Regression approaches for microarray data analysis.

A variety of new procedures have been devised to handle the two-sample comparison (e.g., tumor versus normal tissue) of gene expression values as measured with microarrays. Such new methods are required in part because of some defining characteristics of microarray-based studies: (i) the very large number of genes contributing expression measures which far exceeds the number of samples (observations) available and (ii) the fact that by virtue of pathway/network relationships, the gene expression measures tend to be highly correlated. These concerns are exacerbated in the regression setting, where the objective is to relate gene expression, simultaneously for multiple genes, to some external outcome or phenotype. Correspondingly, several methods have been recently proposed for addressing these issues. We briefly critique some of these methods prior to a detailed evaluation of gene harvesting. This reveals that gene harvesting, without additional constraints, can yield artifactual solutions. Results obtained employing such constraints motivate the use of regularized regression procedures such as the lasso, least angle regression, and support vector machines. Model selection and solution multiplicity issues are also discussed. The methods are evaluated using a microarray-based study of cardiomyopathy in transgenic mice.     

Analysing microarray data using modular regulation analysis

MOTIVATION: Microarray experiments measure complex changes in the abundance of many mRNAs under different conditions. Current analysis methods cannot distinguish between direct and indirect effects on expression, or calculate the relative importance of mRNAs in effecting responses. RESULTS: Application of modular regulation analysis to microarray data reveals and quantifies which mRNA changes are important for cellular responses. The mRNAs are clustered, and then we calculate how perturbations alter each cluster and how strongly those clusters affect an output response. The product of these values quantifies how an input changes a response through each cluster. Two published datasets are analysed. Two mRNA clusters transmit most of the response of yeast doubling time to galactose; one contains mainly galactose metabolic genes, and the other a regulatory gene. Analysis of the response of yeast relative fitness to 2-deoxy-D-glucose reveals that control is distributed between several mRNA clusters, but experimental error limits statistical significance.     

Domain-enhanced analysis of microarray data using GO annotations

MOTIVATION: New biological systems technologies give scientists the ability to measure thousands of bio-molecules including genes, proteins, lipids and metabolites. We use domain knowledge, e.g. the Gene Ontology, to guide analysis of such data. By focusing on domain-aggregated results at, say the molecular function level, increased interpretability is available to biological scientists beyond what is possible if results are presented at the gene level. RESULTS: We use a 'top-down' approach to perform domain aggregation by first combining gene expressions before testing for differentially expressed patterns. This is in contrast to the more standard 'bottom-up' approach, where genes are first tested individually then aggregated by domain knowledge. The benefits are greater sensitivity for detecting signals. Our method, domain-enhanced analysis (DEA) is assessed and compared to other methods using simulation studies and analysis of two publicly available leukemia data sets. AVAILABILITY: Our DEA method uses functions available in R (http://www.r-project.org/) and SAS (http://www.sas.com/). The two experimental data sets used in our analysis are available in R as Bioconductor packages, 'ALL' and 'golubEsets' (http://www.bioconductor.org/). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Dimensionality reduction for microarray data using local mean based discriminant analysis

A new method is proposed for finding a low dimensional subspace of high dimensional microarray data. We developed a new criterion for constructing the weight matrix by using local neighborhood information to discover the intrinsic discriminant structure in the data. Also this approach applies regularized least square technique to extract relevant features. We assess the performance of the proposed methodology by applying it to four publicly available tumor datasets. In a low dimensional subspace, the proposed method classified these tumors accurately and reliably. Also, through a comparison study, we verify the reliability of the dimensionality reduction and discrimination results.     

Recovering filter-based microarray data for pathways analysis using a multipoint alignment strategy

The use of commercial microarrays is rapidly becoming the method of choice for profiling gene expression and assessing various disease states. Research Genetics has provided a series of biological and software tools to the research community for these analyses. The fidelity of data analysis using these tools is dependent on a series of well-defined reference control points in the array. During the course of our investigations, it became apparent that in some instances the reference control points that are required for analysis became lost in background noise. This effectively halted the analysis and the recovery of any information contained within that experiment. To recover this data and to increase analytical veracity, the simple strategy of superimposing a template of reference control points onto the experimental array was developed. The utility of this tool is established in this communication.     

Sample size for FDR-control in microarray data analysis

We consider identifying differentially expressing genes between two patient groups using microarray experiment. We propose a sample size calculation method for a specified number of true rejections while controlling the false discovery rate at a desired level. Input parameters for the sample size calculation include the allocation proportion in each group, the number of genes in each array, the number of differentially expressing genes and the effect sizes among the differentially expressing genes. We have a closed-form sample size formula if the projected effect sizes are equal among differentially expressing genes. Otherwise, our method requires a numerical method to solve an equation. Simulation studies are conducted to show that the calculated sample sizes are accurate in practical settings. The proposed method is demonstrated with a real study.     

Multivariate exploratory tools for microarray data analysis

The ultimate success of microarray technology in basic and applied biological sciences depends critically on the development of statistical methods for gene expression data analysis. The most widely used tests for differential expression of genes are essentially univariate. Such tests disregard the multidimensional structure of microarray data. Multivariate methods are needed to utilize the information hidden in gene interactions and hence to provide more powerful and biologically meaningful methods for finding subsets of differentially expressed genes. The objective of this paper is to develop methods of multidimensional search for biologically significant genes, considering expression signals as mutually dependent random variables. To attain these ends, we consider the utility of a pertinent distance between random vectors and its empirical counterpart constructed from gene expression data. The distance furnishes exploratory procedures aimed at finding a target subset of differentially expressed genes. To determine the size of the target subset, we resort to successive elimination of smaller subsets resulting from each step of a random search algorithm based on maximization of the proposed distance. Different stopping rules associated with this procedure are evaluated. The usefulness of the proposed approach is illustrated with an application to the analysis of two sets of gene expression data.     

Analyzing microarray data using CLANS

Analysis of microarray experiments is complicated by the huge amount of data involved. Searching for groups of co-expressed genes is akin to searching for protein families in a database as, in both cases, small subsets of genes with similar features are to be found within vast quantities of data. CLANS was originally developed to find protein families in large sets of amino acid sequences where the amount of data involved made phylogenetic approaches overly cumbersome. We present a number of improvements that greatly extend the previous version of CLANS and show its application to microarray data as well as its ability of incorporating additional information to facilitate interactive analysis. AVAILABILITY: The program is available for download from: http://bioinfoserver.rsbs.anu.edu.au/downloads/clans/     

Semiparametric clustering method for microarray data analysis

Clustering is a major tool for microarray gene expression data analysis. The existing clustering methods fall mainly into two categories: parametric and nonparametric. The parametric methods generally assume a mixture of parametric subdistributions. When the mixture distribution approximately fits the true data generating mechanism, the parametric methods perform well, but not so when there is nonnegligible deviation between them. On the other hand, the nonparametric methods, which usually do not make distributional assumptions, are robust but pay the price for efficiency loss. In an attempt to utilize the known mixture form to increase efficiency, and to free assumptions about the unknown subdistributions to enhance robustness, we propose a semiparametric method for clustering. The proposed approach possesses the form of parametric mixture, with no assumptions to the subdistributions. The subdistributions are estimated nonparametrically, with constraints just being imposed on the modes. An expectation-maximization (EM) algorithm along with a classification step is invoked to cluster the data, and a modified Bayesian information criterion (BIC) is employed to guide the determination of the optimal number of clusters. Simulation studies are conducted to assess the performance and the robustness of the proposed method. The results show that the proposed method yields reasonable partition of the data. As an illustration, the proposed method is applied to a real microarray data set to cluster genes.     

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, L(D|M), and the expected maximum likelihood of the model given an ensemble of surrogate data with randomly permuted label, L(D(0)|M). Typically, the computational burden for obtaining L(D(0)M) is immense, often exceeding the limits of available computing 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.     

Propagating uncertainty in microarray data analysis

Microarray technology is associated with many sources of experimentaluncertainty. In this review we discuss a number of approachesfor dealing with this uncertainty in the processing of datafrom microarray experiments. We focus here on the analysis ofhigh-density oligonucleotide arrays, such as the popular AffymetrixGeneChip® array, which contain multiple probes for eachtarget. This set of probes can be used to determine an estimatefor the target concentration and can also be used to determinethe experimental uncertainty associated with this measurement.This measurement uncertainty can then be propagated throughthe downstream analysis using probabilistic methods. We giveexamples showing how these credibility intervals can be usedto help identify differential expression, to combine informationfrom replicated experiments and to improve the performance ofprincipal component analysis.      

Pathway analysis of microarray data via regression.

Pathway analysis of microarray data evaluates gene expression profiles of a priori defined biological pathways in association with a phenotype of interest. We propose a unified pathway-analysis method that can be used for diverse phenotypes including binary, multiclass, continuous, count, rate, and censored survival phenotypes. The proposed method also allows covariate adjustments and correlation in the phenotype variable that is encountered in longitudinal, cluster-sampled, and paired designs. These are accomplished by combining the regression-based test statistic for each individual gene in a pathway of interest into a pathway-level test statistic. Applications of the proposed method are illustrated with two real pathway-analysis examples: one evaluating relapse-associated gene expression involving a matched-pair binary phenotype in children with acute lymphoblastic leukemia; and the other investigating gene expression in breast cancer tissues in relation to patients' survival (a censored survival phenotype). Implementations for various phenotypes are available in R. Additionally, an Excel Add-in for a user-friendly interface is currently being developed.     

Interval-valued analysis for discriminative gene selection and tissue sample classification using microarray data

An important application of gene expression data is to classify samples in a variety of diagnostic fields. However, high dimensionality and a small number of noisy samples pose significant challenges to existing classification methods. Focused on the problems of overfitting and sensitivity to noise of the dataset in the classification of microarray data, we propose an interval-valued analysis method based on a rough set technique to select discriminative genes and to use these genes to classify tissue samples of microarray data. We first select a small subset of genes based on interval-valued rough set by considering the preference-ordered domains of the gene expression data, and then classify test samples into certain classes with a term of similar degree. Experiments show that the proposed method is able to reach high prediction accuracies with a small number of selected genes and its performance is robust to noise.     

Analysis of longitudinal data with unmeasured confounders.

Confounding in longitudinal or clustered data creates special problems and opportunities because the relationship between the confounder and covariate of interest may differ across and within individuals or clusters. A well-known example of such confounding in longitudinal data is the presence of cohort and period effects in models of aging in epidemiologic research. We first formulate a data-generating model with confounding and derive the distribution of the response variable unconditional on the confounder. We then examine the properties of the regression coefficient for some analytic approaches when the confounder is omitted from the fitted model. The expected value of the regression coefficient differs in across- and within-individual regression. In the multivariate case, within- and between-individual information is combined and weighted according to the assumed covariance structure. We assume compound symmetry in the fitted covariance matrix and derive the variance, bias, and mean squared error of the slope estimate as a function of the fitted within-individual correlation. We find that even in this simplest multivariate case, the trade-off between bias and variance depends on a large number of parameters. It is generally preferable to fit correlations somewhat above the true correlation to minimize the effect of between-individual confounders or cohort effects. Period effects can lead to situations where it is advantageous to fit correlations that are below the true correlation. The results highlight the trade-offs inherent in the choice of method for analysis of longitudinal data, and show that an appropriate choice can be made only after determining whether within- or between-individual confounding is the major concern.     

Testing for differentially-expressed genes by maximum-likelihood analysis of microarray data.

Although two-color fluorescent DNA microarrays are now standard equipment in many molecular biology laboratories, methods for identifying differentially expressed genes in microarray data are still evolving. Here, we report a refined test for differentially expressed genes which does not rely on gene expression ratios but directly compares a series of repeated measurements of the two dye intensities for each gene. This test uses a statistical model to describe multiplicative and additive errors influencing an array experiment, where model parameters are estimated from observed intensities for all genes using the method of maximum likelihood. A generalized likelihood ratio test is performed for each gene to determine whether, under the model, these intensities are significantly different. We use this method to identify significant differences in gene expression among yeast cells growing in galactose-stimulating versus non-stimulating conditions and compare our results with current approaches for identifying differentially-expressed genes. The effect of sample size on parameter optimization is also explored, as is the use of the error model to compare the within- and between-slide intensity variation intrinsic to an array experiment.     

Between-group analysis of microarray data

MOTIVATION: Most supervised classification methods are limited by the requirement for more cases than variables. In microarray data the number of variables (genes) far exceeds the number of cases (arrays), and thus filtering and pre-selection of genes is required. We describe the application of Between Group Analysis (BGA) to the analysis of microarray data. A feature of BGA is that it can be used when the number of variables (genes) exceeds the number of cases (arrays). BGA is based on carrying out an ordination of groups of samples, using a standard method such as Correspondence Analysis (COA), rather than an ordination of the individual microarray samples. As such, it can be viewed as a method of carrying out COA with grouped data. RESULTS: We illustrate the power of the method using two cancer data sets. In both cases, we can quickly and accurately classify test samples from any number of specified a priori groups and identify the genes which characterize these groups. We obtained very high rates of correct classification, as determined by jack-knife or validation experiments with training and test sets. The results are comparable to those from other methods in terms of accuracy but the power and flexibility of BGA make it an especially attractive method for the analysis of microarray cancer data.     

Improved covariance matrix estimators for weighted analysis of microarray data.

Empirical Bayes models have been shown to be powerful tools for identifying differentially expressed genes from gene expression microarray data. An example is the WAME model, where a global covariance matrix accounts for array-to-array correlations as well as differing variances between arrays. However, the existing method for estimating the covariance matrix is very computationally intensive and the estimator is biased when data contains many regulated genes. In this paper, two new methods for estimating the covariance matrix are proposed. The first method is a direct application of the EM algorithm for fitting the multivariate t-distribution of the WAME model. In the second method, a prior distribution for the log fold-change is added to the WAME model, and a discrete approximation is used for this prior. Both methods are evaluated using simulated and real data. The first method shows equal performance compared to the existing method in terms of bias and variability, but is superior in terms of computer time. For large data sets (>15 arrays), the second method also shows superior computer run time. Moreover, for simulated data with regulated genes the second method greatly reduces the bias. With the proposed methods it is possible to apply the WAME model to large data sets with reasonable computer run times. The second method shows a small bias for simulated data, but appears to have a larger bias for real data with many regulated genes.     

Computational analysis of microarray data

Microarray experiments are providing unprecedented quantities of genome-wide data on gene-expression patterns. Although this technique has been enthusiastically developed and applied in many biological contexts, the management and analysis of the millions of data points that result from these experiments has received less attention. Sophisticated computational tools are available, but the methods that are used to analyse the data can have a profound influence on the interpretation of the results. A basic understanding of these computational tools is therefore required for optimal experimental design and meaningful data analysis.