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.     

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.     

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     

A general framework for analyzing data from two short time-series microarray experiments

We propose a general theoretical framework for analyzing differentially expressed genes and behavior patterns from two homogenous short time-course data. The framework generalizes the recently proposed Hilbert-Schmidt Independence Criterion (HSIC)-based framework adapting it to the time-series scenario by utilizing tensor analysis for data transformation. The proposed framework is effective in yielding criteria that can identify both the differentially expressed genes and time-course patterns of interest between two time-series experiments without requiring to explicitly cluster the data. The results, obtained by applying the proposed framework with a linear kernel formulation, on various data sets are found to be both biologically meaningful and consistent with published studies.     

A random variance model for detection of differential gene expression in small microarray experiments

MOTIVATION: Microarray techniques provide a valuable way of characterizing the molecular nature of disease. Unfortunately expense and limited specimen availability often lead to studies with small sample sizes. This makes accurate estimation of variability difficult, since variance estimates made on a gene by gene basis will have few degrees of freedom, and the assumption that all genes share equal variance is unlikely to be true. RESULTS: We propose a model by which the within gene variances are drawn from an inverse gamma distribution, whose parameters are estimated across all genes. This results in a test statistic that is a minor variation of those used in standard linear models. We demonstrate that the model assumptions are valid on experimental data, and that the model has more power than standard tests to pick up large changes in expression, while not increasing the rate of false positives. AVAILABILITY: This method is incorporated into BRB-ArrayTools version 3.0 (http://linus.nci.nih.gov/BRB-ArrayTools.html). SUPPLEMENTARY MATERIAL: ftp://linus.nci.nih.gov/pub/techreport/RVM_supplement.pdf     

Sample size for gene expression microarray experiments

MOTIVATION: Microarray experiments often involve hundreds or thousands of genes. In a typical experiment, only a fraction of genes are expected to be differentially expressed; in addition, the measured intensities among different genes may be correlated. Depending on the experimental objectives, sample size calculations can be based on one of the three specified measures: sensitivity, true discovery and accuracy rates. The sample size problem is formulated as: the number of arrays needed in order to achieve the desired fraction of the specified measure at the desired family-wise power at the given type I error and (standardized) effect size. RESULTS: We present a general approach for estimating sample size under independent and equally correlated models using binomial and beta-binomial models, respectively. The sample sizes needed for a two-sample z-test are computed; the computed theoretical numbers agree well with the Monte Carlo simulation results. But, under more general correlation structures, the beta-binomial model can underestimate the needed samples by about 1-5 arrays. CONTACT: jchen@nctr.fda.gov.     

Detecting differential expression in microarray data: comparison of optimal procedures

Background  

Many procedures for finding differentially expressed genes in microarray data are based on classical or modified t-statistics. Due to multiple testing considerations, the false discovery rate (FDR) is the key tool for assessing the significance of these test statistics. Two recent papers have generalized two aspects: Storey et al. (2005) have introduced a likelihood ratio test statistic for two-sample situations that has desirable theoretical properties (optimal discovery procedure, ODP), but uses standard FDR assessment; Ploner et al. (2006) have introduced a multivariate local FDR that allows incorporation of standard error information, but uses the standard t-statistic (fdr2d). The relationship and relative performance of these methods in two-sample comparisons is currently unknown.     

Quantitative comparison of microarray experiments with published leukemia related gene expression signatures

Background  

Multiple gene expression signatures derived from microarray experiments have been published in the field of leukemia research. A comparison of these signatures with results from new experiments is useful for verification as well as for interpretation of the results obtained. Currently, the percentage of overlapping genes is frequently used to compare published gene signatures against a signature derived from a new experiment. However, it has been shown that the percentage of overlapping genes is of limited use for comparing two experiments due to the variability of gene signatures caused by different array platforms or assay-specific influencing parameters. Here, we present a robust approach for a systematic and quantitative comparison of published gene expression signatures with an exemplary query dataset.     

A statistical framework for the design of microarray experiments and effective detection of differential gene expression

MOTIVATION: Microarray experiments generate a high data volume. However, often due to financial or experimental considerations, e.g. lack of sample, there is little or no replication of the experiments or hybridizations. These factors combined with the intrinsic variability associated with the measurement of gene expression can result in an unsatisfactory detection rate of differential gene expression (DGE). Our motivation was to provide an easy to use measure of the success rate of DGE detection that could find routine use in the design of microarray experiments or in post-experiment assessment. RESULTS: In this study, we address the problem of both random errors and systematic biases in microarray experimentation. We propose a mathematical model for the measured data in microarray experiments and on the basis of this model present a t-based statistical procedure to determine DGE. We have derived a formula to determine the success rate of DGE detection that takes into account the number of microarrays, the number of genes, the magnitude of DGE, and the variance from biological and technical sources. The formula and look-up tables based on the formula, can be used to assist in the design of microarray experiments. We also propose an ad hoc method for estimating the fraction of non-differentially expressed genes within a set of genes being tested. This will help to increase the power of DGE detection. AVAILABILITY: The functions to calculate the success rate of DGE detection have been implemented as a Java application, which is accessible at http://www.le.ac.uk/mrctox/microarray_lab/Microarray_Softwares/Microarray_Softwares.htm     

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.     

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.     

maSigPro: a method to identify significantly differential expression profiles in time-course microarray experiments

MOTIVATION: Multi-series time-course microarray experiments are useful approaches for exploring biological processes. In this type of experiments, the researcher is frequently interested in studying gene expression changes along time and in evaluating trend differences between the various experimental groups. The large amount of data, multiplicity of experimental conditions and the dynamic nature of the experiments poses great challenges to data analysis. RESULTS: In this work, we propose a statistical procedure to identify genes that show different gene expression profiles across analytical groups in time-course experiments. The method is a two-regression step approach where the experimental groups are identified by dummy variables. The procedure first adjusts a global regression model with all the defined variables to identify differentially expressed genes, and in second a variable selection strategy is applied to study differences between groups and to find statistically significant different profiles. The methodology is illustrated on both a real and a simulated microarray dataset.     

The effect of replication on gene expression microarray experiments

MOTIVATION: We examine the effect of replication on the detection of apparently differentially expressed genes in gene expression microarray experiments. Our analysis is based on a random sampling approach using real data sets from 16 published studies. We consider both the ability to find genes that meet particular statistical criteria as well as the stability of the results in the face of changing levels of replication. RESULTS: While dependent on the data source, our findings suggest that stable results are typically not obtained until at least five biological replicates have been used. Conversely, for most studies, 10-15 replicates yield results that are quite stable, and there is less improvement in stability as the number of replicates is further increased. Our methods will be of use in evaluating existing data sets and in helping to design new studies.     

Analysis techniques for microarray time-series data.

We address possible limitations of publicly available data sets of yeast gene expression. We study the predictability of known regulators via time-series analysis, and show that less than 20% of known regulatory pairs exhibit strong correlations in the Cho/Spellman data sets. By analyzing known regulatory relationships, we designed an edge detection function which identified candidate regulations with greater fidelity than standard correlation methods. We develop general methods for integrated analysis of coarse time-series data sets. These include 1) methods for automated period detection in a predominately cycling data set and 2) phase detection between phase-shifted cyclic data sets. We show how to properly correct for the problem of comparing correlation coefficients between pairs of sequences of different lengths and small alphabets. Finally, we note that the correlation coefficient of sequences over alphabets of size two can exhibit very counterintuitive behavior when compared with the Hamming distance.     

Adjustments and measures of differential expression for microarray data

MOTIVATION: Existing analyses of microarray data often incorporate an obscure data normalization procedure applied prior to data analysis. For example, ratios of microarray channels intensities are normalized to have common mean over the set of genes. We made an attempt to understand the meaning of such procedures from the modeling point of view, and to formulate the model assumptions that underlie them. Given a considerable diversity of data adjustment procedures, the question of their performance, comparison and ranking for various microarray experiments was of interest. RESULTS: A two-step statistical procedure is proposed: data transformation (adjustment for slide-specific effect) followed by a statistical test applied to transformed data. Various methods of analysis for differential expression are compared using simulations and real data on colon cancer cell lines. We found that robust categorical adjustments outperform the ones based on a precisely defined stochastic model, including some commonly used procedures.     

Sample size determination in microarray experiments for class comparison and prognostic classification

Determining sample sizes for microarray experiments is important but the complexity of these experiments, and the large amounts of data they produce, can make the sample size issue seem daunting, and tempt researchers to use rules of thumb in place of formal calculations based on the goals of the experiment. Here we present formulae for determining sample sizes to achieve a variety of experimental goals, including class comparison and the development of prognostic markers. Results are derived which describe the impact of pooling, technical replicates and dye-swap arrays on sample size requirements. These results are shown to depend on the relative sizes of different sources of variability. A variety of common types of experimental situations and designs used with single-label and dual-label microarrays are considered. We discuss procedures for controlling the false discovery rate. Our calculations are based on relatively simple yet realistic statistical models for the data, and provide straightforward sample size calculation formulae.