A Regression-Based Differential Expression Detection Algorithm for Microarray Studies with Ultra-Low Sample Size

Global gene expression analysis using microarrays and, more recently, RNA-seq, has allowed investigators to understand biological processes at a system level. However, the identification of differentially expressed genes in experiments with small sample size, high dimensionality, and high variance remains challenging, limiting the usability of these tens of thousands of publicly available, and possibly many more unpublished, gene expression datasets. We propose a novel variable selection algorithm for ultra-low-n microarray studies using generalized linear model-based variable selection with a penalized binomial regression algorithm called penalized Euclidean distance (PED). Our method uses PED to build a classifier on the experimental data to rank genes by importance. In place of cross-validation, which is required by most similar methods but not reliable for experiments with small sample size, we use a simulation-based approach to additively build a list of differentially expressed genes from the rank-ordered list. Our simulation-based approach maintains a low false discovery rate while maximizing the number of differentially expressed genes identified, a feature critical for downstream pathway analysis. We apply our method to microarray data from an experiment perturbing the Notch signaling pathway in Xenopus laevis embryos. This dataset was chosen because it showed very little differential expression according to limma, a powerful and widely-used method for microarray analysis. Our method was able to detect a significant number of differentially expressed genes in this dataset and suggest future directions for investigation. Our method is easily adaptable for analysis of data from RNA-seq and other global expression experiments with low sample size and high dimensionality.     

A computational method for prediction of excretory proteins and application to identification of gastric cancer markers in urine

A novel computational method for prediction of proteins excreted into urine is presented. The method is based on the identification of a list of distinguishing features between proteins found in the urine of healthy people and proteins deemed not to be urine excretory. These features are used to train a classifier to distinguish the two classes of proteins. When used in conjunction with information of which proteins are differentially expressed in diseased tissues of a specific type versus control tissues, this method can be used to predict potential urine markers for the disease. Here we report the detailed algorithm of this method and an application to identification of urine markers for gastric cancer. The performance of the trained classifier on 163 proteins was experimentally validated using antibody arrays, achieving >80% true positive rate. By applying the classifier on differentially expressed genes in gastric cancer vs normal gastric tissues, it was found that endothelial lipase (EL) was substantially suppressed in the urine samples of 21 gastric cancer patients versus 21 healthy individuals. Overall, we have demonstrated that our predictor for urine excretory proteins is highly effective and could potentially serve as a powerful tool in searches for disease biomarkers in urine in general.     

Prediction of biologically significant components from microarray data: Independently Consistent Expression Discriminator (ICED)

MOTIVATION: Class distinction is a supervised learning approach that has been successfully employed in the analysis of high-throughput gene expression data. Identification of a set of genes that predicts differential biological states allows for the development of basic and clinical scientific approaches to the diagnosis of disease. The Independent Consistent Expression Discriminator (ICED) was designed to provide a more biologically relevant search criterion during predictor selection by embracing the inherent variability of gene expression in any biological state. The four components of ICED include (i) normalization of raw data; (ii) assignment of weights to genes from both classes; (iii) counting of votes to determine optimal number of predictor genes for class distinction; (iv) calculation of prediction strengths for classification results. The search criteria employed by ICED is designed to identify not only genes that are consistently expressed at one level in one class and at a consistently different level in another class but identify genes that are variable in one class and consistent in another. The result is a novel approach to accurately select biologically relevant predictors of differential disease states from a small number of microarray samples. RESULTS: The data described herein utilized ICED to analyze the large AML/ALL training and test data set (Golub et al., 1999, Science, 286, 531-537) in addition to a smaller data set consisting of an animal model of the childhood neurodegenerative disorder, Batten disease, generated for this study. Both of the analyses presented herein have correctly predicted biologically relevant perturbations that can be used for disease classification, irrespective of sample size. Furthermore, the results have provided candidate proteins for future study in understanding the disease process and the identification of potential targets for therapeutic intervention.     

根据GO分类体系选择与实验条件相关的差异表达功能结点进行基因功能深化预测

利用有限个实验条件下的基因表达谱数据,只能对与实验条件相关的基因功能类进行有效预测,所以有必要限定可预测的基因功能类范围。据此,首先基于GeneOntology(GO)选择富集差异表达基因与实验条件相关的功能类。再通过支持向量机分类器,深化预测迄今只注释到实验条件相关功能类的父结点的基因是否属于该实验条件相关功能类。应用于一套酵母基因表达谱数据,结果显示,在剔除了高度不平衡的训练集合后,平均真阳性率(precision)与平均覆盖率(recall)都分别达到了71%与47%以上。     

Sample size calculations based on ranking and selection in microarray experiments

Summary .   We develop formulae to calculate sample sizes for ranking and selection of differentially expressed genes among different clinical subtypes or prognostic classes of disease in genome-wide screening studies with microarrays. The formulae aim to control the probability that a selected subset of genes with fixed size contains enough truly top-ranking informative genes, which can be assessed on the basis of the distribution of ordered statistics from independent genes. We provide strategies for conservative designs to cope with issues of unknown number of informative genes and unknown correlation structure across genes. Application of the formulae to a clinical study for multiple myeloma is given.     

Power and sample size estimation in microarray studies

Background  

Before conducting a microarray experiment, one important issue that needs to be determined is the number of arrays required in order to have adequate power to identify differentially expressed genes. This paper discusses some crucial issues in the problem formulation, parameter specifications, and approaches that are commonly proposed for sample size estimation in microarray experiments. Common methods for sample size estimation are formulated as the minimum sample size necessary to achieve a specified sensitivity (proportion of detected truly differentially expressed genes) on average at a specified false discovery rate (FDR) level and specified expected proportion (π ₁) of the true differentially expression genes in the array. Unfortunately, the probability of detecting the specified sensitivity in such a formulation can be low. We formulate the sample size problem as the number of arrays needed to achieve a specified sensitivity with 95% probability at the specified significance level. A permutation method using a small pilot dataset to estimate sample size is proposed. This method accounts for correlation and effect size heterogeneity among genes.     

Logistic regression for disease classification using microarray data: model selection in a large p and small n case

MOTIVATION: Logistic regression is a standard method for building prediction models for a binary outcome and has been extended for disease classification with microarray data by many authors. A feature (gene) selection step, however, must be added to penalized logistic modeling due to a large number of genes and a small number of subjects. Model selection for this two-step approach requires new statistical tools because prediction error estimation ignoring the feature selection step can be severely downward biased. Generic methods such as cross-validation and non-parametric bootstrap can be very ineffective due to the big variability in the prediction error estimate. RESULTS: We propose a parametric bootstrap model for more accurate estimation of the prediction error that is tailored to the microarray data by borrowing from the extensive research in identifying differentially expressed genes, especially the local false discovery rate. The proposed method provides guidance on the two critical issues in model selection: the number of genes to include in the model and the optimal shrinkage for the penalized logistic regression. We show that selecting more than 20 genes usually helps little in further reducing the prediction error. Application to Golub's leukemia data and our own cervical cancer data leads to highly accurate prediction models. AVAILABILITY: R library GeneLogit at http://geocities.com/jg_liao     

Comparison of methods for identifying differentially expressed genes across multiple conditions from microarray data

Identification of genes differentially expressed across multiple conditions has become an important statistical problem in analyzing large-scale microarray data. Many statistical methods have been developed to address the challenging problem. Therefore, an extensive comparison among these statistical methods is extremely important for experimental scientists to choose a valid method for their data analysis. In this study, we conducted simulation studies to compare six statistical methods: the Bonferroni (B-) procedure, the Benjamini and Hochberg (BH-) procedure, the Local false discovery rate (Localfdr) method, the Optimal Discovery Procedure (ODP), the Ranking Analysis of F-statistics (RAF), and the Significant Analysis of Microarray data (SAM) in identifying differentially expressed genes. We demonstrated that the strength of treatment effect, the sample size, proportion of differentially expressed genes and variance of gene expression will significantly affect the performance of different methods. The simulated results show that ODP exhibits an extremely high power in indentifying differentially expressed genes, but significantly underestimates the False Discovery Rate (FDR) in all different data scenarios. The SAM has poor performance when the sample size is small, but is among the best-performing methods when the sample size is large. The B-procedure is stringent and thus has a low power in all data scenarios. Localfdr and RAF show comparable statistical behaviors with the BH-procedure with favorable power and conservativeness of FDR estimation. RAF performs the best when proportion of differentially expressed genes is small and treatment effect is weak, but Localfdr is better than RAF when proportion of differentially expressed genes is large.     

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     

False discovery rate, sensitivity and sample size for microarray studies

MOTIVATION: In microarray data studies most researchers are keenly aware of the potentially high rate of false positives and the need to control it. One key statistical shift is the move away from the well-known P-value to false discovery rate (FDR). Less discussion perhaps has been spent on the sensitivity or the associated false negative rate (FNR). The purpose of this paper is to explain in simple ways why the shift from P-value to FDR for statistical assessment of microarray data is necessary, to elucidate the determining factors of FDR and, for a two-sample comparative study, to discuss its control via sample size at the design stage. RESULTS: We use a mixture model, involving differentially expressed (DE) and non-DE genes, that captures the most common problem of finding DE genes. Factors determining FDR are (1) the proportion of truly differentially expressed genes, (2) the distribution of the true differences, (3) measurement variability and (4) sample size. Many current small microarray studies are plagued with large FDR, but controlling FDR alone can lead to unacceptably large FNR. In evaluating a design of a microarray study, sensitivity or FNR curves should be computed routinely together with FDR curves. Under certain assumptions, the FDR and FNR curves coincide, thus simplifying the choice of sample size for controlling the FDR and FNR jointly.     

A global approach to identify differentially expressed genes in cDNA (two-color) microarray experiments

MOTIVATION: Currently most of the methods for identifying differentially expressed genes fall into the category of so called single-gene-analysis, performing hypothesis testing on a gene-by-gene basis. In a single-gene-analysis approach, estimating the variability of each gene is required to determine whether a gene is differentially expressed or not. Poor accuracy of variability estimation makes it difficult to identify genes with small fold-changes unless a very large number of replicate experiments are performed. RESULTS: We propose a method that can avoid the difficult task of estimating variability for each gene, while reliably identifying a group of differentially expressed genes with low false discovery rates, even when the fold-changes are very small. In this article, a new characterization of differentially expressed genes is established based on a theorem about the distribution of ranks of genes sorted by (log) ratios within each array. This characterization of differentially expressed genes based on rank is an example of all-gene-analysis instead of single gene analysis. We apply the method to a cDNA microarray dataset and many low fold-changed genes (as low as 1.3 fold-changes) are reliably identified without carrying out hypothesis testing on a gene-by-gene basis. The false discovery rate is estimated in two different ways reflecting the variability from all the genes without the complications related to multiple hypothesis testing. We also provide some comparisons between our approach and single-gene-analysis based methods. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Identification and optimization of classifier genes from multi-class earthworm microarray dataset

Monitoring, assessment and prediction of environmental risks that chemicals pose demand rapid and accurate diagnostic assays. A variety of toxicological effects have been associated with explosive compounds TNT and RDX. One important goal of microarray experiments is to discover novel biomarkers for toxicity evaluation. We have developed an earthworm microarray containing 15,208 unique oligo probes and have used it to profile gene expression in 248 earthworms exposed to TNT, RDX or neither. We assembled a new machine learning pipeline consisting of several well-established feature filtering/selection and classification techniques to analyze the 248-array dataset in order to construct classifier models that can separate earthworm samples into three groups: control, TNT-treated, and RDX-treated. First, a total of 869 genes differentially expressed in response to TNT or RDX exposure were identified using a univariate statistical algorithm of class comparison. Then, decision tree-based algorithms were applied to select a subset of 354 classifier genes, which were ranked by their overall weight of significance. A multiclass support vector machine (MC-SVM) method and an unsupervised K-mean clustering method were applied to independently refine the classifier, producing a smaller subset of 39 and 30 classifier genes, separately, with 11 common genes being potential biomarkers. The combined 58 genes were considered the refined subset and used to build MC-SVM and clustering models with classification accuracy of 83.5% and 56.9%, respectively. This study demonstrates that the machine learning approach can be used to identify and optimize a small subset of classifier/biomarker genes from high dimensional datasets and generate classification models of acceptable precision for multiple classes.     

Analysis of host response to bacterial infection using error model based gene expression microarray experiments

A key step in the analysis of microarray data is the selection of genes that are differentially expressed. Ideally, such experiments should be properly replicated in order to infer both technical and biological variability, and the data should be subjected to rigorous hypothesis tests to identify the differentially expressed genes. However, in microarray experiments involving the analysis of very large numbers of biological samples, replication is not always practical. Therefore, there is a need for a method to select differentially expressed genes in a rational way from insufficiently replicated data. In this paper, we describe a simple method that uses bootstrapping to generate an error model from a replicated pilot study that can be used to identify differentially expressed genes in subsequent large-scale studies on the same platform, but in which there may be no replicated arrays. The method builds a stratified error model that includes array-to-array variability, feature-to-feature variability and the dependence of error on signal intensity. We apply this model to the characterization of the host response in a model of bacterial infection of human intestinal epithelial cells. We demonstrate the effectiveness of error model based microarray experiments and propose this as a general strategy for a microarray-based screening of large collections of biological samples.     

OpenDMAP: An open source, ontology-driven concept analysis engine, with applications to capturing knowledge regarding protein transport, protein interactions and cell-type-specific gene expression

Background

Microarray technology provides an efficient means for globally exploring physiological processes governed by the coordinated expression of multiple genes. However, identification of genes differentially expressed in microarray experiments is challenging because of their potentially high type I error rate. Methods for large-scale statistical analyses have been developed but most of them are applicable to two-sample or two-condition data.

Results

We developed a large-scale multiple-group F-test based method, named ranking analysis of F-statistics (RAF), which is an extension of ranking analysis of microarray data (RAM) for two-sample t-test. In this method, we proposed a novel random splitting approach to generate the null distribution instead of using permutation, which may not be appropriate for microarray data. We also implemented a two-simulation strategy to estimate the false discovery rate. Simulation results suggested that it has higher efficiency in finding differentially expressed genes among multiple classes at a lower false discovery rate than some commonly used methods. By applying our method to the experimental data, we found 107 genes having significantly differential expressions among 4 treatments at <0.7% FDR, of which 31 belong to the expressed sequence tags (ESTs), 76 are unique genes who have known functions in the brain or central nervous system and belong to six major functional groups.

Conclusion

Our method is suitable to identify differentially expressed genes among multiple groups, in particular, when sample size is small.     

Normalization and quantification of differential expression in gene expression microarrays

Array-based gene expression studies frequently serve to identify genes that are expressed differently under two or more conditions. The actual analysis of the data, however, may be hampered by a number of technical and statistical problems. Possible remedies on the level of computational analysis lie in appropriate preprocessing steps, proper normalization of the data and application of statistical testing procedures in the derivation of differentially expressed genes. This review summarizes methods that are available for these purposes and provides a brief overview of the available software tools.