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.     

Information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

Background  

Time-course microarray experiments produce vector gene expression profiles across a series of time points. Clustering genes based on these profiles is important in discovering functional related and co-regulated genes. Early developed clustering algorithms do not take advantage of the ordering in a time-course study, explicit use of which should allow more sensitive detection of genes that display a consistent pattern over time. Peddada et al. [1] proposed a clustering algorithm that can incorporate the temporal ordering using order-restricted statistical inference. This algorithm is, however, very time-consuming and hence inapplicable to most microarray experiments that contain a large number of genes. Its computational burden also imposes difficulty to assess the clustering reliability, which is a very important measure when clustering noisy microarray data.     

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.     

A response to information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

Background  

For gene expression data obtained from a time-course microarray experiment, Liu et al. [1] developed a new algorithm for clustering genes with similar expression profiles over time. Performance of their proposal was compared with three other methods including the order-restricted inference based methodology of Peddada et al. [2, 3]. In this note we point out several inaccuracies in Liu et al. [1] and conclude that the order-restricted inference based methodology of Peddada et al. (programmed in the software ORIOGEN) indeed operates at the desired nominal Type 1 error level, an important feature of a statistical decision rule, while being computationally substantially faster than indicated by Liu et al. [1].     

Statistical tests for differential expression in cDNA microarray experiments

Extracting biological information from microarray data requires appropriate statistical methods. The simplest statistical method for detecting differential expression is the t test, which can be used to compare two conditions when there is replication of samples. With more than two conditions, analysis of variance (ANOVA) can be used, and the mixed ANOVA model is a general and powerful approach for microarray experiments with multiple factors and/or several sources of variation.     

Principal components analysis based methodology to identify differentially expressed genes in time-course microarray data

Background  

Time-course microarray experiments are being increasingly used to characterize dynamic biological processes. In these experiments, the goal is to identify genes differentially expressed in time-course data, measured between different biological conditions. These differentially expressed genes can reveal the changes in biological process due to the change in condition which is essential to understand differences in dynamics.     

Statistical tests for identifying differentially expressed genes in time-course microarray experiments

MOTIVATION: Microarray technology allows the monitoring of expression levels for thousands of genes simultaneously. In time-course experiments in which gene expression is monitored over time, we are interested in testing gene expression profiles for different experimental groups. However, no sophisticated analytic methods have yet been proposed to handle time-course experiment data. RESULTS: We propose a statistical test procedure based on the ANOVA model to identify genes that have different gene expression profiles among experimental groups in time-course experiments. Especially, we propose a permutation test which does not require the normality assumption. For this test, we use residuals from the ANOVA model only with time-effects. Using this test, we detect genes that have different gene expression profiles among experimental groups. The proposed model is illustrated using cDNA microarrays of 3840 genes obtained in an experiment to search for changes in gene expression profiles during neuronal differentiation of cortical stem cells.     

A Laplace mixture model for identification of differential expression in microarray experiments

Microarrays have become an important tool for studying the molecular basis of complex disease traits and fundamental biological processes. A common purpose of microarray experiments is the detection of genes that are differentially expressed under two conditions, such as treatment versus control or wild type versus knockout. We introduce a Laplace mixture model as a long-tailed alternative to the normal distribution when identifying differentially expressed genes in microarray experiments, and provide an extension to asymmetric over- or underexpression. This model permits greater flexibility than models in current use as it has the potential, at least with sufficient data, to accommodate both whole genome and restricted coverage arrays. We also propose likelihood approaches to hyperparameter estimation which are equally applicable in the Normal mixture case. The Laplace model appears to give some improvement in fit to data, though simulation studies show that our method performs similarly to several other statistical approaches to the problem of identification of differential expression.     

Use of within-array replicate spots for assessing differential expression in microarray experiments

MOTIVATION: Spotted arrays are often printed with probes in duplicate or triplicate, but current methods for assessing differential expression are not able to make full use of the resulting information. The usual practice is to average the duplicate or triplicate results for each probe before assessing differential expression. This results in the loss of valuable information about genewise variability. RESULTS: A method is proposed for extracting more information from within-array replicate spots in microarray experiments by estimating the strength of the correlation between them. The method involves fitting separate linear models to the expression data for each gene but with a common value for the between-replicate correlation. The method greatly improves the precision with which the genewise variances are estimated and thereby improves inference methods designed to identify differentially expressed genes. The method may be combined with empirical Bayes methods for moderating the genewise variances between genes. The method is validated using data from a microarray experiment involving calibration and ratio control spots in conjunction with spiked-in RNA. Comparing results for calibration and ratio control spots shows that the common correlation method results in substantially better discrimination of differentially expressed genes from those which are not. The spike-in experiment also confirms that the results may be further improved by empirical Bayes smoothing of the variances when the sample size is small. AVAILABILITY: The methodology is implemented in the limma software package for R, available from the CRAN repository http://www.r-project.org     

Empirical comparison of tests for differential expression on time-series microarray experiments

Methods for identifying differentially expressed genes were compared on time-series microarray data simulated from artificial gene networks. Select methods were further analyzed on existing immune response data of Boldrick et al. (2002, Proc. Natl. Acad. Sci. USA 99, 972-977). Based on the simulations, we recommend the ANOVA variants of Cui and Churchill. Efron and Tibshirani's empirical Bayes Wilcoxon rank sum test is recommended when the background cannot be effectively corrected. Our proposed GSVD-based differential expression method was shown to detect subtle changes. ANOVA combined with GSVD was consistent on background-normalized simulation data. GSVD with empirical Bayes was consistent without background correction. Based on the Boldrick et al. data, ANOVA is best suited to detect changes in temporal data, while GSVD and empirical Bayes effectively detect individual spikes or overall shifts, respectively. For methods tested on simulation data, lowess after background correction improved results. On simulation data without background correction, lowess decreased performance compared to median centering.     

Exploratory differential gene expression analysis in microarray experiments with no or limited replication

We describe an exploratory, data-oriented approach for identifying candidates for differential gene expression in cDNA microarray experiments in terms of α-outliers and outlier regions, using simultaneous tolerance intervals relative to the line of equivalence (Cy5 = Cy3). We demonstrate the improved performance of our approach over existing single-slide methods using public datasets and simulation studies.     

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.