that these evolutionary learning techniques can compete with state-of-the-art methods like support vector machines. The obtained models reach accuracies above 90% in two-level external cross-validation, with the added value of facilitating interpretation by using only combinations of simple if-then-else rules. As a further benefit, a literature mining analysis reveals that prioritizations of informative genes extracted from BioHEL's classification rule sets can outperform gene rankings obtained from a conventional ensemble feature selection in terms of the pointwise mutual information between relevant disease terms and the standardized names of top-ranked genes.     

Covariate adjustment in the analysis of microarray data from clinical studies

There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for follow-up validation studies. We develop two approaches to the analysis of microarray data in non-randomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic (ROC) curve for the analysis of gene expression data. The ideas are illustrated using data from a prostate cancer molecular profiling study.     

The clustering of regression models method with applications in gene expression data

Identification of differentially expressed genes and clustering of genes are two important and complementary objectives addressed with gene expression data. For the differential expression question, many "per-gene" analytic methods have been proposed. These methods can generally be characterized as using a regression function to independently model the observations for each gene; various adjustments for multiplicity are then used to interpret the statistical significance of these per-gene regression models over the collection of genes analyzed. Motivated by this common structure of per-gene models, we proposed a new model-based clustering method--the clustering of regression models method, which groups genes that share a similar relationship to the covariate(s). This method provides a unified approach for a family of clustering procedures and can be applied for data collected with various experimental designs. In addition, when combined with per-gene methods for assessing differential expression that employ the same regression modeling structure, an integrated framework for the analysis of microarray data is obtained. The proposed methodology was applied to two microarray data sets, one from a breast cancer study and the other from a yeast cell cycle study.     

Topology-based cancer classification and related pathway mining using microarray data

Cancer classification is the critical basis for patient-tailored therapy, while pathway analysis is a promising method to discover the underlying molecular mechanisms related to cancer development by using microarray data. However, linking the molecular classification and pathway analysis with gene network approach has not been discussed yet. In this study, we developed a novel framework based on cancer class-specific gene networks for classification and pathway analysis. This framework involves a novel gene network construction, named ordering network, which exhibits the power-law node-degree distribution as seen in correlation networks. The results obtained from five public cancer datasets showed that the gene networks with ordering relationship are better than those with correlation relationship in terms of accuracy and stability of the classification performance. Furthermore, we integrated the ordering networks, classification information and pathway database to develop the topology-based pathway analysis for identifying cancer class-specific pathways, which might be essential in the biological significance of cancer. Our results suggest that the topology-based classification technology can precisely distinguish cancer subclasses and the topology-based pathway analysis can characterize the correspondent biochemical pathways even if there are subtle, but consistent, changes in gene expression, which may provide new insights into the underlying molecular mechanisms of tumorigenesis.     

A comprehensive evaluation of multicategory classification methods for microarray gene expression cancer diagnosis

MOTIVATION: Cancer diagnosis is one of the most important emerging clinical applications of gene expression microarray technology. We are seeking to develop a computer system for powerful and reliable cancer diagnostic model creation based on microarray data. To keep a realistic perspective on clinical applications we focus on multicategory diagnosis. To equip the system with the optimum combination of classifier, gene selection and cross-validation methods, we performed a systematic and comprehensive evaluation of several major algorithms for multicategory classification, several gene selection methods, multiple ensemble classifier methods and two cross-validation designs using 11 datasets spanning 74 diagnostic categories and 41 cancer types and 12 normal tissue types. RESULTS: Multicategory support vector machines (MC-SVMs) are the most effective classifiers in performing accurate cancer diagnosis from gene expression data. The MC-SVM techniques by Crammer and Singer, Weston and Watkins and one-versus-rest were found to be the best methods in this domain. MC-SVMs outperform other popular machine learning algorithms, such as k-nearest neighbors, backpropagation and probabilistic neural networks, often to a remarkable degree. Gene selection techniques can significantly improve the classification performance of both MC-SVMs and other non-SVM learning algorithms. Ensemble classifiers do not generally improve performance of the best non-ensemble models. These results guided the construction of a software system GEMS (Gene Expression Model Selector) that automates high-quality model construction and enforces sound optimization and performance estimation procedures. This is the first such system to be informed by a rigorous comparative analysis of the available algorithms and datasets. AVAILABILITY: The software system GEMS is available for download from http://www.gems-system.org for non-commercial use. CONTACT: alexander.statnikov@vanderbilt.edu.     

Pathway analysis using random forests classification and regression

MOTIVATION: Although numerous methods have been developed to better capture biological information from microarray data, commonly used single gene-based methods neglect interactions among genes and leave room for other novel approaches. For example, most classification and regression methods for microarray data are based on the whole set of genes and have not made use of pathway information. Pathway-based analysis in microarray studies may lead to more informative and relevant knowledge for biological researchers. RESULTS: In this paper, we describe a pathway-based classification and regression method using Random Forests to analyze gene expression data. The proposed methods allow researchers to rank important pathways from externally available databases, discover important genes, find pathway-based outlying cases and make full use of a continuous outcome variable in the regression setting. We also compared Random Forests with other machine learning methods using several datasets and found that Random Forests classification error rates were either the lowest or the second-lowest. By combining pathway information and novel statistical methods, this procedure represents a promising computational strategy in dissecting pathways and can provide biological insight into the study of microarray data. AVAILABILITY: Source code written in R is available from http://bioinformatics.med.yale.edu/pathway-analysis/rf.htm.     

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.     

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.     

Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data

MOTIVATION: An important application of microarray technology is to relate gene expression profiles to various clinical phenotypes of patients. Success has been demonstrated in molecular classification of cancer in which the gene expression data serve as predictors and different types of cancer serve as a categorical outcome variable. However, there has been less research in linking gene expression profiles to the censored survival data such as patients' overall survival time or time to cancer relapse. It would be desirable to have models with good prediction accuracy and parsimony property. RESULTS: We propose to use the L(1) penalized estimation for the Cox model to select genes that are relevant to patients' survival and to build a predictive model for future prediction. The computational difficulty associated with the estimation in the high-dimensional and low-sample size settings can be efficiently solved by using the recently developed least-angle regression (LARS) method. Our simulation studies and application to real datasets on predicting survival after chemotherapy for patients with diffuse large B-cell lymphoma demonstrate that the proposed procedure, which we call the LARS-Cox procedure, can be used for identifying important genes that are related to time to death due to cancer and for building a parsimonious model for predicting the survival of future patients. The LARS-Cox regression gives better predictive performance than the L(2) penalized regression and a few other dimension-reduction based methods. CONCLUSIONS: We conclude that the proposed LARS-Cox procedure can be very useful in identifying genes relevant to survival phenotypes and in building a parsimonious predictive model that can be used for classifying future patients into clinically relevant high- and low-risk groups based on the gene expression profile and survival times of previous patients.     

CASPAR: a hierarchical bayesian approach to predict survival times in cancer from gene expression data

MOTIVATION: DNA microarrays allow the simultaneous measurement of thousands of gene expression levels in any given patient sample. Gene expression data have been shown to correlate with survival in several cancers, however, analysis of the data is difficult, since typically at most a few hundred patients are available, resulting in severely underdetermined regression or classification models. Several approaches exist to classify patients in different risk classes, however, relatively little has been done with respect to the prediction of actual survival times. We introduce CASPAR, a novel method to predict true survival times for the individual patient based on microarray measurements. CASPAR is based on a multivariate Cox regression model that is embedded in a Bayesian framework. A hierarchical prior distribution on the regression parameters is specifically designed to deal with high dimensionality (large number of genes) and low sample size settings, that are typical for microarray measurements. This enables CASPAR to automatically select small, most informative subsets of genes for prediction. RESULTS: Validity of the method is demonstrated on two publicly available datasets on diffuse large B-cell lymphoma (DLBCL) and on adenocarcinoma of the lung. The method successfully identifies long and short survivors, with high sensitivity and specificity. We compare our method with two alternative methods from the literature, demonstrating superior results of our approach. In addition, we show that CASPAR can further refine predictions made using clinical scoring systems such as the International Prognostic Index (IPI) for DLBCL and clinical staging for lung cancer, thus providing an additional tool for the clinician. An analysis of the genes identified confirms previously published results, and furthermore, new candidate genes correlated with survival are identified.     

Meta-analysis of gene expression data: a predictor-based approach

MOTIVATION: With the increasing availability of cancer microarray data sets there is a growing need for integrative computational methods that evaluate multiple independent microarray data sets investigating a common theme or disorder. Meta-analysis techniques are designed to overcome the low sample size typical to microarray experiments and yield more valid and informative results than each experiment separately. RESULTS: We propose a new meta-analysis technique that aims at finding a set of classifying genes, whose expression level may be used to answering the classification question in hand. Specifically, we apply our method to two independent lung cancer microarray data sets and identify a joint core subset of genes which putatively play an important role in tumor genesis of the lung. The robustness of the identified joint core set is demonstrated on a third unseen lung cancer data set, where it leads to successful classification using very few top-ranked genes. Identifying such a set of genes is of significant importance when searching for biologically meaningful biomarkers. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

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.     

Logistic regression for disease classification using microarray data: model selection in a large p and small n case

MOTIVATION: Logistic regression is a standard method for building prediction models for a binary outcome and has been extended for disease classification with microarray data by many authors. A feature (gene) selection step, however, must be added to penalized logistic modeling due to a large number of genes and a small number of subjects. Model selection for this two-step approach requires new statistical tools because prediction error estimation ignoring the feature selection step can be severely downward biased. Generic methods such as cross-validation and non-parametric bootstrap can be very ineffective due to the big variability in the prediction error estimate. RESULTS: We propose a parametric bootstrap model for more accurate estimation of the prediction error that is tailored to the microarray data by borrowing from the extensive research in identifying differentially expressed genes, especially the local false discovery rate. The proposed method provides guidance on the two critical issues in model selection: the number of genes to include in the model and the optimal shrinkage for the penalized logistic regression. We show that selecting more than 20 genes usually helps little in further reducing the prediction error. Application to Golub's leukemia data and our own cervical cancer data leads to highly accurate prediction models. AVAILABILITY: R library GeneLogit at http://geocities.com/jg_liao