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.     

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.     

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.     

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.     

Construction of null statistics in permutation-based multiple testing for multi-factorial microarray experiments

MOTIVATION: The parametric F-test has been widely used in the analysis of factorial microarray experiments to assess treatment effects. However, the normality assumption is often untenable for microarray experiments with small replications. Therefore, permutation-based methods are called for help to assess the statistical significance. The distribution of the F-statistics across all the genes on the array can be regarded as a mixture distribution with a proportion of statistics generated from the null distribution of no differential gene expression whereas the other proportion of statistics generated from the alternative distribution of genes differentially expressed. This results in the fact that the permutation distribution of the F-statistics may not approximate well to the true null distribution of the F-statistics. Therefore, the construction of a proper null statistic to better approximate the null distribution of F-statistic is of great importance to the permutation-based multiple testing in microarray data analysis. RESULTS: In this paper, we extend the ideas of constructing null statistics based on pairwise differences to neglect the treatment effects from the two-sample comparison problem to the multifactorial balanced or unbalanced microarray experiments. A null statistic based on a subpartition method is proposed and its distribution is employed to approximate the null distribution of the F-statistic. The proposed null statistic is able to accommodate unbalance in the design and is also corrected for the undue correlation between its numerator and denominator. In the simulation studies and real biological data analysis, the number of true positives and the false discovery rate (FDR) of the proposed null statistic are compared with those of the permutated version of the F-statistic. It has been shown that our proposed method has a better control of the FDRs and a higher power than the standard permutation method to detect differentially expressed genes because of the better approximated tail probabilities.     

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     

Computational strategies for analyzing data in gene expression microarray experiments

Microarray analysis has become a widely used method for generating gene expression data on a genomic scale. Microarrays have been enthusiastically applied in many fields of biological research, even though several open questions remain about the analysis of such data. A wide range of approaches are available for computational analysis, but no general consensus exists as to standard for microarray data analysis protocol. Consequently, the choice of data analysis technique is a crucial element depending both on the data and on the goals of the experiment. Therefore, basic understanding of bioinformatics is required for optimal experimental design and meaningful interpretation of the results. This review summarizes some of the common themes in DNA microarray data analysis, including data normalization and detection of differential expression. Algorithms are demonstrated by analyzing cDNA microarray data from an experiment monitoring gene expression in T helper cells. Several computational biology strategies, along with their relative merits, are overviewed and potential areas for additional research discussed. The goal of the review is to provide a computational framework for applying and evaluating such bioinformatics strategies. Solid knowledge of microarray informatics contributes to the implementation of more efficient computational protocols for the given data obtained through microarray experiments.     

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     

Nonparametric testing for DNA copy number induced differential mRNA gene expression

Summary .  The central dogma of molecular biology relates DNA with mRNA. Array CGH measures DNA copy number and gene expression microarrays measure the amount of mRNA. Methods that integrate data from these two platforms may uncover meaningful biological relationships that further our understanding of cancer. We develop nonparametric tests for the detection of copy number induced differential gene expression. The tests incorporate the uncertainty of the calling of genomic aberrations. The test is preceded by a "tuning algorithm" that discards certain genes to improve the overall power of the false discovery rate selection procedure. Moreover, the test statistics are "shrunken" to borrow information across neighboring genes that share the same array CGH signature. For each gene we also estimate its effect, its amount of differential expression due to copy number changes, and calculate the coefficient of determination. The method is illustrated on breast cancer data, in which it confirms previously reported findings, now with a more profound statistical underpinning.     

Identifying set-wise differential co-expression in gene expression microarray data

Background  

Previous differential coexpression analyses focused on identification of differentially coexpressed gene pairs, revealing many insightful biological hypotheses. However, this method could not detect coexpression relationships between pairs of gene sets. Considering the success of many set-wise analysis methods for microarray data, a coexpression analysis based on gene sets may elucidate underlying biological processes provoked by the conditional changes. Here, we propose a differentially coexpressed gene sets (dCoxS) algorithm that identifies the differentially coexpressed gene set pairs between conditions.     

Mixture modelling of gene expression data from microarray experiments

MOTIVATION: Hierarchical clustering is one of the major analytical tools for gene expression data from microarray experiments. A major problem in the interpretation of the output from these procedures is assessing the reliability of the clustering results. We address this issue by developing a mixture model-based approach for the analysis of microarray data. Within this framework, we present novel algorithms for clustering genes and samples. One of the byproducts of our method is a probabilistic measure for the number of true clusters in the data. RESULTS: The proposed methods are illustrated by application to microarray datasets from two cancer studies; one in which malignant melanoma is profiled (Bittner et al., Nature, 406, 536-540, 2000), and the other in which prostate cancer is profiled (Dhanasekaran et al., 2001, submitted).     

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.     

Bayesian hierarchical model for identifying changes in gene expression from microarray experiments.

Recent developments in microarrays technology enable researchers to study simultaneously the expression of thousands of genes from one cell line or tissue sample. This new technology is often used to assess changes in mRNA expression upon a specified transfection for a cell line in order to identify target genes. For such experiments, the range of differential expression is moderate, and teasing out the modified genes is challenging and calls for detailed modeling. The aim of this paper is to propose a methodological framework for studies that investigate differential gene expression through microarrays technology that is based on a fully Bayesian mixture approach (Richardson and Green, 1997). A case study that investigated those genes that were differentially expressed in two cell lines (normal and modified by a gene transfection) is provided to illustrate the performance and usefulness of this approach.     

Weighted change-point method for detecting differential gene expression in breast cancer microarray data

In previous work, we proposed a method for detecting differential gene expression based on change-point of expression profile. This non-parametric change-point method gave promising result in both simulation study and public dataset experiment. However, the performance is still limited by the less sensitiveness to the right bound and the statistical significance of the statistics has not been fully explored. To overcome the insensitiveness to the right bound we modified the original method by adding a weight function to the D(n) statistic. Simulation study showed that the weighted change-point statistics method is significantly better than the original NPCPS in terms of ROC, false positive rate, as well as change-point estimate. The mean absolute error of the estimated change-point by weighted change-point method was 0.03, reduced by more than 50% comparing with the original 0.06, and the mean FPR was reduced by more than 55%. Experiment on microarray Dataset I resulted in 3974 differentially expressed genes out of total 5293 genes; experiment on microarray Dataset II resulted in 9983 differentially expressed genes among total 12576 genes. In summary, the method proposed here is an effective modification to the previous method especially when only a small subset of cancer samples has DGE.     

Combination of PCR subtraction and cDNA microarray for differential gene expression profiling.

PCR subtraction hybridization has been used effectively to enrich and single out differentially expressed genes. However identification of these genes by means of cloning and sequencing individual cDNAs is a tedious and lengthy process. In this report, an attempt has been made to combine the use of PCR select cDNA subtraction hybridization and cDNA microarrays to identify differentially expressed genes using a nonradioactive chemiluminescent detection method. mRNA from human prolactin (hPRL) or human prolactin antagonist (hPRL-G129R) treated and non-treated breast cancer cells was isolated, and cDNAs were synthesized and used for the PCR subtraction to enrich the differentially expressed genes in the treated cells. The PCR-amplified and subtracted cDNA pools were purified and labeled using the digoxigenin method. Labeled cDNAs were hybridized to a human apoptosis cDNA microarray membrane and identified by chemiluminescence. The results suggest that the strategy of combining all three methods will allow for a more efficient, nonradioactive way of identifying differentially expressed genes in target cells.