Correcting for selection bias via cross-validation in the classification of microarray data

There is increasing interest in the use of diagnostic rules based on microarray data. These rules are formed by considering the expression levels of thousands of genes in tissue samples taken on patients of known classification with respect to a number of classes, representing, say, disease status or treatment strategy. As the final versions of these rules are usually based on a small subset of the available genes, there is a selection bias that has to be corrected for in the estimation of the associated error rates. We consider the problem using cross-validation. In particular, we present explicit formulae that are useful in explaining the layers of validation that have to be performed in order to avoid improperly cross-validated estimates.Comment: Published in at http://dx.doi.org/10.1214/193940307000000284 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

SUBIC: A Supervised Bi-Clustering Approach for Precision Medicine

Traditional medicine typically applies one-size-fits-all treatment for the entire patient population whereas precision medicine develops tailored treatment schemes for different patient subgroups. The fact that some factors may be more significant for a specific patient subgroup motivates clinicians and medical researchers to develop new approaches to subgroup detection and analysis, which is an effective strategy to personalize treatment. In this study, we propose a novel patient subgroup detection method, called Supervised Biclustring (SUBIC) using convex optimization and apply our approach to detect patient subgroups and prioritize risk factors for hypertension (HTN) in a vulnerable demographic subgroup (African-American). Our approach not only finds patient subgroups with guidance of a clinically relevant target variable but also identifies and prioritizes risk factors by pursuing sparsity of the input variables and encouraging similarity among the input variables and between the input and target variable

An Introduction to Recursive Partitioning: Rationale, Application and Characteristics of Classification and Regression Trees, Bagging and Random Forests

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, that can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine and bioinformatics within the past few years. High dimensional problems are common not only in genetics, but also in some areas of psychological research, where only few subjects can be measured due to time or cost constraints, yet a large amount of data is generated for each subject. Random forests have been shown to achieve a high prediction accuracy in such applications, and provide descriptive variable importance measures reflecting the impact of each variable in both main effects and interactions. The aim of this work is to introduce the principles of the standard recursive partitioning methods as well as recent methodological improvements, to illustrate their usage for low and high dimensional data exploration, but also to point out limitations of the methods and potential pitfalls in their practical application. Application of the methods is illustrated using freely available implementations in the R system for statistical computing

Stable Feature Selection for Biomarker Discovery

Feature selection techniques have been used as the workhorse in biomarker discovery applications for a long time. Surprisingly, the stability of feature selection with respect to sampling variations has long been under-considered. It is only until recently that this issue has received more and more attention. In this article, we review existing stable feature selection methods for biomarker discovery using a generic hierarchal framework. We have two objectives: (1) providing an overview on this new yet fast growing topic for a convenient reference; (2) categorizing existing methods under an expandable framework for future research and development

Robustness of Random Forest-based gene selection methods

Gene selection is an important part of microarray data analysis because it provides information that can lead to a better mechanistic understanding of an investigated phenomenon. At the same time, gene selection is very difficult because of the noisy nature of microarray data. As a consequence, gene selection is often performed with machine learning methods. The Random Forest method is particularly well suited for this purpose. In this work, four state-of-the-art Random Forest-based feature selection methods were compared in a gene selection context. The analysis focused on the stability of selection because, although it is necessary for determining the significance of results, it is often ignored in similar studies. The comparison of post-selection accuracy in the validation of Random Forest classifiers revealed that all investigated methods were equivalent in this context. However, the methods substantially differed with respect to the number of selected genes and the stability of selection. Of the analysed methods, the Boruta algorithm predicted the most genes as potentially important. The post-selection classifier error rate, which is a frequently used measure, was found to be a potentially deceptive measure of gene selection quality. When the number of consistently selected genes was considered, the Boruta algorithm was clearly the best. Although it was also the most computationally intensive method, the Boruta algorithm's computational demands could be reduced to levels comparable to those of other algorithms by replacing the Random Forest importance with a comparable measure from Random Ferns (a similar but simplified classifier). Despite their design assumptions, the minimal optimal selection methods, were found to select a high fraction of false positives

Identification of disease-causing genes using microarray data mining and gene ontology

Background: One of the best and most accurate methods for identifying disease-causing genes is monitoring gene expression values in different samples using microarray technology. One of the shortcomings of microarray data is that they provide a small quantity of samples with respect to the number of genes. This problem reduces the classification accuracy of the methods, so gene selection is essential to improve the predictive accuracy and to identify potential marker genes for a disease. Among numerous existing methods for gene selection, support vector machine-based recursive feature elimination (SVMRFE) has become one of the leading methods, but its performance can be reduced because of the small sample size, noisy data and the fact that the method does not remove redundant genes. Methods: We propose a novel framework for gene selection which uses the advantageous features of conventional methods and addresses their weaknesses. In fact, we have combined the Fisher method and SVMRFE to utilize the advantages of a filtering method as well as an embedded method. Furthermore, we have added a redundancy reduction stage to address the weakness of the Fisher method and SVMRFE. In addition to gene expression values, the proposed method uses Gene Ontology which is a reliable source of information on genes. The use of Gene Ontology can compensate, in part, for the limitations of microarrays, such as having a small number of samples and erroneous measurement results. Results: The proposed method has been applied to colon, Diffuse Large B-Cell Lymphoma (DLBCL) and prostate cancer datasets. The empirical results show that our method has improved classification performance in terms of accuracy, sensitivity and specificity. In addition, the study of the molecular function of selected genes strengthened the hypothesis that these genes are involved in the process of cancer growth. Conclusions: The proposed method addresses the weakness of conventional methods by adding a redundancy reduction stage and utilizing Gene Ontology information. It predicts marker genes for colon, DLBCL and prostate cancer with a high accuracy. The predictions made in this study can serve as a list of candidates for subsequent wet-lab verification and might help in the search for a cure for cancers

A nonparametric empirical Bayes framework for large-scale multiple testing

We propose a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. We use a computationally efficient predictive recursion marginal likelihood procedure to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonparametric empirical Bayes testing procedure, which we call PRtest, based on thresholding the estimated local false discovery rates. Simulations and real-data examples demonstrate that, compared to existing approaches, PRtest's careful handling of the non-null density can give a much better fit in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.Comment: 18 pages, 4 figures, 3 table

A Framework to Discover Emerging Patterns for Application in Microarray Data

Various supervised learning and gene selection methods have been used for cancer diagnosis. Most of these methods do not consider interactions between genes, although this might be interesting biologically and improve classification accuracy. Here we introduce a new CART-based method to discover emerging patterns. Emerging patterns are structures of the form (X1>a1)AND(X2<a2) that have differing frequencies in the considered classes. Interaction structures of this kind are of great interest in cancer research. Moreover, they can be used to define new variables for classification. Using simulated data sets, we show that our method allows the identification of emerging patterns with high efficiency. We also perform classification using two publicly available data sets (leukemia and colon cancer). For each data set, the method allows efficient classification as well as the identification of interesting patterns

Overview of Random Forest Methodology and Practical Guidance with Emphasis on Computational Biology and Bioinformatics

The Random Forest (RF) algorithm by Leo Breiman has become a standard data analysis tool in bioinformatics. It has shown excellent performance in settings where the number of variables is much larger than the number of observations, can cope with complex interaction structures as well as highly correlated variables and returns measures of variable importance. This paper synthesizes ten years of RF development with emphasis on applications to bioinformatics and computational biology. Special attention is given to practical aspects such as the selection of parameters, available RF implementations, and important pitfalls and biases of RF and its variable importance measures (VIMs). The paper surveys recent developments of the methodology relevant to bioinformatics as well as some representative examples of RF applications in this context and possible directions for future research