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...y as well as statistically significant. limma provides a number of options to adjust tests for multiple testing. Users can control either the family-wise type I error rate or the false discovery rate =-=[5]-=-. As well as the usual control for multiple testing across multiple genes, limma is the only software package to provide methods for error rate control across multiple contrasts and genes simultaneous...

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... information between genes in a dynamic way [14, 40]. The fact that the same linear model is fitted to each gene allows us to borrow strength between genes in order to moderate the residual variances =-=[63]-=-. The estimated variance for each gene then becomes a compromise between the gene-wise estimator, obtained from the data for that gene alone, and the global variability across all genes, estimated by ...

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... given gene is differentially expressed. Gene set enrichment analysis (GSEA) is an approach which correlates a large database of coregulated gene sets with respect to a microarray or RNA-seq data set =-=[39, 69]-=-. romer implements a GSEA of a battery of gene sets similar in motivation to Subramanian et al. [69] but designed for use with linear models. It is a competitive test, in that the different gene sets ...

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... from beginning to end in a flexible and statistically rigorous way. The limma package is a core component of Bioconductor, an R-based open-source software development project in statistical genomics =-=[16, 64]-=-. It has proven a popular choice for the analysis of data from experiments involving microarrays [44, 8], high-throughput PCR [20], protein arrays [35] and other platforms. The package is designed in ...

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... established in the biomedical literature that the level of agreement between correlated variables can be usefully examined by plotting differences vs means. Such a plot is called a Bland-Altman plot =-=[36]-=- or a Tukey mean-difference plot [10]. Indeed the concept of DE can be viewed as a measure of disagreement between expression measures for the same genes in different samples. Mean-difference plots we...

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...ures for the same genes in different samples. Mean-difference plots were introduced to the two-color microarray literature by Dudoit et al. [13] and to the single-channel literature by Bolstad et al. =-=[6]-=-, who called them MA-plots. limma generalized the concept of an MA-plot in two ways. First, the idea was extended to apply to sets of single-channel expression values. In this case, the plot is used t...

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... from beginning to end in a flexible and statistically rigorous way. The limma package is a core component of Bioconductor, an R-based open-source software development project in statistical genomics =-=[16, 64]-=-. It has proven a popular choice for the analysis of data from experiments involving microarrays [44, 8], high-throughput PCR [20], protein arrays [35] and other platforms. The package is designed in ...

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...ing the two channels for each array. A popular method is to remove intensity-dependent dye-biases and spatial artifacts from M -values (log-intensity ratios) using locally weighted regression (loess) =-=[78]-=-. The normalizeBetweenArrays function aligns expression values between samples for one-color microarrays and other single channel platforms using methods such as quantile normalization or cyclic loess...

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...ticular molecular pathway or some other biological process of interest. Gene sets are defined by gene annotation external to the current expression study, for example from Gene Ontology (GO) database =-=[3]-=- or from previous expression studies. For gene sets defined by previous studies, the genes may optionally be annotated with the direction and magnitude of expression changes in the earlier experiment....

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...ture that the level of agreement between correlated variables can be usefully examined by plotting differences vs means. Such a plot is called a Bland-Altman plot [36] or a Tukey mean-difference plot =-=[10]-=-. Indeed the concept of DE can be viewed as a measure of disagreement between expression measures for the same genes in different samples. Mean-difference plots were introduced to the two-color microa...

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... viewed as a measure of disagreement between expression measures for the same genes in different samples. Mean-difference plots were introduced to the two-color microarray literature by Dudoit et al. =-=[13]-=- and to the single-channel literature by Bolstad et al. [6], who called them MA-plots. limma generalized the concept of an MA-plot in two ways. First, the idea was extended to apply to sets of single-...

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...d other sequence count data, as well as for data from microarrays and other platforms. Traditionally, RNAseq data requires specialized software based on the negative binomial or similar distributions =-=[57]-=-. limma however is able to analyse RNA-seq read counts with high precision by converting counts to the log-scale and estimating the mean-variance relationship empirically (Figure 3A) and incorporating...

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...by the voom function or can be pre-normalized by adding normalization factors within edgeR. Raw read counts are assembled outside limma using tools such as featureCounts [29], HTSeqcounts [1] or RSEM =-=[27]-=-. The authors of this article find the Subread [28] and featureCounts pipeline particularly convenient because it is fast, acccurate [68] and can be run from the R prompt using the Rsubread package. T...

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... given gene is differentially expressed. Gene set enrichment analysis (GSEA) is an approach which correlates a large database of coregulated gene sets with respect to a microarray or RNA-seq data set =-=[39, 69]-=-. romer implements a GSEA of a battery of gene sets similar in motivation to Subramanian et al. [69] but designed for use with linear models. It is a competitive test, in that the different gene sets ...

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...normalizeBetweenArrays also implements separate channel normalization methods for two-color arrays [79, 67]. limma is the only software to allow the use of quantitative weights in loess normalization =-=[66]-=-, giving it the ability to downweight less reliable probes or to give higher priority to control probes or housekeeping genes. The latter ability has been exploited for normalizing assays when the pro...

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...ure is then incorporated into the linear model fit and hence into all tests for DE. Originally the idea was used to estimate the correlation between replicate copies of the same probe on a microarray =-=[65]-=-. The correlation strategy preserves more information than simply averaging the replicate probe copies. More generally, the same idea is also used to model the correlation between related RNA samples,...

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...hly parallel nature of gene expression experiments lends itself to a particular class of statistical methods, called parametric empirical Bayes, that borrow information between genes in a dynamic way =-=[14, 40]-=-. The fact that the same linear model is fitted to each gene allows us to borrow strength between genes in order to moderate the residual variances [63]. The estimated variance for each gene then beco...

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...een samples by the voom function or can be pre-normalized by adding normalization factors within edgeR. Raw read counts are assembled outside limma using tools such as featureCounts [29], HTSeqcounts =-=[1]-=- or RSEM [27]. The authors of this article find the Subread [28] and featureCounts pipeline particularly convenient because it is fast, acccurate [68] and can be run from the R prompt using the Rsubre...

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...). Panel (B) displays background corrected but non-normalized intensities from one typical array. Panel (C) was generated from a subset of 30 of the control arrays after print-tip loess normalization =-=(12)-=-. Figure 4 shows example DE summary plots. Panels (A) and (B) were generated using the two-colour microarray data from GEO series GSE2593. Intensities were background corrected and normalized as previ...

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... ‘LargeDataObject’ for which a show method is defined to display the leading rows of a large vector, matrix or data.frame. 7.2 Computational efficiency The limma package is implemented primarily in R =-=[50]-=- and includes some C code to speed up computationally intensive steps. At every stage, effort has been expended to achieve high numerical reliability and efficiency. The memory requirements are linear...

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...as a building block or as the underlying computational engine by a number of software projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI =-=[70]-=-, WebArray [76], RACE [49], CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degu...

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...mbination of methods to use will depend upon the biological question, platform used (microarray/RNA-seq) and experimental design. Being R-based, reports of limma analyses can be compiled using Sweave =-=[25]-=- or knitr [77] and provided along with the raw data in a compendium to promote reproducible research in genomics [15]. Applications of limma’s linear modelling strategy beyond the intended analysis of...

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... accessible for RNA-seq data from within the voom function. Alternatively, voom has the ability to respect normalization factors computed outside of limma by methods such as trimmed mean of M -values =-=[58]-=- or conditional quantile normalization [18]. 4.4 Graphical exploration of data quality Diagnostic plots allow the user to visually inspect data from a designed experiment in order to identify potentia...

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...ompetitive tests, the different gene sets are pitted against one another. In self-contained tests, only the genes in the gene set are considered and whether they are associated with the sample groups =-=[17]-=-. If the primary interest is to use Gene Ontology (GO [3]) terms as gene sets, the goana function is available. It applies a generalized hypergeometric test for enrichment of each GO term in the up an...

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...normalizeBetweenArrays also implements separate channel normalization methods for two-colour arrays (36,37). limma is the only software to allow the use of quantitative weights in loess normalization =-=(38)-=-, giving it the ability to downweigh less reliable probes or to give higher priority to control probes or house-keeping genes. The latter ability has been exploited for normalizing assays when the pro...

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...hly parallel nature of gene expression experiments lends itself to a particular class of statistical methods, called parametric empirical Bayes, that borrow information between genes in a dynamic way =-=[14, 40]-=-. The fact that the same linear model is fitted to each gene allows us to borrow strength between genes in order to moderate the residual variances [63]. The estimated variance for each gene then beco...

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...ssment and normalization, through to linear modelling, DE and gene signature analyses. MATERIALS AND METHODS Figure 3 shows example diagnostic plots. Panel (A) shows RNA-seq data from Pickrell et al. =-=(9)-=- that has been analysed as described by Law et al. (10). Panels (B) and (C) display the two-colour microarray quality control data set presented by Ritchie et al. (11). Panel (B) displays background c...

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...ion. Like camera and mroast, it can be used with a battery of gene sets and with any linear model. The limma authors maintain mouse and human versions of the Molecular Signatures Database collections =-=(64)-=- in R binary format that can be conveniently used with camera, mroast or romer (http://bioinf.wehi.edu. au/software/MSigDB). The use of gene sets require that gene symbols and annotation be matched be...

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...f replicates is small. In recent years, the empirical Bayes procedures of limma have been enhanced in two important ways. First, the global variance estimate can now incorporate a mean-variance trend =-=[59, 47, 24]-=-. This is important because many gene expression technologies produce data that is less reliable at lower intensities or abundances. Second, the relative weighting of the gene-wise and global variance...

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...ifferent methods. The default is based on averaging local false discovery rates across the p-values [46]. Other methods are the histogram method of [41, 42], the convex decreasing density estimate of =-=[22]-=-, and a very simple estimate based on averaging the p-values. 6.1 Genuine association of gene expression profiles Gene expression experiments typically involve a number of different treatment conditio...

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...plementation of lowess curves and normalization using quantitative weights. The guiding principle in the pre-processing steps is to preserve information, avoiding missing values or inflated variances =-=[55]-=-. Normalized intensities are offset from zero before transforming to the log-scale to avoid missing values or large variances. Offsets in a range of moderate values have been shown to achieve an effec...

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...est a large number of gene sets, roast is most useful for linking different datasets by finding similarities in gene expression patterns using gene weights from other differential expression analyses =-=[31, 30, 4, 74]-=-. Potential applications for roast include those where the set might not be made up of genes, e.g., exon-level expression analyses to test whether any exon of a given gene is differentially expressed....

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...ntal design. Being R-based, reports of limma analyses can be compiled using Sweave [25] or knitr [77] and provided along with the raw data in a compendium to promote reproducible research in genomics =-=[15]-=-. Applications of limma’s linear modelling strategy beyond the intended analysis of gene expression data have been made in a variety of applications, including the analysis of data from Nuclear Magnet...

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...-handed [55]. The limma backgroundCorrect function offers a range of more sophisticated alternatives, most unique to the package. These include a method based on a convolution of normal distributions =-=[21]-=- and a normal-exponential (normexp) convolution [55] with different options for parameter estimation [62]. The plotFB function plots foreground against background intensities for each array and is use...

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...ding normalization factors within edgeR. Raw read counts are assembled outside limma using tools such as featureCounts [29], HTSeqcounts [1] or RSEM [27]. The authors of this article find the Subread =-=[28]-=- and featureCounts pipeline particularly convenient because it is fast, acccurate [68] and can be run from the R prompt using the Rsubread package. The data input to limma should be counts, rather tha...

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...est a large number of gene sets, roast is most useful for linking different datasets by finding similarities in gene expression patterns using gene weights from other differential expression analyses =-=[31, 30, 4, 74]-=-. Potential applications for roast include those where the set might not be made up of genes, e.g., exon-level expression analyses to test whether any exon of a given gene is differentially expressed....

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...est for over-representation of GO terms in one or more sets of genes. goana includes the ability to adjust for gene length or abundance biases in DE detection in a similar way to the goseq package 15 =-=[80]-=-. Another simple approach is implemented in the geneSetTest/wilcoxGST functions which perform rank-based tests (as used in Michaud et al. [38]). Such tests assess how highly ranked a group of genes is...

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...t of Bioconductor, an R-based open-source software development project in statistical genomics [16, 64]. It has proven a popular choice for the analysis of data from experiments involving microarrays =-=[44, 8]-=-, high-throughput PCR [20], protein arrays [35] and other platforms. The package is designed in such a way that, after initial pre-processing and normalization, the same analysis pipeline is used for ...

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...tic p-values in competitive gene set tests. More sophisticated competitive tests that take into account dependence of the genes in the linear modelling framework have also been implemented via camera =-=[75, 74]-=-. Camera is a variance adjusted mean-rank testing method. The variance of the summary statistics would be higher than estimated, if the (mostly) positive average inter-gene correlation in a gene set i...

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...lock or as the underlying computational engine by a number of software projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray =-=[76]-=-, RACE [49], CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www....

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... linear model. The function implements a number of different methods. The default is based on averaging local false discovery rates across the p-values [46]. Other methods are the histogram method of =-=[41, 42]-=-, the convex decreasing density estimate of [22], and a very simple estimate based on averaging the p-values. 6.1 Genuine association of gene expression profiles Gene expression experiments typically ...

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...computational engine by a number of software projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray [76], RACE [49], CarmaWEB =-=[51]-=-, Goulphar [26], MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www. vicbioinformatics.com/deg...

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...the underlying computational engine by a number of software projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray [76], RACE =-=[49]-=-, CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www. vicbioinfo...

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...ed. When one has a particular cut-off for log-fold-change in mind, the treat function can be used to test whether the log2-fold-change is greater than a threshold rather than merely different to zero =-=[37]-=-. This can be effective for prioritizing results that are biologically as well as statistically significant. limma provides a number of options to adjust tests for multiple testing. Users can control ...

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...e voom function. Alternatively, voom has the ability to respect normalization factors computed outside of limma by methods such as trimmed mean of M -values [58] or conditional quantile normalization =-=[18]-=-. 4.4 Graphical exploration of data quality Diagnostic plots allow the user to visually inspect data from a designed experiment in order to identify potential quality problems, such as degraded sample...

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...t of Bioconductor, an R-based open-source software development project in statistical genomics [16, 64]. It has proven a popular choice for the analysis of data from experiments involving microarrays =-=[44, 8]-=-, high-throughput PCR [20], protein arrays [35] and other platforms. The package is designed in such a way that, after initial pre-processing and normalization, the same analysis pipeline is used for ...

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...GUI [71], affylmGUI [70], WebArray [76], RACE [49], CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas =-=[45]-=-, Guide [9] and Degust (http://www. vicbioinformatics.com/degust). 7.4 Documentation The limma package provides three levels of documentation. First, each function has its own documentation page that ...

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...elf. The use of weights increases power to detect differentially expressed genes, and having a model based approach avoids the need for ad-hoc decisions on which observations or samples to filter out =-=[54]-=-. 2.6 RNA-seq and sequence data All the downstream analysis features of limma are available for RNA-seq and other sequence count data, as well as for data from microarrays and other platforms. Traditi...

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...m zero before transforming to the log-scale to avoid missing values or large variances. Offsets in a range of moderate values have been shown to achieve an effective compromise between noise and bias =-=[61]-=-. 2.10 Mean-difference plots Measuring expression in multiple RNA samples produces columns of correlated expression values, which are highly correlated because they are measured on the same set of gen...

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... linear model. The function implements a number of different methods. The default is based on averaging local false discovery rates across the p-values [46]. Other methods are the histogram method of =-=[41, 42]-=-, the convex decreasing density estimate of [22], and a very simple estimate based on averaging the p-values. 6.1 Genuine association of gene expression profiles Gene expression experiments typically ...

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...This avoids overly optimistic p-values in the test results. The roast (rotation gene set tests) method tests the self-contained null hypotheses of whether a given gene set is differentially expressed =-=[73]-=-. Instead of permutation, it uses rotation, which is a smoothed version of permutation suitable for linear models [23]. For genes in the set, the residual space orthogonal to the nuisance parameters i...

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...eam commands as microarrays. The resulting pipeline gives comparable performance to the best of the negative binomial based software packages but with greater speed and reliability for large datasets =-=[52, 24]-=-. Additionally, and conveniently, only minimal pipeline changes are required when switching between analyses for RNA-seq and microarray experiments within limma. This also means that the same statisti...

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...ethods to use will depend upon the biological question, platform used (microarray/RNA-seq) and experimental design. Being R-based, reports of limma analyses can be compiled using Sweave [25] or knitr =-=[77]-=- and provided along with the raw data in a compendium to promote reproducible research in genomics [15]. Applications of limma’s linear modelling strategy beyond the intended analysis of gene expressi...

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...contained null hypotheses of whether a given gene set is differentially expressed [73]. Instead of permutation, it uses rotation, which is a smoothed version of permutation suitable for linear models =-=[23]-=-. For genes in the set, the residual space orthogonal to the nuisance parameters in the linear model is randomly rotated to generate the distribution of the parameter of interest under the null hypoth...

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...f replicates is small. In recent years, the empirical Bayes procedures of limma have been enhanced in two important ways. First, the global variance estimate can now incorporate a mean-variance trend =-=[59, 47, 24]-=-. This is important because many gene expression technologies produce data that is less reliable at lower intensities or abundances. Second, the relative weighting of the gene-wise and global variance...

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... Both functions provide a range of different normalization methods suitable for different platforms. normalizeBetweenArrays also implements separate channel normalization methods for two-color arrays =-=[79, 67]-=-. limma is the only software to allow the use of quantitative weights in loess normalization [66], giving it the ability to downweight less reliable probes or to give higher priority to control probes...

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...be normalized between samples by the voom function or can be pre-normalized by adding normalization factors within edgeR. Raw read counts are assembled outside limma using tools such as featureCounts =-=[29]-=-, HTSeqcounts [1] or RSEM [27]. The authors of this article find the Subread [28] and featureCounts pipeline particularly convenient because it is fast, acccurate [68] and can be run from the R prompt...

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...genes that are induced (red) or repressed (blue) upon the transition from large cycling pre-B cells to small resting pre-B cells during normal B cell development according to the published literature =-=[19]-=- The plot shows a strong positive concordance between Pax5 restoration and the large to small cell transition. The roast function can be used to assign statistical significance to this correlation. us...

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...ty to control probes or housekeeping genes. The latter ability has been exploited for normalizing assays when the proportion of differentially expressed genes may be high, for example boutique arrays =-=[43]-=-, miRNA arrays [72], PCR arrays, protein arrays or protein mass spectrometry. Other enhancements include the ability to replace the loess curve with a spline curve that has high robustness breakdown p...

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...est a large number of gene sets, roast is most useful for linking different datasets by finding similarities in gene expression patterns using gene weights from other differential expression analyses =-=[31, 30, 4, 74]-=-. Potential applications for roast include those where the set might not be made up of genes, e.g., exon-level expression analyses to test whether any exon of a given gene is differentially expressed....

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... procedures suitable for different types of DNA microarrays or protein arrays. Notable are the maximum likelihood implementation of the normal5 exponential convolution model for background correction =-=[62]-=- and the implementation of lowess curves and normalization using quantitative weights. The guiding principle in the pre-processing steps is to preserve information, avoiding missing values or inflated...

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...ngine by a number of software projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray [76], RACE [49], CarmaWEB [51], Goulphar =-=[26]-=-, MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www. vicbioinformatics.com/degust). 7.4 Docum...

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... development project in statistical genomics [16, 64]. It has proven a popular choice for the analysis of data from experiments involving microarrays [44, 8], high-throughput PCR [20], protein arrays =-=[35]-=- and other platforms. The package is designed in such a way that, after initial pre-processing and normalization, the same analysis pipeline is used for data from all technologies. Recently, the capab...

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... in DE detection in a similar way to the goseq package 15 [80]. Another simple approach is implemented in the geneSetTest/wilcoxGST functions which perform rank-based tests (as used in Michaud et al. =-=[38]-=-). Such tests assess how highly ranked a group of genes is in a particular contrast relative to other genes using a test statistic for DE. They assume the expression level of each gene is independent ...

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...ecific to these arrays [61]. The propexpr function compares intensities to those of negative control probes to estimate the total proportion of probes on each array that correspond to expressed genes =-=[60]-=-. This provides an estimate of the size of the transcriptome in each sample and is useful for deciding how many probes to filter from downstream analyses. 9 4.3 Normalization Before meaningful compari...

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... of applications, including the analysis of data from Nuclear Magnetic Resonance spectroscopy, PCR (including Nanostring), quantitative proteomics [7], DNA methylation arrays and comparative ChIP-seq =-=[33]-=-. As the cost of collecting genome-wide profiles continues to fall, we expect the popularity of this approach to continue to grow, with new applications in the analysis of single cell gene expression ...

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...r instance, applying genas to a microarray study looking at the relationship between polycomb repressor complex (PRC) 1 and PRC2 facilitated the discovery of the opposing roles of these two complexes =-=[34]-=-. This relationship would have been missed if the analysis were restricted to the statistically significant genes from each contrast alone. 6.2 Gene set testing Gene set analyses assess the overall si...

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...umber of software projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray [76], RACE [49], CarmaWEB [51], Goulphar [26], MAGMA =-=[53]-=-, Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www. vicbioinformatics.com/degust). 7.4 Documentation The...

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...ified set of genes is more highly ranked in an ordered list of all genes thanwould be expected by chance. These tests have been found to give an effective ranking of biologically significant pathways =-=(54)-=-, but they implicitly assume that the expression level of each gene is conditionally independent of other genes and hence give optimistic P-values (55). More sophisticated competitive tests that take ...

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... open-source software development project in statistical genomics [16, 64]. It has proven a popular choice for the analysis of data from experiments involving microarrays [44, 8], high-throughput PCR =-=[20]-=-, protein arrays [35] and other platforms. The package is designed in such a way that, after initial pre-processing and normalization, the same analysis pipeline is used for data from all technologies...

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...s of gene expression data have been made in a variety of applications, including the analysis of data from Nuclear Magnetic Resonance spectroscopy, PCR (including Nanostring), quantitative proteomics =-=[7]-=-, DNA methylation arrays and comparative ChIP-seq [33]. As the cost of collecting genome-wide profiles continues to fall, we expect the popularity of this approach to continue to grow, with new applic...

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... decrease. It is known that the DE status of genes outside the gene set will not impact on the significance of a self-contained test, so the power of romer can be higher than camera in this situation =-=[34, 2]-=-. To perform romer, mroast or camera gene set tests with a database of gene sets, we need to know the indices of the gene sets in the expression data matrix. A simple way to match between gene identif...

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... fall, we expect the popularity of this approach to continue to grow, with new applications in the analysis of single cell gene expression data, CRISPR/Cas9 knock-out screens and methylation analysis =-=[48]-=-. Funding This research was supported by NHMRC Project grant 1050661 (MER, GKS), Project Grant 1023454 (GKS, MER, WS), Program grant 1054618 (GKS), Victorian State Government Operational Infrastructur...

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...s or housekeeping genes. The latter ability has been exploited for normalizing assays when the proportion of differentially expressed genes may be high, for example boutique arrays [43], miRNA arrays =-=[72]-=-, PCR arrays, protein arrays or protein mass spectrometry. Other enhancements include the ability to replace the loess curve with a spline curve that has high robustness breakdown properties, and the ...

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...f replicates is small. In recent years, the empirical Bayes procedures of limma have been enhanced in two important ways. First, the global variance estimate can now incorporate a mean-variance trend =-=[59, 47, 24]-=-. This is important because many gene expression technologies produce data that is less reliable at lower intensities or abundances. Second, the relative weighting of the gene-wise and global variance...

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... Both functions provide a range of different normalization methods suitable for different platforms. normalizeBetweenArrays also implements separate channel normalization methods for two-color arrays =-=[79, 67]-=-. limma is the only software to allow the use of quantitative weights in loess normalization [66], giving it the ability to downweight less reliable probes or to give higher priority to control probes...

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...limma have expanded significantly in two important directions. First, the package can now perform both differential expression (DE) and differential splicing analyses of RNA sequencing (RNA-seq) data =-=[32, 68]-=-. All the downstream analysis tools previously restricted to microarray data are now available for RNA-seq as well. These capabilities allow users to analyse both RNA-seq and microarray data with very...

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...ablished in the biomedical literature that the level of agreement between correlated variables can be usefully examined by plotting differences versus means. Such a plot is called a Bland–Altman plot =-=(25)-=- or a Tukey meandifference plot (26). Indeed the concept ofDE can be viewedsat Pennsylvania State U niversity on Septem ber 15, 2016 http://nar.oxfordjournals.org/ D ow nloaded from Nucleic Acids Rese...

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...ed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray [76], RACE [49], CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias [12], GenePattern =-=[11]-=-, GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www. vicbioinformatics.com/degust). 7.4 Documentation The limma package provides three lev...

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...re projects designed to provide user-interfaces for gene expression data analysis including limmaGUI [71], affylmGUI [70], WebArray [76], RACE [49], CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias =-=[12]-=-, GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide [9] and Degust (http://www. vicbioinformatics.com/degust). 7.4 Documentation The limma package ...

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...ld they exist. 5.3 Quality weights and heteroscedasticity limma is the only package that allows variations in quality to be handled in a graduated way via quantitative weights. Both observation-level =-=[56, 64, 24]-=- and sample-specific weights [54] can be used in an analysis. For microarray data, the arrayWeights function estimates relative array variances, which are converted to weights which can be used in the...

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...tic p-values in competitive gene set tests. More sophisticated competitive tests that take into account dependence of the genes in the linear modelling framework have also been implemented via camera =-=[75, 74]-=-. Camera is a variance adjusted mean-rank testing method. The variance of the summary statistics would be higher than estimated, if the (mostly) positive average inter-gene correlation in a gene set i...

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...fylmGUI [70], WebArray [76], RACE [49], CarmaWEB [51], Goulphar [26], MAGMA [53], Asterias [12], GenePattern [11], GEO2R (http://www.ncbi. nlm.nih.gov/geo/geo2r), the EBI expression atlas [45], Guide =-=[9]-=- and Degust (http://www. vicbioinformatics.com/degust). 7.4 Documentation The limma package provides three levels of documentation. First, each function has its own documentation page that concisely b...

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...limma have expanded significantly in two important directions. First, the package can now perform both differential expression (DE) and differential splicing analyses of RNA sequencing (RNA-seq) data =-=[32, 68]-=-. All the downstream analysis tools previously restricted to microarray data are now available for RNA-seq as well. These capabilities allow users to analyse both RNA-seq and microarray data with very...

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...obal variance estimators no longer needs to be the same for all genes. This allows a sophisticated robust empirical Bayes procedure in which hyper-variable genes are identified and treated separately =-=[46, 47]-=-. Both of these enhancements improve statistical power and accuracy by improving the modelling of the global characteristics of the data in a more flexible way. 2.5 Quantitative weights allow for uneq...