BACKGROUND: Analysis of time-resolved postprandial metabolomics data can improve the understanding of metabolic mechanisms, potentially revealing biomarkers for early diagnosis of metabolic diseases and advancing precision nutrition and medicine. Postprandial metabolomics measurements at several time points from multiple subjects can be arranged as a subjects by metabolites by time points array. Traditional analysis methods are limited in terms of revealing subject groups, related metabolites, and temporal patterns simultaneously from such three-way data. RESULTS: We introduce an unsupervised multiway analysis approach based on the CANDECOMP/PARAFAC (CP) model for improved analysis of postprandial metabolomics data guided by a simulation study. Because of the lack of ground truth in real data, we generate simulated data using a comprehensive human metabolic model. This allows us to assess the performance of CP models in terms of revealing subject groups and underlying metabolic processes. We study three analysis approaches: analysis of fasting-state data using principal component analysis, T0-corrected data (i.e., data corrected by subtracting fasting-state data) using a CP model and full-dynamic (i.e., full postprandial) data using CP. Through extensive simulations, we demonstrate that CP models capture meaningful and stable patterns from simulated meal challenge data, revealing underlying mechanisms and differences between diseased versus healthy groups. CONCLUSIONS: Our experiments show that it is crucial to analyze both fasting-state and T0-corrected data for understanding metabolic differences among subject groups. Depending on the nature of the subject group structure, the best group separation may be achieved by CP models of T0-corrected or full-dynamic data. This study introduces an improved analysis approach for postprandial metabolomics data while also shedding light on the debate about correcting baseline values in longitudinal data analysis.

The intricate dependency structure of biological "omics" data, particularly those originating from longitudinal intervention studies with frequently sampled repeated measurements renders the analysis of such data challenging. The high-dimensionality, inter-relatedness of multiple outcomes, and heterogeneity in the studied systems all add to the difficulty in deriving meaningful information. In addition, the subtle differences in dynamics often deemed meaningful in nutritional intervention studies can be particularly challenging to quantify. In this work we demonstrate the use of quantitative longitudinal models within the repeated-measures ANOVA simultaneous component analysis+ (RM-ASCA+) framework to capture the dynamics in frequently sampled longitudinal data with multivariate outcomes. We illustrate the use of linear mixed models with polynomial and spline basis expansion of the time variable within RM-ASCA+ in order to quantify non-linear dynamics in a simulation study as well as in a metabolomics data set. We show that the proposed approach presents a convenient and interpretable way to systematically quantify and summarize multivariate outcomes in longitudinal studies while accounting for proper within subject dependency structures.

BACKGROUND: Analysis of dynamic metabolomics data holds the promise to improve our understanding of underlying mechanisms in metabolism. For example, it may detect changes in metabolism due to the onset of a disease. Dynamic or time-resolved metabolomics data can be arranged as a three-way array with entries organized according to a subjects mode, a metabolites mode and a time mode. While such time-evolving multiway data sets are increasingly collected, revealing the underlying mechanisms and their dynamics from such data remains challenging. For such data, one of the complexities is the presence of a superposition of several sources of variation: induced variation (due to experimental conditions or inborn errors), individual variation, and measurement error. Multiway data analysis (also known as tensor factorizations) has been successfully used in data mining to find the underlying patterns in multiway data. To explore the performance of multiway data analysis methods in terms of revealing the underlying mechanisms in dynamic metabolomics data, simulated data with known ground truth can be studied. RESULTS: We focus on simulated data arising from different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, and a human cholesterol model. We generate data with induced variation as well as individual variation. Systematic experiments are performed to demonstrate the advantages and limitations of multiway data analysis in analyzing such dynamic metabolomics data and their capacity to disentangle the different sources of variations. We choose to use simulations since we want to understand the capability of multiway data analysis methods which is facilitated by knowing the ground truth. CONCLUSION: Our numerical experiments demonstrate that despite the increasing complexity of the studied dynamic metabolic models, tensor factorization methods CANDECOMP/PARAFAC(CP) and Parallel Profiles with Linear Dependences (Paralind) can disentangle the sources of variations and thereby reveal the underlying mechanisms and their dynamics.

Longitudinal intervention studies with repeated measurements over time are an important type of experimental design in biomedical research. Due to the advent of "omics"-sciences (genomics, transcriptomics, proteomics, metabolomics), longitudinal studies generate increasingly multivariate outcome data. Analysis of such data must take both the longitudinal intervention structure and multivariate nature of the data into account. The ASCA+-framework combines general linear models with principal component analysis and can be used to separate and visualize the multivariate effect of different experimental factors. However, this methodology has not yet been developed for the more complex designs often found in longitudinal intervention studies, which may be unbalanced, involve randomized interventions, and have substantial missing data. Here we describe a new methodology, repeated measures ASCA+ (RM-ASCA+), and show how it can be used to model metabolic changes over time, and compare metabolic changes between groups, in both randomized and non-randomized intervention studies. Tools for both visualization and model validation are discussed. This approach can facilitate easier interpretation of data from longitudinal clinical trials with multivariate outcomes.

The field of transcriptomics uses and measures mRNA as a proxy of gene expression. There are currently two major platforms in use for quantifying mRNA, microarray and RNA-Seq. Many comparative studies have shown that their results are not always consistent. In this study we aim to find a robust method to increase comparability of both platforms enabling data analysis of merged data from both platforms. We transformed high dimensional transcriptomics data from two different platforms into a lower dimensional, and biologically relevant dataset by calculating enrichment scores based on gene set collections for all samples. We compared the similarity between data from both platforms based on the raw data and on the enrichment scores. We show that the performed data transforms the data in a biologically relevant way and filters out noise which leads to increased platform concordance. We validate the procedure using predictive models built with microarray based enrichment scores to predict subtypes of breast cancer using enrichment scores based on sequenced data. Although microarray and RNA-Seq expression levels might appear different, transforming them into biologically relevant gene set enrichment scores significantly increases their correlation, which is a step forward in data integration of the two platforms. The gene set collections were shown to contain biologically relevant gene sets. More in-depth investigation on the effect of the composition, size, and number of gene sets that are used for the transformation is suggested for future research.

Motivation: Genome-wide measurements of genetic and epigenetic alterations are generating more and more high-dimensional binary data. The special mathematical characteristics of binary data make the direct use of the classical principal component analysis (PCA) model to explore low-dimensional structures less obvious. Although there are several PCA alternatives for binary data in the psychometric, data analysis and machine learning literature, they are not well known to the bioinformatics community. Results: In this article, we introduce the motivation and rationale of some parametric and nonparametric versions of PCA specifically geared for binary data. Using both realistic simulations of binary data as well as mutation, CNA and methylation data of the Genomic Determinants of Sensitivity in Cancer 1000 (GDSC1000), the methods were explored for their performance with respect to finding the correct number of components, overfit, finding back the correct low-dimensional structure, variable importance, etc. The results show that if a low-dimensional structure exists in the data, that most of the methods can find it. When assuming a probabilistic generating process is underlying the data, we recommend to use the parametric logistic PCA model, while when such an assumption is not valid and the data are considered as given, the nonparametric Gifi model is recommended. Availability: The codes to reproduce the results in this article are available at the homepage of the Biosystems Data Analysis group (www.bdagroup.nl).

Motivation: In biology, we are often faced with multiple datasets recorded on the same set of objects, such as multi-omics and phenotypic data of the same tumors. These datasets are typically not independent from each other. For example, methylation may influence gene expression, which may, in turn, influence drug response. Such relationships can strongly affect analyses performed on the data, as we have previously shown for the identification of biomarkers of drug response. Therefore, it is important to be able to chart the relationships between datasets. Results: We present iTOP, a methodology to infer a topology of relationships between datasets. We base this methodology on the RV coefficient, a measure of matrix correlation, which can be used to determine how much information is shared between two datasets. We extended the RV coefficient for partial matrix correlations, which allows the use of graph reconstruction algorithms, such as the PC algorithm, to infer the topologies. In addition, since multi-omics data often contain binary data (e.g. mutations), we also extended the RV coefficient for binary data. Applying iTOP to pharmacogenomics data, we found that gene expression acts as a mediator between most other datasets and drug response: only proteomics clearly shares information with drug response that is not present in gene expression. Based on this result, we used TANDEM, a method for drug response prediction, to identify which variables predictive of drug response were distinct to either gene expression or proteomics. Availability and implementation: An implementation of our methodology is available in the R package iTOP on CRAN. Additionally, an R Markdown document with code to reproduce all figures is provided as Supplementary Material. Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Joint and individual variation explained (JIVE), distinct and common simultaneous component analysis (DISCO) and O2-PLS, a two-block (X-Y) latent variable regression method with an integral OSC filter can all be used for the integrated analysis of multiple data sets and decompose them in three terms: a low(er)-rank approximation capturing common variation across data sets, low(er)-rank approximations for structured variation distinctive for each data set, and residual noise. In this paper these three methods are compared with respect to their mathematical properties and their respective ways of defining common and distinctive variation. RESULTS: The methods are all applied on simulated data and mRNA and miRNA data-sets from GlioBlastoma Multiform (GBM) brain tumors to examine their overlap and differences. When the common variation is abundant, all methods are able to find the correct solution. With real data however, complexities in the data are treated differently by the three methods. CONCLUSIONS: All three methods have their own approach to estimate common and distinctive variation with their specific strength and weaknesses. Due to their orthogonality properties and their used algorithms their view on the data is slightly different. By assuming orthogonality between common and distinctive, true natural or biological phenomena that may not be orthogonal at all might be misinterpreted.

With a goal of identifying biomarkers/patterns related to certain conditions or diseases, metabolomics focuses on the detection of chemical substances in biological samples such as urine and blood using a number of analytical techniques, including nuclear magnetic resonance (NMR) spectroscopy, liquid chromatography-mass spectrometry (LC-MS), and fluorescence spectroscopy. Data sets measured using these methods provide partly complementary information, and their joint analysis has the potential to reveal underlying structures, which are, otherwise, difficult to extract. While we can collect vast amounts of data using different analytical methods, data fusion remains a challenging task, in particular, when the goal is to capture the underlying factors and use them for interpretation, e.g., for biomarker identification. Furthermore, many data fusion applications require joint analysis of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining applications, and discuss its extension to a structure-revealing data fusion model, i.e., a data fusion model that can identify shared and unshared factors. The traditional methods commonly used for data fusion in the presence of shared/unshared factors are matrix factorization-based methods. Using both simulations and prototypical experimental coupled data sets, we assess the performance of various state-of-the-art data fusion methods and demonstrate that while matrix factorization-based approaches have limitations when used for joint analysis of heterogeneous data sets, the structure-revealing CMTF model can successfully capture the underlying factors by exploiting the low-rank structure of higher order data sets.

In functional genomics it is more rule than exception that experimental designs are used to generate the data. The samples of the resulting data sets are thus organized according to this design and for each sample many biochemical compounds are measured, e.g. typically thousands of gene-expressions or hundreds of metabolites. This results in high-dimensional data sets with an underlying experimental design. Several methods have recently become available for analyzing such data while utilizing the underlying design. We review these methods by putting them in a unifying and general framework to facilitate understanding the (dis-)similarities between the methods. The biological question dictates which method to use and the framework allows for building new methods to accommodate a range of such biological questions. The framework is built on well known fixed-effect ANOVA models and subsequent dimension reduction. We present the framework both in matrix algebra as well as in more insightful geometrical terms. We show the workings of the different special cases of our framework with a real-life metabolomics example from nutritional research and a gene-expression example from the field of virology.

BACKGROUND: High-throughput functional genomics technologies generate large amount of data with hundreds or thousands of measurements per sample. The number of sample is usually much smaller in the order of ten or hundred. This poses statistical challenges and calls for appropriate solutions for the analysis of this kind of data. RESULTS: Principal component discriminant analysis (PCDA), an adaptation of classical linear discriminant analysis (LDA) for high-dimensional data, has been selected as an example of a base learner. The multiple versions of PCDA models from repeated double cross-validation were aggregated, and the final classification was performed by majority voting. The performance of this approach was evaluated by simulation, genomics, proteomics and metabolomics data sets. CONCLUSIONS: The aggregating PCDA learner can improve the prediction performance, provide more stable result, and help to know the variability of the models. The disadvantage and limitations of aggregating were also discussed.

MOTIVATION: Modern functional genomics generates high-dimensional datasets. It is often convenient to have a single simple number characterizing the relationship between pairs of such high-dimensional datasets in a comprehensive way. Matrix correlations are such numbers and are appealing since they can be interpreted in the same way as Pearson's correlations familiar to biologists. The high-dimensionality of functional genomics data is, however, problematic for existing matrix correlations. The motivation of this article is 2-fold: (i) we introduce the idea of matrix correlations to the bioinformatics community and (ii) we give an improvement of the most promising matrix correlation coefficient (the RV-coefficient) circumventing the problems of high-dimensional data. RESULTS: The modified RV-coefficient can be used in high-dimensional data analysis studies as an easy measure of common information of two datasets. This is shown by theoretical arguments, simulations and applications to two real-life examples from functional genomics, i.e. a transcriptomics and metabolomics example. AVAILABILITY: The Matlab m-files of the methods presented can be downloaded from http://www.bdagroup.nl.

BACKGROUND: In contemporary biology, complex biological processes are increasingly studied by collecting and analyzing measurements of the same entities that are collected with different analytical platforms. Such data comprise a number of data blocks that are coupled via a common mode. The goal of collecting this type of data is to discover biological mechanisms that underlie the behavior of the variables in the different data blocks. The simultaneous component analysis (SCA) family of data analysis methods is suited for this task. However, a SCA may be hampered by the data blocks being subjected to different amounts of measurement error, or noise. To unveil the true mechanisms underlying the data, it could be fruitful to take noise heterogeneity into consideration in the data analysis. Maximum likelihood based SCA (MxLSCA-P) was developed for this purpose. In a previous simulation study it outperformed normal SCA-P. This previous study, however, did not mimic in many respects typical functional genomics data sets, such as, data blocks coupled via the experimental mode, more variables than experimental units, and medium to high correlations between variables. Here, we present a new simulation study in which the usefulness of MxLSCA-P compared to ordinary SCA-P is evaluated within a typical functional genomics setting. Subsequently, the performance of the two methods is evaluated by analysis of a real life Escherichia coli metabolomics data set. RESULTS: In the simulation study, MxLSCA-P outperforms SCA-P in terms of recovery of the true underlying scores of the common mode and of the true values underlying the data entries. MxLSCA-P further performed especially better when the simulated data blocks were subject to different noise levels. In the analysis of an E. coli metabolomics data set, MxLSCA-P provided a slightly better and more consistent interpretation. CONCLUSION: MxLSCA-P is a promising addition to the SCA family. The analysis of coupled functional genomics data blocks could benefit from its ability to take different noise levels per data block into consideration and improve the recovery of the true patterns underlying the data. Moreover, the maximum likelihood based approach underlying MxLSCA-P could be extended to custom-made solutions to specific problems encountered.

BACKGROUND: Data 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. RESULTS: We 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. CONCLUSION: Of 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.

BACKGROUND: Many plant species show induced responses that protect them against exogenous attacks. These responses involve the production of many different bioactive compounds. Plant species belonging to the Brassicaceae family produce defensive glucosinolates, which may greatly influence their favorable nutritional properties for humans. Each responding compound may have its own dynamic profile and metabolic relationships with other compounds. The chemical background of the induced response is therefore highly complex and may therefore not reveal all the properties of the response in any single model. RESULTS: This study therefore aims to describe the dynamics of the glucosinolate response, measured at three time points after induction in a feral Brassica, by a three-faceted approach, based on Principal Component Analysis. First the large-scale aspects of the response are described in a 'global model' and then each time-point in the experiment is individually described in 'local models' that focus on phenomena that occur at specific moments in time. Although each local model describes the variation among the plants at one time-point as well as possible, the response dynamics are lost. Therefore a novel method called the 'Crossfit' is described that links the local models of different time-points to each other. CONCLUSIONS: Each element of the described analysis approach reveals different aspects of the response. The crossfit shows that smaller dynamic changes may occur in the response that are overlooked by global models, as illustrated by the analysis of a metabolic profiling dataset of the same samples.

BACKGROUND: In the fields of life sciences, so-called designed studies are used for studying complex biological systems. The data derived from these studies comply with a study design aimed at generating relevant information while diminishing unwanted variation (noise). Knowledge about the study design can be used to decompose the total data into data blocks that are associated with specific effects. Subsequent statistical analysis can be improved by this decomposition if these are applied on selected combinations of effects. RESULTS: The benefit of this approach was demonstrated with an analysis that combines multivariate PLS (Partial Least Squares) regression with data decomposition from ANOVA (Analysis of Variance): ANOVA-PLS. As a case, a nutritional intervention study is used on Apoliprotein E3-Leiden (APOE3Leiden) transgenic mice to study the relation between liver lipidomics and a plasma inflammation marker, Serum Amyloid A. The ANOVA-PLS performance was compared to PLS regression on the non-decomposed data with respect to the quality of the modelled relation, model reliability, and interpretability. CONCLUSION: It was shown that ANOVA-PLS leads to a better statistical model that is more reliable and better interpretable compared to standard PLS analysis. From a following biological interpretation, more relevant metabolites were derived from the model. The concept of combining data composition with a subsequent statistical analysis, as in ANOVA-PLS, is however not limited to PLS regression in metabolomics but can be applied for many statistical methods and many different types of data.

MOTIVATION: Designed microarray experiments are used to investigate the effects that controlled experimental factors have on gene expression and learn about the transcriptional responses associated with external variables. In these datasets, signals of interest coexist with varying sources of unwanted noise in a framework of (co)relation among the measured variables and with the different levels of the studied factors. Discovering experimentally relevant transcriptional changes require methodologies that take all these elements into account. RESULTS: In this work, we develop the application of the Analysis of variance-simultaneous component analysis (ANOVA-SCA) Smilde et al. Bioinformatics, (2005) to the analysis of multiple series time course microarray data as an example of multifactorial gene expression profiling experiments. We denoted this implementation as ASCA-genes. We show how the combination of ANOVA-modeling and a dimension reduction technique is effective in extracting targeted signals from data by-passing structural noise. The methodology is valuable for identifying main and secondary responses associated with the experimental factors and spotting relevant experimental conditions. We additionally propose a novel approach for gene selection in the context of the relation of individual transcriptional patterns to global gene expression signals. We demonstrate the methodology on both real and synthetic datasets. AVAILABILITY: ASCA-genes has been implemented in the statistical language R and is available at http://www.ivia.es/centrodegenomica/bioinformatics.htm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Innovative extensions of (M) ANOVA gain common ground for the analysis of designed metabolomics experiments. ASCA is such a multivariate analysis method; it has successfully estimated effects in megavariate metabolomics data from biological experiments. However, rigorous statistical validation of megavariate effects is still problematic because megavariate extensions of the classical F-test do not exist. METHODS: A permutation approach is used to validate megavariate effects observed with ASCA. By permuting the class labels of the underlying experimental design, a distribution of no-effect is calculated. If the observed effect is clearly different from this distribution the effect is deemed significant RESULTS: The permutation approach is studied using simulated data which gave successful results. It was then used on real-life metabolomics data set dealing with bromobenzene-dosed rats. In this metabolomics experiment the dosage and time-interaction effect were validated, both effects are significant. Histological screening of the treated rats' liver agrees with this finding. CONCLUSION: The suggested procedure gives approximate p-values for testing effects underlying metabolomics data sets. Therefore, performing model validation is possible using the proposed procedure.

MOTIVATION: Datasets resulting from metabolomics or metabolic profiling experiments are becoming increasingly complex. Such datasets may contain underlying factors, such as time (time-resolved or longitudinal measurements), doses or combinations thereof. Currently used biostatistics methods do not take the structure of such complex datasets into account. However, incorporating this structure into the data analysis is important for understanding the biological information in these datasets. RESULTS: We describe ASCA, a new method that can deal with complex multivariate datasets containing an underlying experimental design, such as metabolomics datasets. It is a direct generalization of analysis of variance (ANOVA) for univariate data to the multivariate case. The method allows for easy interpretation of the variation induced by the different factors of the design. The method is illustrated with a dataset from a metabolomics experiment with time and dose factors.

MOTIVATION: Metabolomics datasets are generally large and complex. Using principal component analysis (PCA), a simplified view of the variation in the data is obtained. The PCA model can be interpreted and the processes underlying the variation in the data can be analysed. In metabolomics, often a priori information is present about the data. Various forms of this information can be used in an unsupervised data analysis with weighted PCA (WPCA). A WPCA model will give a view on the data that is different from the view obtained using PCA, and it will add to the interpretation of the information in a metabolomics dataset. RESULTS: A method is presented to translate spectra of repeated measurements into weights describing the experimental error. These weights are used in the data analysis with WPCA. The WPCA model will give a view on the data where the non-uniform experimental error is accounted for. Therefore, the WPCA model will focus more on the natural variation in the data. AVAILABILITY: M-files for MATLAB for the algorithm used in this research are available at http://www-its.chem.uva.nl/research/pac/Software/pcaw.zip.