Scaling in ANOVA-simultaneous component analysis.
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ABSTRACT:
SUBMITTER: Timmerman ME
PROVIDER: S-EPMC4559107 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:When analyzing experimental chemical data, it is often necessary to incorporate the structure of the study design into the chemometric/statistical models to effectively address the research questions of interest. ANOVA-Simultaneous Component Analysis (ASCA) is one of the most prominent methods to include such information in the quantitative analysis of multivariate data, especially when the number of variables is large. This tutorial review intends to explain in a simple way how ASCA works, how it is operated and how to correctly interpret ASCA results, with approachable mathematical and visual descriptions. Two examples are given: the first, a simulated chemical reaction, serves to illustrate the ASCA steps and the second, from a real chemical ecology data set, the interpretation of results. An overview of methods closely related to ASCA is also provided, pointing out their differences and scope, to give a wide-ranging picture of the available options to build multivariate models that take experimental design into account. Graphical abstract Image 1 Highlights • ASCA is a multivariate method for analysis of multi-factor data.• An overview of the (mathematical) principles of ASCA is presented.• Key aspects for practical application of ASCA are discussed.• Detailed explanation of ASCA output in terms of score and loading plots is given.• Literature review of other multivariate techniques for analysis of multi-factor data.
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Project description:Interdisciplinary research often involves analyzing data obtained from different data sources with respect to the same subjects, objects, or experimental units. For example, global positioning systems (GPS) data have been coupled with travel diary data, resulting in a better understanding of traveling behavior. The GPS data and the travel diary data are very different in nature, and, to analyze the two types of data jointly, one often uses data integration techniques, such as the regularized simultaneous component analysis (regularized SCA) method. Regularized SCA is an extension of the (sparse) principle component analysis model to the cases where at least two data blocks are jointly analyzed, which - in order to reveal the joint and unique sources of variation - heavily relies on proper selection of the set of variables (i.e., component loadings) in the components. Regularized SCA requires a proper variable selection method to either identify the optimal values for tuning parameters or stably select variables. By means of two simulation studies with various noise and sparseness levels in simulated data, we compare six variable selection methods, which are cross-validation (CV) with the "one-standard-error" rule, repeated double CV (rdCV), BIC, Bolasso with CV, stability selection, and index of sparseness (IS) - a lesser known (compared to the first five methods) but computationally efficient method. Results show that IS is the best-performing variable selection method.
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Project description:In order to identify genes with differential gene expression or alternative splicing between the groups naive and activated we study 4 hybridizations on the Human Exon 1.0 ST array using mixed model analysis of variance. 1904 genes with significant gene expression differences between the groups and 1603 genes with significant exon-group interaction (a symptom of alternative splicing) were found, including 427 genes with both gene and possible splicing differences (p<0.01). Contingency table analysis of the set of studied genes and a dataset of known pathways and gene classifications revealed that the set of alternatively spliced and expressed genes were found to be significantly over-represented in groups of the GOMolFn, GOProcess, GOCellLoc, and Pathway classes (p<0.01). Algorithm ANOVA study of 4 Human Exon 1.0 ST files.
2008-06-20 | GSE11832 | GEO
Project description:Experimental variance is a major challenge when dealing with high-throughput sequencing data. This variance has several sources: sampling replication, technical replication, variability within biological conditions, and variability between biological conditions. The high per-sample cost of RNA-Seq often precludes the large number of experiments needed to partition observed variance into these categories as per standard ANOVA models. We show that the partitioning of within-condition to between-condition variation cannot reasonably be ignored, whether in single-organism RNA-Seq or in Meta-RNA-Seq experiments, and further find that commonly-used RNA-Seq analysis tools, as described in the literature, do not enforce the constraint that the sum of relative expression levels must be one, and thus report expression levels that are systematically distorted. These two factors lead to misleading inferences if not properly accommodated. As it is usually only the biological between-condition and within-condition differences that are of interest, we developed ALDEx, an ANOVA-like differential expression procedure, to identify genes with greater between- to within-condition differences. We show that the presence of differential expression and the magnitude of these comparative differences can be reasonably estimated with even very small sample sizes.
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Project description:Component models such as PCA and ICA are often used to reduce neuroimaging data into a smaller number of components, which are thought to reflect latent brain networks. When data from multiple subjects are available, the components are typically estimated simultaneously (i.e., for all subjects combined) using either tensor ICA or group ICA. As we demonstrate in this paper, neither of these approaches is ideal if one hopes to find latent brain networks that cross-validate to new samples of data. Specifically, we note that the tensor ICA model is too rigid to capture real-world heterogeneity in the component time courses, whereas the group ICA approach is too flexible to uniquely identify latent brain networks. For multi-subject component analysis, we recommend comparing a hierarchy of simultaneous component analysis (SCA) models. Our proposed model hierarchy includes a flexible variant of the SCA framework (the Parafac2 model), which is able to both (i) model heterogeneity in the component time courses, and (ii) uniquely identify latent brain networks. Furthermore, we propose cross-validation methods to tune the relevant model parameters, which reduces the potential of over-fitting the observed data. Using simulated and real data examples, we demonstrate the benefits of the proposed approach for finding credible components that reveal interpretable individual and group differences in latent brain networks.
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Project description:The integration of event-related potential (ERP) and functional magnetic resonance imaging (fMRI) can contribute to characterizing neural networks with high temporal and spatial resolution. This research aimed to determine the sensitivity and limitations of applying joint independent component analysis (jICA) within-subjects, for ERP and fMRI data collected simultaneously in a parametric auditory frequency oddball paradigm. In a group of 20 subjects, an increase in ERP peak amplitude ranging 1-8 ?V in the time window of the P300 (350-700 ms), and a correlated increase in fMRI signal in a network of regions including the right superior temporal and supramarginal gyri, was observed with the increase in deviant frequency difference. JICA of the same ERP and fMRI group data revealed activity in a similar network, albeit with stronger amplitude and larger extent. In addition, activity in the left pre- and post-central gyri, likely associated with right hand somato-motor response, was observed only with the jICA approach. Within-subject, the jICA approach revealed significantly stronger and more extensive activity in the brain regions associated with the auditory P300 than the P300 linear regression analysis. The results suggest that with the incorporation of spatial and temporal information from both imaging modalities, jICA may be a more sensitive method for extracting common sources of activity between ERP and fMRI.
| S-EPMC3321114 | biostudies-literature
Project description:BackgroundData integration is currently one of the main challenges in the biomedical sciences. Often different pieces of information are gathered on the same set of entities (e.g., tissues, culture samples, biomolecules) with the different pieces stemming, for example, from different measurement techniques. This implies that more and more data appear that consist of two or more data arrays that have a shared mode. An integrative analysis of such coupled data should be based on a simultaneous analysis of all data arrays. In this respect, the family of simultaneous component methods (e.g., SUM-PCA, unrestricted PCovR, MFA, STATIS, and SCA-P) is a natural choice. Yet, different simultaneous component methods may lead to quite different results.ResultsWe offer a structured overview of simultaneous component methods that frames them in a principal components setting such that both the common core of the methods and the specific elements with regard to which they differ are highlighted. An overview of principles is given that may guide the data analyst in choosing an appropriate simultaneous component method. Several theoretical and practical issues are illustrated with an empirical example on metabolomics data for Escherichia coli as obtained with different analytical chemical measurement methods.ConclusionOf the aspects in which the simultaneous component methods differ, pre-processing and weighting are consequential. Especially, the type of weighting of the different matrices is essential for simultaneous component analysis. These types are shown to be linked to different specifications of the idea of a fair integration of the different coupled arrays.
| S-EPMC2752463 | biostudies-literature
Project description:Microarrays have been utilized in many biological, physiological and pharmacological studies as a high-throughput genomic technique. Several generations of Affymetrix GeneChip microarrays are widely used in gene expression studies. However, differences in intensities of signals for different probe sets that represent the same gene on various types of Affymetrix chips make comparison of datasets complicated.A power coefficient scaling factor was applied in the pharmacokinetic/pharmacodynamic (PK/PD) modeling to account for differences in probe set sensitivities (i.e., signal intensities). Microarray data from muscle and liver following methylprednisolone 50 mg/kg i.v. bolus and 0.3 mg/kg/h infusion regimens were taken as an exemplar.The scaling factor applied to the pharmacodynamic output function was used to solve the problem of intensity differences between probe sets. This approach yielded consistent pharmacodynamic parameters for the applied models.Modeling of pharmacodynamic/pharmacogenomic (PD/PG) data from diverse chips should be performed with caution due to differential probe set intensities. In such circumstances, a power scaling factor can be applied in the modeling.
| S-EPMC4181592 | biostudies-literature
Project description:BackgroundHigh throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account.ResultsWe propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks.ConclusionSparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform (group lasso approach) as well as structures that involve all data platforms (Elitist lasso approach).AvailabilityThe additional file contains a MATLAB implementation of the sparse simultaneous component method.
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Project description:The success of stereoelectroencephalographic (SEEG) investigations depends crucially on the hypotheses on the putative location of the seizure onset zone. This information is derived from non-invasive data either based on visual analysis or advanced source localization algorithms. While source localization applied to interictal spikes recorded on scalp is the classical method, it does not provide unequivocal information regarding the seizure onset zone. Raw ictal activity contains a mixture of signals originating from several regions of the brain as well as EMG artifacts, hampering direct input to the source localization algorithms. We therefore introduce a methodology that disentangles the various sources contributing to the scalp ictal activity using independent component analysis and uses equivalent current dipole localization as putative locus of ictal sources. We validated the results of our analysis pipeline by performing long-term simultaneous scalp - intracerebral (SEEG) recordings in 14 patients and analyzing the wavelet coherence between the independent component encoding the ictal discharge and the SEEG signals in 8 patients passing the inclusion criteria. Our results show that invasively recorded ictal onset patterns, including low-voltage fast activity, can be captured by the independent component analysis of scalp EEG. The visibility of the ictal activity strongly depends on the depth of the sources. The equivalent current dipole localization can point to the seizure onset zone (SOZ) with an accuracy that can be as high as 10 mm for superficially located sources, that gradually decreases for deeper seizure generators, averaging at 47 mm in the 8 analyzed patients. Independent component analysis is therefore shown to have a promising SOZ localizing value, indicating whether the seizure onset zone is neocortical, and its approximate location, or located in mesial structures. That may contribute to a better crafting of the hypotheses used as basis of the stereo-EEG implantations.
| S-EPMC8503578 | biostudies-literature