A permutation-based multiple testing method for time-course microarray experiments

Background  

Time-course microarray experiments are widely used to study the temporal profiles of gene expression. Storey et al. (2005) developed a method for analyzing time-course microarray studies that can be applied to discovering genes whose expression trajectories change over time within a single biological group, or those that follow different time trajectories among multiple groups. They estimated the expression trajectories of each gene using natural cubic splines under the null (no time-course) and alternative (time-course) hypotheses, and used a goodness of fit test statistic to quantify the discrepancy. The null distribution of the statistic was approximated through a bootstrap method. Gene expression levels in microarray data are often complicatedly correlated. An accurate type I error control adjusting for multiple testing requires the joint null distribution of test statistics for a large number of genes. For this purpose, permutation methods have been widely used because of computational ease and their intuitive interpretation.     

Nonparametric tests for differential gene expression and interaction effects in multi-factorial microarray experiments

Background  

Numerous nonparametric approaches have been proposed in literature to detect differential gene expression in the setting of two user-defined groups. However, there is a lack of nonparametric procedures to analyze microarray data with multiple factors attributing to the gene expression. Furthermore, incorporating interaction effects in the analysis of microarray data has long been of great interest to biological scientists, little of which has been investigated in the nonparametric framework.     

Sample size calculation for multiple testing in microarray data analysis

Microarray technology is rapidly emerging for genome-wide screening of differentially expressed genes between clinical subtypes or different conditions of human diseases. Traditional statistical testing approaches, such as the two-sample t-test or Wilcoxon test, are frequently used for evaluating statistical significance of informative expressions but require adjustment for large-scale multiplicity. Due to its simplicity, Bonferroni adjustment has been widely used to circumvent this problem. It is well known, however, that the standard Bonferroni test is often very conservative. In the present paper, we compare three multiple testing procedures in the microarray context: the original Bonferroni method, a Bonferroni-type improved single-step method and a step-down method. The latter two methods are based on nonparametric resampling, by which the null distribution can be derived with the dependency structure among gene expressions preserved and the family-wise error rate accurately controlled at the desired level. We also present a sample size calculation method for designing microarray studies. Through simulations and data analyses, we find that the proposed methods for testing and sample size calculation are computationally fast and control error and power precisely.     

Intensity-based hierarchical Bayes method improves testing for differentially expressed genes in microarray experiments

Background  

The small sample sizes often used for microarray experiments result in poor estimates of variance if each gene is considered independently. Yet accurately estimating variability of gene expression measurements in microarray experiments is essential for correctly identifying differentially expressed genes. Several recently developed methods for testing differential expression of genes utilize hierarchical Bayesian models to "pool" information from multiple genes. We have developed a statistical testing procedure that further improves upon current methods by incorporating the well-documented relationship between the absolute gene expression level and the variance of gene expression measurements into the general empirical Bayes framework.     

Estimation and control of multiple testing error rates for microarray studies

The analysis of microarray data often involves performing a large number of statistical tests, usually at least one test per queried gene. Each test has a certain probability of reaching an incorrect inference; therefore, it is crucial to estimate or control error rates that measure the occurrence of erroneous conclusions in reporting and interpreting the results of a microarray study. In recent years, many innovative statistical methods have been developed to estimate or control various error rates for microarray studies. Researchers need guidance choosing the appropriate statistical methods for analysing these types of data sets. This review describes a family of methods that use a set of P-values to estimate or control the false discovery rate and similar error rates. Finally, these methods are classified in a manner that suggests the appropriate method for specific applications and diagnostic procedures that can identify problems in the analysis are described.     

Bayesian models based on test statistics for multiple hypothesis testing problems

Motivation: We propose a Bayesian method for the problem ofmultiple hypothesis testing that is routinely encountered inbioinformatics research, such as the differential gene expressionanalysis. Our algorithm is based on modeling the distributionsof test statistics under both null and alternative hypotheses.We substantially reduce the complexity of the process of definingposterior model probabilities by modeling the test statisticsdirectly instead of modeling the full data. Computationally,we apply a Bayesian FDR approach to control the number of rejectionsof null hypotheses. To check if our model assumptions for thetest statistics are valid for various bioinformatics experiments,we also propose a simple graphical model-assessment tool. Results: Using extensive simulations, we demonstrate the performanceof our models and the utility of the model-assessment tool.In the end, we apply the proposed methodology to an siRNA screeningand a gene expression experiment. Contact: yuanji{at}mdanderson.org Supplementary information: Supplementary data are availableat Bioinformatics online. Associate Editor: Chris Stoeckert     

A powerful truncated tail strength method for testing multiple null hypotheses in one dataset

This article re-analyses a prey-predator model with a refuge introduced by one of the founders of population ecology Gause and his co-workers to explain discrepancies between their observations and predictions of the Lotka-Volterra prey-predator model. They replaced the linear functional response used by Lotka and Volterra by a saturating functional response with a discontinuity at a critical prey density. At concentrations below this critical density prey were effectively in a refuge while at a higher densities they were available to predators. Thus, their functional response was of the Holling type III. They analyzed this model and predicted existence of a limit cycle in predator-prey dynamics. In this article I show that their model is ill posed, because trajectories are not well defined. Using the Filippov method, I define and analyze solutions of the Gause model. I show that depending on parameter values, there are three possibilities: (1) trajectories converge to a limit cycle, as predicted by Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity.     

A friendly statistics package for microarray analysis

SUMMARY: The friendly statistics package for microarray analysis (FSPMA) is a tool that aims to fill the gap between simple to use and powerful analysis. FSPMA is a platform-independent R-package that allows efficient exploration of microarray data without the need for computer programming. Analysis is based on a mixed model ANOVA library (YASMA) that was extended to allow more flexible comparisons and other useful operations like k nearest neighbour imputing and spike-based normalization. Processing is controlled by a definition file that specifies all the steps necessary to derive analysis results from quantified microarray data. In addition to providing analysis without programming, the definition file also serves as exact documentation of all the analysis steps. AVAILABILITY: The library is available under GPL 2 license and, together with additional information, provided at http://www.ccbi.cam.ac.uk/software/psyk/software.html#fspma     

Correlation statistics for cDNA microarray image analysis

In this paper, correlation of the pixels comprising a microarray spot is investigated. Subsequently, correlation statistics, namely, Pearson correlation and Spearman rank correlation, are used to segment the foreground and background intensity of microarray spots. The performance of correlation-based segmentation is compared to clustering-based (PAM, k-means) and seeded-region growing techniques (SPOT). It is shown that correlation-based segmentation is useful in flagging poorly hybridized spots, thus minimizing false-positives. The present study also raises the intriguing question of whether a change in correlation can be an indicator of differential gene expression.     

Towards accurate estimation of the proportion of true null hypotheses in multiple testing

BACKGROUND: Biomedical researchers are now often faced with situations where it is necessary to test a large number of hypotheses simultaneously, eg, in comparative gene expression studies using high-throughput microarray technology. To properly control false positive errors the FDR (false discovery rate) approach has become widely used in multiple testing. The accurate estimation of FDR requires the proportion of true null hypotheses being accurately estimated. To date many methods for estimating this quantity have been proposed. Typically when a new method is introduced, some simulations are carried out to show the improved accuracy of the new method. However, the simulations are often very limited to covering only a few points in the parameter space. RESULTS: Here I have carried out extensive in silico experiments to compare some commonly used methods for estimating the proportion of true null hypotheses. The coverage of these simulations is unprecedented thorough over the parameter space compared to typical simulation studies in the literature. Thus this work enables us to draw conclusions globally as to the performance of these different methods. It was found that a very simple method gives the most accurate estimation in a dominantly large area of the parameter space. Given its simplicity and its overall superior accuracy I recommend its use as the first choice for estimating the proportion of true null hypotheses in multiple testing.     

The optimal discovery procedure for large-scale significance testing, with applications to comparative microarray experiments

As much of the focus of genetics and molecular biology has shifted toward the systems level, it has become increasingly important to accurately extract biologically relevant signal from thousands of related measurements. The common property among these high-dimensional biological studies is that the measured features have a rich and largely unknown underlying structure. One example of much recent interest is identifying differentially expressed genes in comparative microarray experiments. We propose a new approach aimed at optimally performing many hypothesis tests in a high-dimensional study. This approach estimates the optimal discovery procedure (ODP), which has recently been introduced and theoretically shown to optimally perform multiple significance tests. Whereas existing procedures essentially use data from only one feature at a time, the ODP approach uses the relevant information from the entire data set when testing each feature. In particular, we propose a generally applicable estimate of the ODP for identifying differentially expressed genes in microarray experiments. This microarray method consistently shows favorable performance over five highly used existing methods. For example, in testing for differential expression between two breast cancer tumor types, the ODP provides increases from 72% to 185% in the number of genes called significant at a false discovery rate of 3%. Our proposed microarray method is freely available to academic users in the open-source, point-and-click EDGE software package.     

Spotting effect in microarray experiments

Background  

Microarray data must be normalized because they suffer from multiple biases. We have identified a source of spatial experimental variability that significantly affects data obtained with Cy3/Cy5 spotted glass arrays. It yields a periodic pattern altering both signal (Cy3/Cy5 ratio) and intensity across the array.     

Gene selection for sample classifications in microarray experiments

DNA microarray technology provides useful tools for profiling global gene expression patterns in different cell/tissue samples. One major challenge is the large number of genes relative to the number of samples. The use of all genes can suppress or reduce the performance of a classification rule due to the noise of nondiscriminatory genes. Selection of an optimal subset from the original gene set becomes an important prestep in sample classification. In this study, we propose a family-wise error (FWE) rate approach to selection of discriminatory genes for two-sample or multiple-sample classification. The FWE approach controls the probability of the number of one or more false positives at a prespecified level. A public colon cancer data set is used to evaluate the performance of the proposed approach for the two classification methods: k nearest neighbors (k-NN) and support vector machine (SVM). The selected gene sets from the proposed procedure appears to perform better than or comparable to several results reported in the literature using the univariate analysis without performing multivariate search. In addition, we apply the FWE approach to a toxicogenomic data set with nine treatments (a control and eight metals, As, Cd, Ni, Cr, Sb, Pb, Cu, and AsV) for a total of 55 samples for a multisample classification. Two gene sets are considered: the gene set omegaF formed by the ANOVA F-test, and a gene set omegaT formed by the union of one-versus-all t-tests. The predicted accuracies are evaluated using the internal and external crossvalidation. Using the SVM classification, the overall accuracies to predict 55 samples into one of the nine treatments are above 80% for internal crossvalidation. OmegaF has slightly higher accuracy rates than omegaT. The overall predicted accuracies are above 70% for the external crossvalidation; the two gene sets omegaT and omegaF performed equally well.     

Statistical designs for two-color spotted microarray experiments

Two-color cDNA or oligonucleotide-based spotted microarrays have been commonly used in measuring the expression levels of thousands of genes simultaneously. To realize the immense potential of this powerful new technology, budgeted within limited resources or other constraints, practical designs with high efficiencies are in demand. In this study, we address the design issue concerning the arrangement of the mRNA samples labeled with fluorescent dyes and hybridized on the slides. A normalization model is proposed to characterize major sources of systematic variation in a two-color microarray experiment. This normalization model establishes a connection between designs for two-color microarray experiments with a particular class of classical row-column designs. A heuristic algorithm for constructing A-optimal or highly efficient designs is provided. Statistical optimality results are found for some of the designs generated from the algorithm. It is believed that the constructed designs are the best or very close to the best possible for estimating the relative gene expression levels among the mRNA samples of interest.     

Robust test method for time-course microarray experiments

Background  

In a time-course microarray experiment, the expression level for each gene is observed across a number of time-points in order to characterize the temporal trajectories of the gene-expression profiles. For many of these experiments, the scientific aim is the identification of genes for which the trajectories depend on an experimental or phenotypic factor. There is an extensive recent body of literature on statistical methodology for addressing this analytical problem. Most of the existing methods are based on estimating the time-course trajectories using parametric or non-parametric mean regression methods. The sensitivity of these regression methods to outliers, an issue that is well documented in the statistical literature, should be of concern when analyzing microarray data.     

Functional interpretation of microarray experiments

Over the past few years, due to the popularisation of high-throughput methodologies such as DNA microarrays, the possibility of obtaining experimental data has increased significantly. Nevertheless, the interpretation of the results, which involves translating these data into useful biological knowledge, still remains a challenge. The methods and strategies used for this interpretation are in continuous evolution and new proposals are constantly arising. Initially, a two-step approach was used in which genes of interest were initially selected, based on thresholds that consider only experimental values, and then in a second, independent step the enrichment of these genes in biologically relevant terms, was analysed. For different reasons, these methods are relatively poor in terms of performance and a new generation of procedures, which draw inspiration from systems biology criteria, are currently under development. Such procedures, aim to directly test the behaviour of blocks of functionally related genes, instead of focusing on single genes.