Identifying differentially expressed genes from microarray experiments via statistic synthesis

MOTIVATION: A common objective of microarray experiments is the detection of differential gene expression between samples obtained under different conditions. The task of identifying differentially expressed genes consists of two aspects: ranking and selection. Numerous statistics have been proposed to rank genes in order of evidence for differential expression. However, no one statistic is universally optimal and there is seldom any basis or guidance that can direct toward a particular statistic of choice. RESULTS: Our new approach, which addresses both ranking and selection of differentially expressed genes, integrates differing statistics via a distance synthesis scheme. Using a set of (Affymetrix) spike-in datasets, in which differentially expressed genes are known, we demonstrate that our method compares favorably with the best individual statistics, while achieving robustness properties lacked by the individual statistics. We further evaluate performance on one other microarray study.     

A Robust Statistical Method for Detecting Differentially Expressed Genes

DNA microarray technology allows researchers to monitor the expressions of thousands of genes under different conditions, and to measure the levels of thousands of different DNA molecules at a given point in the life of an organism, tissue or cell. A wide variety of different diseases that are characterised by unregulated gene expression, DNA replication, cell division and cell death, can be detected early using microarrays. One of the major objectives of microarray experiments is to identify differentially expressed genes under various conditions. The detection of differential gene expression under two different conditions is very important in biological studies, and allows us to identify experimental variables that affect different biological processes. Most of the tests available in the literature are based on the assumption of normal distribution. However, the assumption of normality may not be true in real-life data, particularly with respect to microarray data.A test is proposed for the identification of differentially expressed genes in replicated microarray experiments conducted under two different conditions. The proposed test does not assume the distribution of the parent population; thus, the proposed test is strictly nonparametric in nature. We calculate the p-value and the asymptotic power function of the proposed test statistic. The proposed test statistic is compared with some of its competitors under normal, gamma and exponential population setup using the Monte Carlo simulation technique. The application of the proposed test statistic is presented using microarray data. The proposed test is robust and highly efficient when populations are non-normal.     

Identifying differentially expressed genes in human acute leukemia and mouse brain microarray datasets utilizing QTModel

One of the essential issues in microarray data analysis is to identify differentially expressed genes (DEGs) under different experimental treatments. In this article, a statistical procedure was proposed to identify the DEGs for gene expression data with or without missing observations from microarray experiment with one- or two-treatment factors. An F statistic based on Henderson method III was constructed to test the significance of differential expression for each gene under different treatment(s) levels. The cutoff P value was adjusted to control the experimental-wise false discovery rate. A human acute leukemia dataset corrected from 38 leukemia patients was reanalyzed by the proposed method. In comparison to the results from significant analysis of microarray (SAM) and microarray analysis of variance (MAANOVA), it was indicated that the proposed method has similar performance with MAANOVA for data with one-treatment factor, but MAANOVA cannot directly handle missing data. In addition, a mouse brain dataset collected from six brain regions of two inbred strains (two-treatment factors) was reanalyzed to identify genes with distinct regional-specific expression patterns. The results showed that the proposed method could identify more distinct regional-specific expression patterns than the previous analysis of the same dataset. Moreover, a computer program was developed and incorporated in the software QTModel, which is freely available at .     

Hotelling's T2 multivariate profiling for detecting differential expression in microarrays

The most widely used statistical methods for finding differentially expressed genes (DEGs) are essentially univariate. In this study, we present a new T(2) statistic for analyzing microarray data. We implemented our method using a multiple forward search (MFS) algorithm that is designed for selecting a subset of feature vectors in high-dimensional microarray datasets. The proposed T2 statistic is a corollary to that originally developed for multivariate analyses and possesses two prominent statistical properties. First, our method takes into account multidimensional structure of microarray data. The utilization of the information hidden in gene interactions allows for finding genes whose differential expressions are not marginally detectable in univariate testing methods. Second, the statistic has a close relationship to discriminant analyses for classification of gene expression patterns. Our search algorithm sequentially maximizes gene expression difference/distance between two groups of genes. Including such a set of DEGs into initial feature variables may increase the power of classification rules. We validated our method by using a spike-in HGU95 dataset from Affymetrix. The utility of the new method was demonstrated by application to the analyses of gene expression patterns in human liver cancers and breast cancers. Extensive bioinformatics analyses and cross-validation of DEGs identified in the application datasets showed the significant advantages of our new algorithm.     

Bayesian hierarchical error model for analysis of gene expression data

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.     

Power estimation of the t test for detecting differential gene expression

There exist now a number of statistical methods for detecting differential gene expression in experiments with microarray data. In trials under two conditions, a version of the two-sample t statistic is usually used. However, the problem of estimating the power for these tests has so far been insufficiently studied. In this paper, we propose a method to calculate the power of the robust t test for detecting differential gene expression in experiments with twins. We discuss also the results of the implementation of this method to simulated data.     

ROTS: reproducible RNA-seq biomarker detector—prognostic markers for clear cell renal cell cancer

Recent comprehensive assessments of RNA-seq technology support its utility in quantifying gene expression in various samples. The next step of rigorously quantifying differences between sample groups, however, still lacks well-defined best practices. Although a number of advanced statistical methods have been developed, several studies demonstrate that their performance depends strongly on the data under analysis, which compromises practical utility in real biomedical studies. As a solution, we propose to use a data-adaptive procedure that selects an optimal statistic capable of maximizing reproducibility of detections. After demonstrating its improved sensitivity and specificity in a controlled spike-in study, the utility of the procedure is confirmed in a real biomedical study by identifying prognostic markers for clear cell renal cell carcinoma (ccRCC). In addition to identifying several genes previously associated with ccRCC prognosis, several potential new biomarkers among genes regulating cell growth, metabolism and solute transport were detected.     

Understanding the physics of oligonucleotide microarrays: the Affymetrix spike-in data reanalysed

The Affymetrix U95 and U133 Latin-Square spike-in datasets are reanalysed, together with a dataset from a version of the U95 spike-in experiment without a complex non-specific background. The approach uses a physico-chemical model which includes the effects of the specific and non-specific hybridization and probe folding at the microarray surface, target folding and hybridization in the bulk RNA target solution and duplex dissociation during the post-hybridization washing phase. The model predicts a three-parameter hyperbolic response function that fits well with fluorescence intensity data from all the three datasets. The importance of the various hybridization and washing effects in determining each of the three parameters is examined, and some guidance is given as to how a practical algorithm for determining specific target concentrations might be developed.     

On the use of permutation in and the performance of a class of nonparametric methods to detect differential gene expression

MOTIVATION: Recently a class of nonparametric statistical methods, including the empirical Bayes (EB) method, the significance analysis of microarray (SAM) method and the mixture model method (MMM), have been proposed to detect differential gene expression for replicated microarray experiments conducted under two conditions. All the methods depend on constructing a test statistic Z and a so-called null statistic z. The null statistic z is used to provide some reference distribution for Z such that statistical inference can be accomplished. A common way of constructing z is to apply Z to randomly permuted data. Here we point our that the distribution of z may not approximate the null distribution of Z well, leading to possibly too conservative inference. This observation may apply to other permutation-based nonparametric methods. We propose a new method of constructing a null statistic that aims to estimate the null distribution of a test statistic directly. RESULTS: Using simulated data and real data, we assess and compare the performance of the existing method and our new method when applied in EB, SAM and MMM. Some interesting findings on operating characteristics of EB, SAM and MMM are also reported. Finally, by combining the idea of SAM and MMM, we outline a simple nonparametric method based on the direct use of a test statistic and a null statistic.     

Probe-level measurement error improves accuracy in detecting differential gene expression

MOTIVATION: Finding differentially expressed genes is a fundamental objective of a microarray experiment. Numerous methods have been proposed to perform this task. Existing methods are based on point estimates of gene expression level obtained from each microarray experiment. This approach discards potentially useful information about measurement error that can be obtained from an appropriate probe-level analysis. Probabilistic probe-level models can be used to measure gene expression and also provide a level of uncertainty in this measurement. This probe-level measurement error provides useful information which can help in the identification of differentially expressed genes. RESULTS: We propose a Bayesian method to include probe-level measurement error into the detection of differentially expressed genes from replicated experiments. A variational approximation is used for efficient parameter estimation. We compare this approximation with MAP and MCMC parameter estimation in terms of computational efficiency and accuracy. The method is used to calculate the probability of positive log-ratio (PPLR) of expression levels between conditions. Using the measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we test PPLR on a spike-in dataset and a mouse time-course dataset. Results show that the inclusion of probe-level measurement error improves accuracy in detecting differential gene expression. AVAILABILITY: The MAP approximation and variational inference described in this paper have been implemented in an R package pplr. The MCMC method is implemented in Matlab. Both software are available from http://umber.sbs.man.ac.uk/resources/puma.     

Improved statistical tests for differential gene expression by shrinking variance components estimates

Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the James-Stein shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic is compared with other statistics used to test for differential expression: the gene-specific F test (F1), the pooled-variance F statistic (F3), a hybrid statistic (F2) that uses the average of the individual and pooled variances, the regularized t-statistic, the posterior odds statistic B, and the SAM t-test. The FS-test shows best or nearly best power for detecting differentially expressed genes over a wide range of simulated data in which the variance components associated with individual genes are either homogeneous or heterogeneous. Thus FS provides a powerful and robust approach to test differential expression of genes that utilizes information not available in individual gene testing approaches and does not suffer from biases of the pooled variance approach.     

Using weighted permutation scores to detect differential gene expression with microarray data

A class of nonparametric statistical methods, including a nonparametric empirical Bayes (EB) method, the Significance Analysis of Microarrays (SAM) and the mixture model method (MMM) have been proposed to detect differential gene expression for replicated microarray experiments. They all depend on constructing a test statistic, for example, a t-statistic, and then using permutation to draw inferences. However, due to special features of microarray data, using standard permutation scores may not estimate the null distribution of the test statistic well, leading to possibly too conservative inferences. We propose a new method of constructing weighted permutation scores to overcome the problem: posterior probabilities of having no differential expression from the EB method are used as weights for genes to better estimate the null distribution of the test statistic. We also propose a weighted method to estimate the false discovery rate (FDR) using the posterior probabilities. Using simulated data and real data for time-course microarray experiments, we show the improved performance of the proposed methods when implemented in MMM, EB and SAM.     

Multidimensional local false discovery rate for microarray studies

MOTIVATION: The false discovery rate (fdr) is a key tool for statistical assessment of differential expression (DE) in microarray studies. Overall control of the fdr alone, however, is not sufficient to address the problem of genes with small variance, which generally suffer from a disproportionally high rate of false positives. It is desirable to have an fdr-controlling procedure that automatically accounts for gene variability. METHODS: We generalize the local fdr as a function of multiple statistics, combining a common test statistic for assessing DE with its standard error information. We use a non-parametric mixture model for DE and non-DE genes to describe the observed multi-dimensional statistics, and estimate the distribution for non-DE genes via the permutation method. We demonstrate this fdr2d approach for simulated and real microarray data. RESULTS: The fdr2d allows objective assessment of DE as a function of gene variability. We also show that the fdr2d performs better than commonly used modified test statistics. AVAILABILITY: An R-package OCplus containing functions for computing fdr2d() and other operating characteristics of microarray data is available at http://www.meb.ki.se/~yudpaw.     

Empirical evaluation of data transformations and ranking statistics for microarray analysis

There are many options in handling microarray data that can affect study conclusions, sometimes drastically. Working with a two-color platform, this study uses ten spike-in microarray experiments to evaluate the relative effectiveness of some of these options for the experimental goal of detecting differential expression. We consider two data transformations, background subtraction and intensity normalization, as well as six different statistics for detecting differentially expressed genes. Findings support the use of an intensity-based normalization procedure and also indicate that local background subtraction can be detrimental for effectively detecting differential expression. We also verify that robust statistics outperform t-statistics in identifying differentially expressed genes when there are few replicates. Finally, we find that choice of image analysis software can also substantially influence experimental conclusions.     

Increased power of microarray analysis by use of an algorithm based on a multivariate procedure

MOTIVATION: The power of microarray analyses to detect differential gene expression strongly depends on the statistical and bioinformatical approaches used for data analysis. Moreover, the simultaneous testing of tens of thousands of genes for differential expression raises the 'multiple testing problem', increasing the probability of obtaining false positive test results. To achieve more reliable results, it is, therefore, necessary to apply adjustment procedures to restrict the family-wise type I error rate (FWE) or the false discovery rate. However, for the biologist the statistical power of such procedures often remains abstract, unless validated by an alternative experimental approach. RESULTS: In the present study, we discuss a multiplicity adjustment procedure applied to classical univariate as well as to recently proposed multivariate gene-expression scores. All procedures strictly control the FWE. We demonstrate that the use of multivariate scores leads to a more efficient identification of differentially expressed genes than the widely used MAS5 approach provided by the Affymetrix software tools (Affymetrix Microarray Suite 5 or GeneChip Operating Software). The practical importance of this finding is successfully validated using real time quantitative PCR and data from spike-in experiments. AVAILABILITY: The R-code of the statistical routines can be obtained from the corresponding author. CONTACT: Schuster@imise.uni-leipzig.de     

How accurately can we control the FDR in analyzing microarray data?

SUMMARY: We want to evaluate the performance of two FDR-based multiple testing procedures by Benjamini and Hochberg (1995, J. R. Stat. Soc. Ser. B, 57, 289-300) and Storey (2002, J. R. Stat. Soc. Ser. B, 64, 479-498) in analyzing real microarray data. These procedures commonly require independence or weak dependence of the test statistics. However, expression levels of different genes from each array are usually correlated due to coexpressing genes and various sources of errors from experiment-specific and subject-specific conditions that are not adjusted for in data analysis. Because of high dimensionality of microarray data, it is usually impossible to check whether the weak dependence condition is met for a given dataset or not. We propose to generate a large number of test statistics from a simulation model which has asymptotically (in terms of the number of arrays) the same correlation structure as the test statistics that will be calculated from the given data and to investigate how accurately the FDR-based testing procedures control the FDR on the simulated data. Our approach is to directly check the performance of these procedures for a given dataset, rather than to check the weak dependency requirement. We illustrate the proposed method with real microarray datasets, one where the clinical endpoint is disease group and another where it is survival.     

基因芯片筛选差异表达基因方法比较

摘要: 使用计算机模拟数据和真实的芯片数据, 对8种筛选差异表达基因的方法进行了比较分析, 旨在比较不同方法对基因芯片数据的筛选效果。模拟数据分析表明, 所使用的8种方法对均匀分布的差异表达基因有很好的识别、检出作用。算法方面, SAM和Wilcoxon秩和检验方法较好; 数据分布方面, 正态分布的识别效果较好, 卡方分布和指数分布的识别效果较差。杨树cDNA芯片分析表明, SAM、Samroc和回归模型方法相近, 而Wilcoxon秩和检验方法与它们有较大差异。     

The loss in power when the test of differential expression is performed under a wrong scale.

One of the most common and important goals of microarray studies is to identify genes that are differentially expressed between cells of different conditions. T-test and ANOVA models on the expression data are common practices to gauge the significance of the observed difference in expression levels. Transformation of the microarray data is often applied in order to satisfy the model assumptions being entertained. However, the distributional properties of the expression are gene specific, and it is impractical to find a single transformation that is universally optimal for all the genes. This difficulty results in the situation that some genes have to violate the assumptions of the model (e.g., homogeneity in variance, normality). It is thus the interest of this paper to evaluate the impact on the inference of differential expression when the test is performed under an inappropriate scale. Particularly, we quantitatively assess the loss of power when the test is performed under a wrong scale. Normal distribution and log-normal distribution of the expression data are considered. The loss in power is investigated in two scenarios: a transformation is misused, or a transformation fails to be applied. Log transformation and power transformation are particularly considered due to the fact that Box-Cox types of transformation are commonly used in practice. The impact of using a wrong scale is investigated analytically and based on simulations. The loss in power is assessed both as a function of the degree to which the assumptions are violated and as a function of the effect size. Simulations are conducted to quantitatively assess the power loss when tests are performed under a wrong scale. A public experimental microarray dataset is used to illustrate the impact of transformation on the results of testing differential expression. The results show that the loss of power is a function of CV and fold-change (effect size). The loss in power depends on the true model and on how severely the assumptions are violated.     

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.