Extreme Value Distribution Based Gene Selection Criteria for Discriminant Microarray Data Analysis Using Logistic Regression

One important issue commonly encountered in the analysis of microarray data is to decide which and how many genes should be selected for further studies. For discriminant microarray data analyses based on statistical models, such as the logistic regression models, gene selection can be accomplished by a comparison of the maximum likelihood of the model given the real data, $\hat{L}(D|M)$, and the expected maximum likelihood of the model given an ensemble of surrogate data with randomly permuted label, $\hat{L}(D_0|M)$. Typically, the computational burden for obtaining $\hat{L}(D_0|M)$ is immense, often exceeding the limits of computing available resources by orders of magnitude. Here, we propose an approach that circumvents such heavy computations by mapping the simulation problem to an extreme-value problem. We present the derivation of an asymptotic distribution of the extreme-value as well as its mean, median, and variance. Using this distribution, we propose two gene selection criteria, and we apply them to two microarray datasets and three classification tasks for illustration.Comment: to be published in Journal of Computational Biology (2004

GOexpress: an R/Bioconductor package for the identification and visualisation of robust gene ontology signatures through supervised learning of gene expression data

Background: Identification of gene expression profiles that differentiate experimental groups is critical for discovery and analysis of key molecular pathways and also for selection of robust diagnostic or prognostic biomarkers. While integration of differential expression statistics has been used to refine gene set enrichment analyses, such approaches are typically limited to single gene lists resulting from simple two-group comparisons or time-series analyses. In contrast, functional class scoring and machine learning approaches provide powerful alternative methods to leverage molecular measurements for pathway analyses, and to compare continuous and multi-level categorical factors. Results: We introduce GOexpress, a software package for scoring and summarising the capacity of gene ontology features to simultaneously classify samples from multiple experimental groups. GOexpress integrates normalised gene expression data (e.g., from microarray and RNA-seq experiments) and phenotypic information of individual samples with gene ontology annotations to derive a ranking of genes and gene ontology terms using a supervised learning approach. The default random forest algorithm allows interactions between all experimental factors, and competitive scoring of expressed genes to evaluate their relative importance in classifying predefined groups of samples. Conclusions: GOexpress enables rapid identification and visualisation of ontology-related gene panels that robustly classify groups of samples and supports both categorical (e.g., infection status, treatment) and continuous (e.g., time-series, drug concentrations) experimental factors. The use of standard Bioconductor extension packages and publicly available gene ontology annotations facilitates straightforward integration of GOexpress within existing computational biology pipelines.Department of Agriculture, Food and the MarineEuropean Commission - Seventh Framework Programme (FP7)Science Foundation IrelandUniversity College Dubli

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

Application of Volcano Plots in Analyses of mRNA Differential Expressions with Microarrays

Volcano plot displays unstandardized signal (e.g. log-fold-change) against noise-adjusted/standardized signal (e.g. t-statistic or -log10(p-value) from the t test). We review the basic and an interactive use of the volcano plot, and its crucial role in understanding the regularized t-statistic. The joint filtering gene selection criterion based on regularized statistics has a curved discriminant line in the volcano plot, as compared to the two perpendicular lines for the "double filtering" criterion. This review attempts to provide an unifying framework for discussions on alternative measures of differential expression, improved methods for estimating variance, and visual display of a microarray analysis result. We also discuss the possibility to apply volcano plots to other fields beyond microarray.Comment: 8 figure

The Reproducibility of Lists of Differentially Expressed Genes in Microarray Studies

Reproducibility is a fundamental requirement in scientific experiments and clinical contexts. Recent publications raise concerns about the reliability of microarray technology because of the apparent lack of agreement between lists of differentially expressed genes (DEGs). In this study we demonstrate that (1) such discordance may stem from ranking and selecting DEGs solely by statistical significance (P) derived from widely used simple t-tests; (2) when fold change (FC) is used as the ranking criterion, the lists become much more reproducible, especially when fewer genes are selected; and (3) the instability of short DEG lists based on P cutoffs is an expected mathematical consequence of the high variability of the t-values. We recommend the use of FC ranking plus a non-stringent P cutoff as a baseline practice in order to generate more reproducible DEG lists. The FC criterion enhances reproducibility while the P criterion balances sensitivity and specificity

Algebraic Comparison of Partial Lists in Bioinformatics

The outcome of a functional genomics pipeline is usually a partial list of genomic features, ranked by their relevance in modelling biological phenotype in terms of a classification or regression model. Due to resampling protocols or just within a meta-analysis comparison, instead of one list it is often the case that sets of alternative feature lists (possibly of different lengths) are obtained. Here we introduce a method, based on the algebraic theory of symmetric groups, for studying the variability between lists ("list stability") in the case of lists of unequal length. We provide algorithms evaluating stability for lists embedded in the full feature set or just limited to the features occurring in the partial lists. The method is demonstrated first on synthetic data in a gene filtering task and then for finding gene profiles on a recent prostate cancer dataset

A framework for list representation, enabling list stabilization through incorporation of gene exchangeabilities

Analysis of multivariate data sets from e.g. microarray studies frequently results in lists of genes which are associated with some response of interest. The biological interpretation is often complicated by the statistical instability of the obtained gene lists with respect to sampling variations, which may partly be due to the functional redundancy among genes, implying that multiple genes can play exchangeable roles in the cell. In this paper we use the concept of exchangeability of random variables to model this functional redundancy and thereby account for the instability attributable to sampling variations. We present a flexible framework to incorporate the exchangeability into the representation of lists. The proposed framework supports straightforward robust comparison between any two lists. It can also be used to generate new, more stable gene rankings incorporating more information from the experimental data. Using a microarray data set from lung cancer patients we show that the proposed method provides more robust gene rankings than existing methods with respect to sampling variations, without compromising the biological significance

An evaluation of DNA-damage response and cell-cycle pathways for breast cancer classification

Accurate subtyping or classification of breast cancer is important for ensuring proper treatment of patients and also for understanding the molecular mechanisms driving this disease. While there have been several gene signatures proposed in the literature to classify breast tumours, these signatures show very low overlaps, different classification performance, and not much relevance to the underlying biology of these tumours. Here we evaluate DNA-damage response (DDR) and cell cycle pathways, which are critical pathways implicated in a considerable proportion of breast tumours, for their usefulness and ability in breast tumour subtyping. We think that subtyping breast tumours based on these two pathways could lead to vital insights into molecular mechanisms driving these tumours. Here, we performed a systematic evaluation of DDR and cell-cycle pathways for subtyping of breast tumours into the five known intrinsic subtypes. Homologous Recombination (HR) pathway showed the best performance in subtyping breast tumours, indicating that HR genes are strongly involved in all breast tumours. Comparisons of pathway based signatures and two standard gene signatures supported the use of known pathways for breast tumour subtyping. Further, the evaluation of these standard gene signatures showed that breast tumour subtyping, prognosis and survival estimation are all closely related. Finally, we constructed an all-inclusive super-signature by combining (union of) all genes and performing a stringent feature selection, and found it to be reasonably accurate and robust in classification as well as prognostic value. Adopting DDR and cell cycle pathways for breast tumour subtyping achieved robust and accurate breast tumour subtyping, and constructing a super-signature which contains feature selected mix of genes from these molecular pathways as well as clinical aspects is valuable in clinical practice.Comment: 28 pages, 7 figures, 6 table

EFSIS: Ensemble Feature Selection Integrating Stability

Ensemble learning that can be used to combine the predictions from multiple learners has been widely applied in pattern recognition, and has been reported to be more robust and accurate than the individual learners. This ensemble logic has recently also been more applied in feature selection. There are basically two strategies for ensemble feature selection, namely data perturbation and function perturbation. Data perturbation performs feature selection on data subsets sampled from the original dataset and then selects the features consistently ranked highly across those data subsets. This has been found to improve both the stability of the selector and the prediction accuracy for a classifier. Function perturbation frees the user from having to decide on the most appropriate selector for any given situation and works by aggregating multiple selectors. This has been found to maintain or improve classification performance. Here we propose a framework, EFSIS, combining these two strategies. Empirical results indicate that EFSIS gives both high prediction accuracy and stability.Comment: 20 pages, 3 figure