A Nonparametric Likelihood Ratio Test to Identify Differentially Expressed Genes from Microarray Data

Microarray experiments contribute significantly to the progress in disease treatment by enabling a precise and early diagnosis. One of the major objectives of microarray experiments is to identify differentially expressed genes under various conditions. The statistical methods currently used to analyse microarray data are inadequate, mainly due to the lack of understanding of the distribution of microarray data. We present a nonparametric likelihood ratio (NPLR) test to identify differentially expressed genes using microarray data. The NPLR test is highly robust against extreme values and does not assume the distribution of the parent population. Simulation studies show that the NPLR test is more powerful than some of the commonly used methods, such as the two-sample t-test, the Mann-Whitney U-test and significance analysis of microarrays (SAM). When applied to microarray data, we found that the NPLR test identifies more differentially expressed genes than its competitors. The asymptotic distribution of the NPLR test statistic and the p-value function is presented. The application of the NPLR method is shown, using both synthetic and real-life data. The biological significance of some of the genes detected only by the NPLR method is discussed.     

The Baumgartner-Weiss-Schindler test for the detection of differentially expressed genes in replicated microarray experiments

MOTIVATION: An important application of microarray experiments is to identify differentially expressed genes. Because microarray data are often not distributed according to a normal distribution nonparametric methods were suggested for their statistical analysis. Here, the Baumgartner-Weiss-Schindler test, a novel and powerful test based on ranks, is investigated and compared with the parametric t-test as well as with two other nonparametric tests (Wilcoxon rank sum test, Fisher-Pitman permutation test) recently recommended for the analysis of gene expression data. RESULTS: Simulation studies show that an exact permutation test based on the Baumgartner-Weiss-Schindler statistic B is preferable to the other three tests. It is less conservative than the Wilcoxon test and more powerful, in particular in case of asymmetric or heavily tailed distributions. When the underlying distribution is symmetric the differences in power between the tests are relatively small. Thus, the Baumgartner-Weiss-Schindler is recommended for the usual situation that the underlying distribution is a priori unknown. AVAILABILITY: SAS code available on request from the authors.     

A generalized likelihood ratio test to identify differentially expressed genes from microarray data

MOTIVATION: Microarray technology emerges as a powerful tool in life science. One major application of microarray technology is to identify differentially expressed genes under various conditions. Currently, the statistical methods to analyze microarray data are generally unsatisfactory, mainly due to the lack of understanding of the distribution and error structure of microarray data. RESULTS: We develop a generalized likelihood ratio (GLR) test based on the two-component model proposed by Rocke and Durbin to identify differentially expressed genes from microarray data. Simulation studies show that the GLR test is more powerful than commonly used methods, like the fold-change method and the two-sample t-test. When applied to microarray data, the GLR test identifies more differentially expressed genes than the t-test, has a lower false discovery rate and shows more consistency over independently repeated experiments. AVAILABILITY: The approach is implemented in software called GLR, which is freely available for downloading at http://www.cc.utah.edu/~jw27c60     

Rank products: a simple, yet powerful, new method to detect differentially regulated genes in replicated microarray experiments

One of the main objectives in the analysis of microarray experiments is the identification of genes that are differentially expressed under two experimental conditions. This task is complicated by the noisiness of the data and the large number of genes that are examined simultaneously. Here, we present a novel technique for identifying differentially expressed genes that does not originate from a sophisticated statistical model but rather from an analysis of biological reasoning. The new technique, which is based on calculating rank products (RP) from replicate experiments, is fast and simple. At the same time, it provides a straightforward and statistically stringent way to determine the significance level for each gene and allows for the flexible control of the false-detection rate and familywise error rate in the multiple testing situation of a microarray experiment. We use the RP technique on three biological data sets and show that in each case it performs more reliably and consistently than the non-parametric t-test variant implemented in Tusher et al.'s significance analysis of microarrays (SAM). We also show that the RP results are reliable in highly noisy data. An analysis of the physiological function of the identified genes indicates that the RP approach is powerful for identifying biologically relevant expression changes. In addition, using RP can lead to a sharp reduction in the number of replicate experiments needed to obtain reproducible results.     

Detecting differentially expressed genes by relative entropy

DNA microarray experiments have generated large amount of gene expression measurements across different conditions. One crucial step in the analysis of these data is to detect differentially expressed genes. Some parametric methods, including the two-sample t-test (T-test) and variations of it, have been used. Alternatively, a class of non-parametric algorithms, such as the Wilcoxon rank sum test (WRST), significance analysis of microarrays (SAM) of Tusher et al. (2001), the empirical Bayesian (EB) method of Efron et al. (2001), etc., have been proposed. Most available popular methods are based on t-statistic. Due to the quality of the statistic that they used to describe the difference between groups of data, there are situations when these methods are inefficient, especially when the data follows multi-modal distributions. For example, some genes may display different expression patterns in the same cell type, say, tumor or normal, to form some subtypes. Most available methods are likely to miss these genes. We developed a new non-parametric method for selecting differentially expressed genes by relative entropy, called SDEGRE, to detect differentially expressed genes by combining relative entropy and kernel density estimation, which can detect all types of differences between two groups of samples. The significance of whether a gene is differentially expressed or not can be estimated by resampling-based permutations. We illustrate our method on two data sets from Golub et al. (1999) and Alon et al. (1999). Comparing the results with those of the T-test, the WRST and the SAM, we identified novel differentially expressed genes which are of biological significance through previous biological studies while they were not detected by the other three methods. The results also show that the genes selected by SDEGRE have a better capability to distinguish the two cell types.     

Ranking analysis for identifying differentially expressed genes

Microarrays allow researchers to examine the expression of thousands of genes simultaneously. However, identification of genes differentially expressed in microarray experiments is challenging. With an optimal test statistic, we rank genes and estimate a threshold above which genes are considered to be differentially expressed genes (DE). This overcomes the embarrassing shortcoming of many statistical methods to determine the cut-off values in ranking analysis. Experiments demonstrate that our method is a good performance and avoids the problems with graphical examination and multiple hypotheses testing that affect alternative approaches. Comparing to those well known methods, our method is more sensitive to data sets with small differentially expressed values and not biased in favor of data sets based on certain distribution models.     

Functional cohesion of gene sets determined by latent semantic indexing of PubMed abstracts

High-throughput genomic technologies enable researchers to identify genes that are co-regulated with respect to specific experimental conditions. Numerous statistical approaches have been developed to identify differentially expressed genes. Because each approach can produce distinct gene sets, it is difficult for biologists to determine which statistical approach yields biologically relevant gene sets and is appropriate for their study. To address this issue, we implemented Latent Semantic Indexing (LSI) to determine the functional coherence of gene sets. An LSI model was built using over 1 million Medline abstracts for over 20,000 mouse and human genes annotated in Entrez Gene. The gene-to-gene LSI-derived similarities were used to calculate a literature cohesion p-value (LPv) for a given gene set using a Fisher's exact test. We tested this method against genes in more than 6,000 functional pathways annotated in Gene Ontology (GO) and found that approximately 75% of gene sets in GO biological process category and 90% of the gene sets in GO molecular function and cellular component categories were functionally cohesive (LPv<0.05). These results indicate that the LPv methodology is both robust and accurate. Application of this method to previously published microarray datasets demonstrated that LPv can be helpful in selecting the appropriate feature extraction methods. To enable real-time calculation of LPv for mouse or human gene sets, we developed a web tool called Gene-set Cohesion Analysis Tool (GCAT). GCAT can complement other gene set enrichment approaches by determining the overall functional cohesion of data sets, taking into account both explicit and implicit gene interactions reported in the biomedical literature. Availability: GCAT is freely available at http://binf1.memphis.edu/gcat.     

Density based pruning for identification of differentially expressed genes from microarray data

Motivation

Identification of differentially expressed genes from microarray datasets is one of the most important analyses for microarray data mining. Popular algorithms such as statistical t-test rank genes based on a single statistics. The false positive rate of these methods can be improved by considering other features of differentially expressed genes.

Results

We proposed a pattern recognition strategy for identifying differentially expressed genes. Genes are mapped to a two dimension feature space composed of average difference of gene expression and average expression levels. A density based pruning algorithm (DB Pruning) is developed to screen out potential differentially expressed genes usually located in the sparse boundary region. Biases of popular algorithms for identifying differentially expressed genes are visually characterized. Experiments on 17 datasets from Gene Omnibus Database (GEO) with experimentally verified differentially expressed genes showed that DB pruning can significantly improve the prediction accuracy of popular identification algorithms such as t-test, rank product, and fold change.

Conclusions

Density based pruning of non-differentially expressed genes is an effective method for enhancing statistical testing based algorithms for identifying differentially expressed genes. It improves t-test, rank product, and fold change by 11% to 50% in the numbers of identified true differentially expressed genes. The source code of DB pruning is freely available on our website http://mleg.cse.sc.edu/degprune

     

Investigating the effect of paralogs on microarray gene-set analysis

Background  

In order to interpret the results obtained from a microarray experiment, researchers often shift focus from analysis of individual differentially expressed genes to analyses of sets of genes. These gene-set analysis (GSA) methods use previously accumulated biological knowledge to group genes into sets and then aim to rank these gene sets in a way that reflects their relative importance in the experimental situation in question. We suspect that the presence of paralogs affects the ability of GSA methods to accurately identify the most important sets of genes for subsequent research.     

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.     

An associative analysis of gene expression array data

MOTIVATION: We face the absence of optimized standards to guide normalization, comparative analysis, and interpretation of data sets. One aspect of this is that current methods of statistical analysis do not adequately utilize the information inherent in the large data sets generated in a microarray experiment and require a tradeoff between detection sensitivity and specificity. RESULTS: We present a multistep procedure for analysis of mRNA expression data obtained from cDNA array methods. To identify and classify differentially expressed genes, results from standard paired t-test of normalized data are compared with those from a novel method, denoted an associative analysis. This method associates experimental gene expressions presented as residuals in regression analysis against control averaged expressions to a common standard-the family of similarly computed residuals for low variability genes derived from control experiments. By associating changes in expression of a given gene to a large family of equally expressed genes of the control group, this method utilizes the large data sets inherent in microarray experiments to increase both specificity and sensitivity. The overall procedure is illustrated by tabulation of genes whose expression differs significantly between Snell dwarf mice (dw/dw) and their phenotypically normal littermates (dw/+, +/+). Of the 2,352 genes examined only 450-500 were expressed above the background levels observed in nonexpressed genes and of these 120 were established as differentially expressed in dwarf mice at a significance level that excludes appearance of false positive determinations.     

Leveraging two-way probe-level block design for identifying differential gene expression with high-density oligonucleotide arrays

Background  

To identify differentially expressed genes across experimental conditions in oligonucleotide microarray experiments, existing statistical methods commonly use a summary of probe-level expression data for each probe set and compare replicates of these values across conditions using a form of the t-test or rank sum test. Here we propose the use of a statistical method that takes advantage of the built-in redundancy architecture of high-density oligonucleotide arrays.     

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。     

EVE (external variance estimation) increases statistical power for detecting differentially expressed genes

Accurately identifying differentially expressed genes from microarray data is not a trivial task, partly because of poor variance estimates of gene expression signals. Here, after analyzing 380 replicated microarray experiments, we found that probesets have typical, distinct variances that can be estimated based on a large number of microarray experiments. These probeset-specific variances depend at least in part on the function of the probed gene: genes for ribosomal or structural proteins often have a small variance, while genes implicated in stress responses often have large variances. We used these variance estimates to develop a statistical test for differentially expressed genes called EVE (external variance estimation). The EVE algorithm performs better than the t-test and LIMMA on some real-world data, where external information from appropriate databases is available. Thus, EVE helps to maximize the information gained from a typical microarray experiment. Nonetheless, only a large number of replicates will guarantee to identify nearly all truly differentially expressed genes. However, our simulation studies suggest that even limited numbers of replicates will usually result in good coverage of strongly differentially expressed genes.     

Rank-invariant resampling based estimation of false discovery rate for analysis of small sample microarray data

Background  

The evaluation of statistical significance has become a critical process in identifying differentially expressed genes in microarray studies. Classical p-value adjustment methods for multiple comparisons such as family-wise error rate (FWER) have been found to be too conservative in analyzing large-screening microarray data, and the False Discovery Rate (FDR), the expected proportion of false positives among all positives, has been recently suggested as an alternative for controlling false positives. Several statistical approaches have been used to estimate and control FDR, but these may not provide reliable FDR estimation when applied to microarray data sets with a small number of replicates.     

Multivariate exploratory tools for microarray data analysis

The ultimate success of microarray technology in basic and applied biological sciences depends critically on the development of statistical methods for gene expression data analysis. The most widely used tests for differential expression of genes are essentially univariate. Such tests disregard the multidimensional structure of microarray data. Multivariate methods are needed to utilize the information hidden in gene interactions and hence to provide more powerful and biologically meaningful methods for finding subsets of differentially expressed genes. The objective of this paper is to develop methods of multidimensional search for biologically significant genes, considering expression signals as mutually dependent random variables. To attain these ends, we consider the utility of a pertinent distance between random vectors and its empirical counterpart constructed from gene expression data. The distance furnishes exploratory procedures aimed at finding a target subset of differentially expressed genes. To determine the size of the target subset, we resort to successive elimination of smaller subsets resulting from each step of a random search algorithm based on maximization of the proposed distance. Different stopping rules associated with this procedure are evaluated. The usefulness of the proposed approach is illustrated with an application to the analysis of two sets of gene expression data.     

Gene selection with multiple ordering criteria

Background  

A microarray study may select different differentially expressed gene sets because of different selection criteria. For example, the fold-change and p-value are two commonly known criteria to select differentially expressed genes under two experimental conditions. These two selection criteria often result in incompatible selected gene sets. Also, in a two-factor, say, treatment by time experiment, the investigator may be interested in one gene list that responds to both treatment and time effects.     

Modified nonparametric approaches to detecting differentially expressed genes in replicated microarray experiments

MOTIVATION: An important goal in analyzing microarray data is to determine which genes are differentially expressed across two kinds of tissue samples or samples obtained under two experimental conditions. Various parametric tests, such as the two-sample t-test, have been used, but their possibly too strong parametric assumptions or large sample justifications may not hold in practice. As alternatives, a class of three nonparametric statistical methods, including the empirical Bayes method of Efron et al. (2001), the significance analysis of microarray (SAM) method of Tusher et al. (2001) and the mixture model method (MMM) of Pan et al. (2001), have been proposed. All the three methods depend on constructing a test statistic and a so-called null statistic such that the null statistic's distribution can be used to approximate the null distribution of the test statistic. However, relatively little effort has been directed toward assessment of the performance or the underlying assumptions of the methods in constructing such test and null statistics. RESULTS: We point out a problem of a current method to construct the test and null statistics, which may lead to largely inflated Type I errors (i.e. false positives). We also propose two modifications that overcome the problem. In the context of MMM, the improved performance of the modified methods is demonstrated using simulated data. In addition, our numerical results also provide evidence to support the utility and effectiveness of MMM.     

Identification of differentially expressed genes using multi-resolution wavelet transformation analysis combined with SAM

Although many statistical methods have been proposed for identifying differentially expressed genes, the optimal approach has still not been resolved. Therefore, it is necessary to develop more efficient methods of finding differentially expressed genes while accounting for noise and false discovery rate (FDR). We propose a method based on multi-resolution wavelet transformation analysis combined with SAM for identifying differentially expressed genes by adjusting the Δ and computing the FDR. This method was applied to a microarray expression dataset from adenoma patients and normal subjects. The number of differentially expressed genes gradually reduced with an increasing Δ value, and the FDR was reduced after wavelet transformation. At a given Δ value, the FDR was also reduced before and after wavelet transformation. In conclusion, a greater number and quality of differentially expressed genes were detected using the method when compared to non-transformed data, and the FDRs were notably more controlled and reduced.