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In sensory data analysis, assessor-dependent scaling effects may hinder the analysis of product differences. Romano et al. (2008) compared several approaches to reduce scaling differences between assessors by their ability to maximise the product effect F-values in a mixed ANOVA analysis. Their study on a sensory dataset of 14 cheese samples assessed by twelve assessors on a continuous scale showed that some of these approaches apparently improved the F-value of the product effect. However, this direct comparison is only legitimate if these F-values originate from the same null distribution. To obtain the null distributions of the different correction methods, we employed a permutation approach on the same cheese dataset also used by Romano et al. (2008) and a random noise simulation approach. Based on the empirically obtained null distributions, we calculated the corrected product effect significance to directly compare the performance of the preprocessing methods. Our results show that the null distributions of some preprocessing methods do not correspond to the expected F-distribution. In particular for the ten Berge method, the null distribution is shifted towards higher F-values. Therefore, an observed increase of the product effect F-value, as compared to the F-value on raw data, does not necessarily lead to increased product effect significance. If p-values are calculated based on such inflated F-values, significance may thus be overestimated. In contrast, calculation of p-values directly from the empirical null distributions obtained by permutation provides a common ground to properly compare method performance. Moreover, we show that differences in reproducibility between assessors, as they exist in real-world sensory datasets, may lead to overestimation of product effect significance by the mixed assessor model (MAM).

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 asubjectsbymetabolitesbytime pointsarray. Traditional analysis methods are limited in revealing subject groups, related metabolites, and temporal patterns simultaneously from such three-way data. In this paper, 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 offasting-statedata using Principal Component Analysis,T0-correcteddata (i.e., data corrected by subtractingfasting-statedata) using a CP model andfull-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 vs. healthy groups. Our simulations also show that it is crucial to analyze bothfasting-stateandT0-correcteddata 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 ofT0-correctedorfull-dynamicdata. Furthermore, we show that the proposed approach reveals differences between subject groups (according to body mass index) in terms of their response to a real meal challenge test. 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.Author summaryPostprandial metabolomics data can mirror the ability of the human body to cope with a meal challenge. Analysis of such data can reveal differences among subject groups, discover biomarkers related to (early-onset) disease and holds the promise to guide personalized nutrition. However, traditional analysis methods are limited in terms of revealing the underlying patterns from such time-resolved data which is inherently a multiway array: asubjectsbymetabolitesbytime pointsarray. In this paper, we introduce an unsupervised approach based on multiway data analysis for postprandial metabolomics data, and assess its performance using simulated data based on a comprehensive human metabolic model. We demonstrate that the overall picture of metabolic differences among subject groups (e.g., healthy vs. diseased) and the underlying metabolic processes can be captured through the analysis offasting-statedata and multiway analysis of thedynamicdata. We show the promise of the proposed approach through real postprandial metabolomics data analysis and discuss the patterns revealing metabolic differences among subject groups (according to body mass index (BMI)) in terms of their response to a meal challenge test.

The plant microbiome plays an essential role in supporting plant growth and health, but plant molecular mechanisms underlying its recruitment are still unclear. Multi-omics data integration methods can be used to unravel new signalling relationships. Here, we review the effects of plant genetics and root exudates on root microbiome recruitment, and discuss methodological advances in data integration approaches that can help us to better understand and optimise the crop-microbiome interaction for a more sustainable agriculture.

Computational phenotyping allows for unsupervised discovery of subgroups of patients as well as corresponding co-occurring medical conditions from electronic health records (EHR). Typically, EHR data contains demographic information, diagnoses and laboratory results. Discovering (novel) phenotypes has the potential to be of prognostic and therapeutic value. Providing medical practitioners with transparent and interpretable results is an important requirement and an essential part for advancing precision medicine. Low-rank data approximation methods such as matrix (e.g., non-negative matrix factorization) and tensor decompositions (e.g., CANDECOMP/PARAFAC) have demonstrated that they can provide such transparent and interpretable insights. Recent developments have adapted low-rank data approximation methods by incorporating different constraints and regularizations that facilitate interpretability further. In addition, they offer solutions for common challenges within EHR data such as high dimensionality, data sparsity and incompleteness. Especially extracting temporal phenotypes from longitudinal EHR has received much attention in recent years. In this paper, we provide a comprehensive review of low-rank approximation-based approaches for computational phenotyping. The existing literature is categorized into temporal vs. static phenotyping approaches based on matrix vs. tensor decompositions. Furthermore, we outline different approaches for the validation of phenotypes, i.e., the assessment of clinical significance., 28 pages, 5 figures

In the current era of systems biological research there is a need for the integrative analysis of binary and quantitative genomics data sets measured on the same objects. One standard tool of exploring the underlying dependence structure present in multiple quantitative data sets is simultaneous component analysis (SCA) model. However, it does not have any provisions when a part of the data are binary. To this end, we propose the generalized SCA (GSCA) model, which takes into account the distinct mathematical properties of binary and quantitative measurements in the maximum likelihood framework. Like in the SCA model, a common low dimensional subspace is assumed to represent the shared information between these two distinct types of measurements. However, the GSCA model can easily be overfitted when a rank larger than one is used, leading to some of the estimated parameters to become very large. To achieve a low rank solution and combat overfitting, we propose to use a concave variant of the nuclear norm penalty. An efficient majorization algorithm is developed to fit this model with different concave penalties. Realistic simulations (low signal-to-noise ratio and highly imbalanced binary data) are used to evaluate the performance of the proposed model in recovering the underlying structure. Also, a missing value based cross validation procedure is implemented for model selection. We illustrate the usefulness of the GSCA model for exploratory data analysis of quantitative gene expression and binary copy number aberration (CNA) measurements obtained from the GDSC1000 data sets., Comment: 19 pages, 10 figures

Background Characterization of lipoprotein particle profiles (LPPs) (including main classes and subclasses) by means of ultracentrifugation (UC) is highly requested given its clinical potential. However, rapid methods are required to replace the very labor-intensive UC method and one solution is to calibrate rapid nuclear magnetic resonance (NMR)-based prediction models, but the reliability of the UC-response method required for the NMR calibration has been largely overlooked. Methods This study provides a comprehensive repeatability and reproducibility study of various UC-based lipid measurements (cholesterol, triglycerides [TGs], free cholesterol, phospholipids, apolipoprotein [apo]A1 and apoB) in different main classes and subclasses of 25 duplicated fresh plasma samples and of 42 quality control (QC) frozen pooled plasma samples of healthy individuals. Results Cholesterol, apoA1 and apoB measurements were very repeatable in all classes (intraclass correlation coefficient [ICC]: 92.93%–99.54%). Free cholesterol and phospholipid concentrations in main classes and subclasses and TG concentrations in high-density lipoproteins (HDL), HDL subclasses and low-density lipoproteins (LDL) subclasses, showed worse repeatability (ICC: 19.21%–99.08%) attributable to low concentrations, variability introduced during UC and assay limitations. On frozen QC samples, the reproducibility of cholesterol, apoA1 and apoB concentrations was found to be better than for the free cholesterol, phospholipids and TGs concentrations. Conclusions This study shows that for LPPs measurements near or below the limit of detection (LOD) in some of the subclasses, as well as the use of frozen samples, results in worsened repeatability and reproducibility. Furthermore, we show that the analytical assay coupled to UC for free cholesterol and phospholipids have different repeatability and reproducibility. All of this needs to be taken into account when calibrating future NMR-based models.

Lipoprotein subfractions are biomarkers for the early diagnosis of cardiovascular diseases. The reference method, ultracentrifugation, for measuring lipoproteins is time-consuming, and there is a need to develop a rapid method for cohort screenings. This study presents partial least-squares regression models developed using 1H nuclear magnetic resonance (NMR) spectra and concentrations of lipoproteins as measured by ultracentrifugation on 316 healthy Danes. This study explores, for the first time, different regions of the 1H NMR spectrum representing signals of molecules in lipoprotein particles and different lipid species to develop parsimonious, reliable, and optimal prediction models. A total of 65 lipoprotein main and subfractions were predictable with high accuracy, Q2 of >0.6, using an optimal spectral region (1.4–0.6 ppm) containing methylene and methyl signals from lipids. The models were subsequently tested on an independent cohort of 290 healthy Swedes with predicted and reference values matching by up to 85–95%. In addition, an open software tool was developed to predict lipoproteins concentrations in human blood from standardized 1H NMR spectral recordings.

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.

Lipoprotein subfractions are biomarkers for the early diagnosis of cardiovascular diseases. The reference method, ultracentrifugation, for measuring lipoproteins is time-consuming, and there is a need to develop a rapid method for cohort screenings. This study presents partial least-squares regression models developed using

In analytical chemistry spectroscopy is attractive for high-throughput quantification, which often relies on inverse regression, like partial least squares regression. Due to a multivariate nature of spectroscopic measurements an analyte can be quantified in presence of interferences. However, if the model is not fully selective against interferences, analyte predictions may be biased. The degree of model selectivity against an interferent is defined by the inner relation between the regression vector and the pure interfering signal. If the regression vector is orthogonal to the signal, this inner relation equals zero and the model is fully selective. The degree of model selectivity largely depends on calibration data quality. Strong correlations may deteriorate calibration data resulting in poorly selective models. We show this using a fructose-maltose model system. Furthermore, we modify the NIPALS algorithm to improve model selectivity when calibration data are deteriorated. This modification is done by incorporating a projection matrix into the algorithm, which constrains regression vector estimation to the null-space of known interfering signals. This way known interfering signals are handled, while unknown signals are accounted for by latent variables. We test the modified algorithm and compare it to the conventional NIPALS algorithm using both simulated and industrial process data. The industrial process data consist of mid-infrared measurements obtained on mixtures of beta-lactoglobulin (analyte of interest), and alpha-lactalbumin and caseinoglycomacropeptide (interfering species). The root mean squared error of beta-lactoglobulin (% w/w) predictions of a test set was 0.92 and 0.33 when applying the conventional and the modified NIPALS algorithm, respectively. Our modification of the algorithm returns simpler models with improved selectivity and analyte predictions. This paper shows how known interfering signals may be utilized in a direct fashion, while benefitting from a latent variable approach. The modified algorithm can be viewed as a fusion between ordinary least squares regression and partial least squares regression and may be very useful when knowledge of some (but not all) interfering species is available.

This paper is about the use of the multiblock regression method sequential and orthogonalized partial least squares (SO-PLS) for path modeling. The paper is a follow up of previously published papers on the same topic and presents a number of new results for the method. First of all, the paper discusses more thoroughly the aspect of how to incorporate blocks in the models and relates this to standard concepts in the area of graphical modeling. Second, the paper defines the concept of direct and indirect effects more precisely in terms of population parameters and shows how they are related to the additional effect in SO-PLS modeling. The paper illustrates the theory by simple graphs, simulations, and a real example from process monitoring.

Increasing evidence indicates that the gut microbiome (GM) plays an important role in the etiology of dyslipidemia. To date, however, no in-depth characterization of the associations between GM and its metabolic attributes with deep profiling of lipoproteins distributions (LPD) among healthy individuals has been conducted. To determine associations and contributions of GM composition and its cofactors with distribution profiles of lipoprotein subfractions, we studied blood plasma LPD, fecal short-chain fatty acids (SCFA) and GM of 262 healthy Danish subjects aged 19-89 years.Stratification of LPD segregated subjects into three clusters of profiles that reflected differences in the lipoprotein subclasses, corresponded well with limits of recommended levels of main lipoprotein fractions and were largely explained by host characteristics such as age and body mass index. Higher levels of HDL, particularly driven by large subfractions (HDL2a and HDL2b), were associated with a higher relative abundance of Ruminococcaceae and Christensenellaceae. Increasing levels of total cholesterol and LDL, which were primarily associated with large 1 and 2 subclasses, were positively associated with Lachnospiraceae and Coriobacteriaceae, and negatively with Bacteroidaceae and Bifidobacteriaceae. Metagenome sequencing showed a higher abundance of genes involved in the biosynthesis of multiple B-vitamins and SCFA metabolism among subjects with healthier LPD profiles. Metagenomic assembled genomes (MAGs) affiliated mainly to Eggerthellaceae and Clostridiales were identified as the contributors of these genes and whose relative abundance correlated positively with larger subfractions of HDL.The results of this study demonstrate that remarkable differences in composition and metabolic traits of the GM are associated with variations in LPD among healthy subjects. Findings from this study provide evidence for GM considerations in future research aiming to shade light on mechanisms of the GM – dyslipidemia axis.

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA). It combines variance maximization and sparsity with the ultimate goal of improving data interpretation. A main application of sPCA is to handle high-dimensional data, for example biological omics data. In Part I of this series, we illustrated limitations of several state-of-the-art sPCA algorithms when modeling noise-free data, simulated following an exact sPCA model. In this Part II we provide a thorough analysis of the limitations of sPCA methods that use deflation for calculating subsequent, higher order, components. We show, both theoretically and numerically, that deflation can lead to problems in the model interpretation, even for noise free data. In addition, we contribute diagnostics to identify modeling problems in real-data analysis.

Introduction The relationship between the chemical composition of food products and their sensory profile is a complex association confronting many challenges. However, new untargeted methodologies are helping correlate metabolites with sensory characteristics in a simpler manner. Nevertheless, in the pilot phase of a project, where only a small set of products are used to explore the relationships, choices have to be made about the most appropriate untargeted metabolomics methodology. Objective To provide a framework for selecting a metabolite-sensory methodology based on: the quality of measurements, the relevance of the detected metabolites in terms of distinguishing between products or in terms of whether they can be related to the sensory attributes of the products. Methods In this paper we introduce a systematic approach to explore all these different aspects driving the choice for the most appropriate metabolomics method. Results As an example we have used a tomato soup project where the choice between two sampling methods (SPME and SBSE) had to be made. The results are not always consistently pointing to the same method as being the best. SPME was able to detect metabolites with a better precision, SBSE seemed to be able to provide a better distinction between the soups. Conclusion The three levels of comparison provide information on how the methods could perform in a follow up study and will help the researcher to make a final selection for the most appropriate method based on their strengths and weaknesses.

Lipoprotein subfractions are biomarkers for the early diagnosis of cardiovascular diseases. The reference method, ultracentrifugation, for measuring lipoproteins is time-consuming, and there is a need to develop a rapid method for cohort screenings. This study presents partial least-squares regression models developed using 1H nuclear magnetic resonance (NMR) spectra and concentrations of lipoproteins as measured by ultracentrifugation on 316 healthy Danes. This study explores, for the first time, different regions of the 1H NMR spectrum representing signals of molecules in lipoprotein particles and different lipid species to develop parsimonious, reliable, and optimal prediction models. A total of 65 lipoprotein main and subfractions were predictable with high accuracy, Q2 of >0.6, using an optimal spectral region (1.4-0.6 ppm) containing methylene and methyl signals from lipids. The models were subsequently tested on an independent cohort of 290 healthy Swedes with predicted and reference values matching by up to 85-95%. In addition, an open software tool was developed to predict lipoproteins concentrations in human blood from standardized 1H NMR spectral recordings.

Integration of unstructured and very diverse data is often required for a deeper understanding of the complex biological systems. In order to uncover communalities between heterogeneous data, the data are often harmonized by constructing a kernel and perform numerical integration. In this study, we propose a method for data integration in the framework of an undirected graphical model, where the nodes represent individual data sources of varying nature in terms of complexity and underlying distribution and where the edges represent the partial correlations between two blocks of data. We propose a modified GLASSO for estimation of the graph, with a combination of cross-validation and extended Bayes Information Criterion for sparsity tuning. Furthermore, hierarchical clustering on the weighted consensus kernels from a fixed network is used to partitioning the samples into different classes. Simulations show increasing ability to uncover true edges with increasing sample size and signal to noise. Likewise, identification of nonexisting edges towards disconnected nodes is feasible. The framework is demonstrated for integration of longitudinal symptom burden data, from the second and third year of life, combined with 21 diseases precursors and information of the development of asthma and eczema at the age of 6 years, from 403 children from the COPSAC2010 mother-child cohort. This suggests that maternal predisposition as well as being born preterm indirectly lead to a higher risk of asthma via an increased respiratory symptom burden.

The current routine use of adjuvants in human vaccines provides a strong incentive to increase our understanding of how adjuvants differ in their ability to stimulate innate immunity and consequently enhance vaccine immunogenicity. Here, we evaluated gene expression profiles in cells from whole blood elicited in naive subjects receiving the hepatitis B surface antigen formulated with different adjuvants. We identified a core innate gene signature emerging 1 day after the second vaccination and that was shared by the recipients of vaccines formulated with adjuvant systems AS01B, AS01E, or AS03. This core signature associated with the magnitude of the hepatitis B surface-specific antibody response and was characterized by positive regulation of genes associated with interferon-related responses or the innate cell compartment and by negative regulation of natural killer cell-associated genes. Analysis at the individual subject level revealed that the higher immunogenicity of AS01B-adjuvanted vaccine was linked to its ability to induce this signature in most vaccinees even after the first vaccination. Therefore, our data suggest that adjuvanticity is not strictly defined by the nature of the receptors or signaling pathways it activates but by the ability of the adjuvant to consistently induce a core inflammatory signature across individuals.

Metabolomics is becoming a mature part of analytical chemistry as evidenced by the growing number of publications and attendees of international conferences dedicated to this topic. Yet, a systematic treatment of the fundamental structure and properties of metabolomics data is lagging behind. We want to fill this gap by introducing two fundamental theories concerning metabolomics data: data theory and measurement theory. Our approach is to ask simple questions, the answers of which require applying these theories to metabolomics. We show that we can distinguish at least four different levels of metabolomics data with different properties and warn against confusing data with numbers. This treatment provides a theoretical underpinning for preprocessing and postprocessing methods in metabolomics and also argues for a proper match between type of metabolomics data and the biological question to be answered. The approach can be extended to other omics measurements such as proteomics and is thus of relevance for a large analytical chemistry community.

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., Author summary 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 the high dimensional transcriptomics data from the two different platforms into lower dimensional, and biologically relevant gene set scores. These gene sets were defined a-priori as specific combination of genes (e.g. up-regulated in a certain pathway). We observed that although microarray and RNA-Seq expression levels might appear different, using these gene sets to transform the data significantly increases their correlation. This is a step forward in data integration of the two platforms. 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.

Intermediate species are hypothesized to play an important role in the toxicity of amyloid formation, a process associated with many diseases. This process can be monitored with conventional and two-dimensional infrared spectroscopy, vibrational circular dichroism, and optical and electron microscopy. Here, we present how combining these techniques provides insight into the aggregation of the hexapeptide VEALYL (Val-Glu-Ala-Leu-Tyr-Leu), the B-chain residue 12-17 segment of insulin that forms amyloid fibrils (intermolecularly hydrogen-bonded β-sheets) when the pH is lowered below 4. Under such circumstances, the aggregation commences after approximately an hour and continues to develop over a period of weeks. Singular value decompositions of one-dimensional and two-dimensional infrared spectroscopy spectra indicate that intermediate species are formed during the aggregation process. Multivariate curve resolution analyses of the one and two-dimensional infrared spectroscopy data show that the intermediates are more fibrillar and deprotonated than the monomers, whereas they are less ordered than the final fibrillar structure that is slowly formed from the intermediates. A comparison between the vibrational circular dichroism spectra and the scanning transmission electron microscopy and optical microscope images shows that the formation of mature fibrils of VEALYL correlates with the appearance of spherulites that are on the order of several micrometers, which give rise to a "giant" vibrational circular dichroism effect.

Integration of unstructured and very diverse data is often required for a deeper understanding of complex biological systems. In order to uncover communalities between heterogeneous data, the data is often harmonized by constructing a kernel and numerical integration is performed. In this study we propose a method for data integration in the framework of an undirected graphical model, where the nodes represent individual data sources of varying nature in terms of complexity and underlying distribution, and where the edges represent the partial correlation between two blocks of data. We propose a modified GLASSO for estimation of the graph, with a combination of cross-validation and extended Bayes Information Criterion for sparsity tuning. Furthermore, hierarchical clustering on the weighted consensus kernels from a fixed network is used to partitioning the samples into different classes. Simulations show increasing ability to uncover true edges with increasing sample size and signal to noise. Likewise, identification of non existing edges towards disconnected nodes is feasible. The framework is demonstrated for integration of longitudinal symptom burden data from the 2nd and 3rd year of life with 21 diseases precursors as well as the development of asthma and eczema at the age of 6 years from 403 children from the COPSAC2010 mother-child cohort, suggesting that maternal predisposition as well as being born preterm indirectly lead to higher risk of asthma via increased respiratory symptom burden.

Correlation coefficients are abundantly used in the life sciences. Their use can be limited to simple exploratory analysis or to construct association networks for visualization but they are also basic ingredients for sophisticated multivariate data analysis methods. It is therefore important to have reliable estimates for correlation coefficients. In modern life sciences, comprehensive measurement techniques are used to measure metabolites, proteins, gene-expressions and other types of data. All these measurement techniques have errors. Whereas in the old days, with simple measurements, the errors were also simple, that is not the case anymore. Errors are heterogeneous, non-constant and not independent. This hampers the quality of the estimated correlation coefficients seriously. We will discuss the different types of errors as present in modern comprehensive life science data and show with theory, simulations and real-life data how these affect the correlation coefficients. We will briefly discuss ways to improve the estimation of such coefficients.

Introduction Integrative analysis of multiple data sets can provide complementary information about the studied biological system. However, data fusion of multiple biological data sets can be complicated as data sets might contain different sources of variation due to underlying experimental factors. Therefore, taking the experimental design of data sets into account could be of importance in data fusion concept. Objectives In the present work, we aim to incorporate the experimental design information in the integrative analysis of multiple designed data sets. Methods Here we describe penalized exponential ANOVA simultaneous component analysis (PE-ASCA), a new method for integrative analysis of data sets from multiple compartments or analytical platforms with the same underlying experimental design. Results Using two simulated cases, the result of simultaneous component analysis (SCA), penalized exponential simultaneous component analysis (P-ESCA) and ANOVA-simultaneous component analysis (ASCA) are compared with the proposed method. Furthermore, real metabolomics data obtained from NMR analysis of two different brains tissues (hypothalamus and midbrain) from the same piglets with an underlying experimental design is investigated by PE-ASCA. Conclusions This method provides an improved understanding of the common and distinct variation in response to different experimental factors.

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., Author summary Clinical trials are increasingly generating large amounts of complex biological data. Examples can include measuring metabolism or gene expression in tissue or blood sampled repeatedly over the course of a treatment. In such cases, one might wish to compare changes in not one, but hundreds, or thousands of variables simultaneously. In order to effectively analyze such data, both the study design and the multivariate nature of the data should be considered during data analysis. ANOVA simultaneous component analysis+ (ASCA+) is a statistical method which combines general linear models with principal component analysis, and provides a way to separate and visualize the effects of different factors on complex biological data. In this work, we describe how repeated measures linear mixed models, a class of models commonly used when analyzing changes over time and treatment effects in longitudinal studies, can be used together with ASCA+ for analyzing clinical trials in a novel method called repeated measures-ASCA+ (RM-ASCA+).

Lipoprotein profiling of human blood by 1H nuclear magnetic resonance (NMR) spectroscopy is a rapid and promising approach to monitor health and disease states in medicine and nutrition. However, lack of standardization of measurement protocols has prevented the use of NMR-based lipoprotein profiling in metastudies. In this study, a standardized NMR measurement protocol was applied in a ring test performed across three different laboratories in Europe on plasma and serum samples from 28 individuals. Data was evaluated in terms of (i) spectral differences, (ii) differences in LPD predictions obtained using an existing prediction model, and (iii) agreement of predictions with cholesterol concentrations in high- and low-density lipoproteins (HDL and LDL) particles measured by standardized clinical assays. ANOVA-simultaneous component analysis (ASCA) of the ring test spectral ensemble that contains methylene and methyl peaks (1.4-0.6 ppm) showed that 97.99% of the variance in the data is related to subject, 1.62% to sample type (serum or plasma), and 0.39% to laboratory. This interlaboratory variation is in fact smaller than the maximum acceptable intralaboratory variation on quality control samples. It is also shown that the reproducibility between laboratories is good enough for the LPD predictions to be exchangeable when the standardized NMR measurement protocol is followed. With the successful implementation of this protocol, which results in reproducible prediction of lipoprotein distributions across laboratories, a step is taken toward bringing NMR more into scope of prognostic and diagnostic biomarkers, reducing the need for less efficient methods such as ultracentrifugation or high-performance liquid chromatography (HPLC).

Ambient light intensity is signaled directly to hypothalamic areas that regulate energy metabolism. Observational studies have shown associations between ambient light intensity and plasma glucose and lipid levels, but human data on the acute metabolic effects of light are scarce. Since light is the main signal indicating the onset of the diurnal phase of physical activity and food intake in humans, we hypothesized that bright light would affect glucose and lipid metabolism. Therefore, we determined the acute effects of bright light on plasma glucose and lipid concentrations in 2 randomized crossover trials: (1) in 8 healthy lean men and (2) in 8 obese men with type 2 diabetes. From 0730 h, subjects were exposed to either bright light (4000 lux) or dim light (10 lux) for 5 h. After 1 h of light exposure, subjects consumed a 600-kcal mixed meal. Primary endpoints were fasting and postprandial plasma glucose levels. In healthy men, bright light did not affect fasting or postprandial plasma glucose levels. However, bright light increased fasting and postprandial plasma triglycerides. In men with type 2 diabetes, bright light increased fasting and postprandial glucose levels. In men with type 2 diabetes, bright light did not affect fasting triglyceride levels but increased postprandial triglyceride levels. We show that ambient light intensity acutely affects human plasma glucose and triglyceride levels. Our findings warrant further research into the consequences of the metabolic effects of light for the diagnosis and prevention of hyperglycemia and dyslipidemia.

Correlation coefficients are abundantly used in the life sciences. Their use can be limited to simple exploratory analysis or to construct association networks for visualization but they are also basic ingredients for sophisticated multivariate data analysis methods. It is therefore important to have reliable estimates for correlation coefficients. In modern life sciences, comprehensive measurement techniques are used to measure metabolites, proteins, gene-expressions and other types of data. All these measurement techniques have errors. Whereas in the old days, with simple measurements, the errors were also simple, that is not the case anymore. Errors are heterogeneous, non-constant and not independent. This hampers the quality of the estimated correlation coefficients seriously. We will discuss the different types of errors as present in modern comprehensive life science data and show with theory, simulations and real-life data how these affect the correlation coefficients. We will briefly discuss ways to improve the estimation of such coefficients.

This paper presents a new approach to path modeling named SO‐PLS path modeling (SO‐PLS‐PM) and compares it with the more well‐known PLS path modeling (PLS‐PM). The new method is flexible and graphically oriented and allows for handling multidimensional blocks and diagnosing missing paths. In order to allow for a thorough comparison between the two methods, new definitions of total, direct, and indirect effects in terms of explained variances are proposed, along with new methods for graphical representation. The two PLS methods are tested on two well‐known data sets in the PLS‐PM literature from customer satisfaction analysis and descriptive sensory analysis. The find- ings from the empirical applications serve as a basis for recommendations and guidelines regarding the use of the SO‐PLS‐PM versus PLS‐PM.

Multiple sets of measurements on the same objects obtained from different platforms may reflect partially complementary information of the studied system. The integrative analysis of such data sets not only provides us with the opportunity of a deeper understanding of the studied system, but also introduces some new statistical challenges. First, the separation of information that is common across all or some of the data sets, and the information that is specific to each data set is problematic. Furthermore, these data sets are often a mix of quantitative and discrete (binary or categorical) data types, while commonly used data fusion methods require all data sets to be quantitative. In this paper, we propose an exponential family simultaneous component analysis (ESCA) model to tackle the potential mixed data types problem of multiple data sets. In addition, a structured sparse pattern of the loading matrix is induced through a nearly unbiased group concave penalty to disentangle the global, local common and distinct information of the multiple data sets. A Majorization-Minimization based algorithm is derived to fit the proposed model. Analytic solutions are derived for updating all the parameters of the model in each iteration, and the algorithm will decrease the objective function in each iteration monotonically. For model selection, a missing value based cross validation procedure is implemented. The advantages of the proposed method in comparison with other approaches are assessed using comprehensive simulations as well as the analysis of real data from a chronic lymphocytic leukaemia (CLL) study. Availability: the codes to reproduce the results in this article are available at https://gitlab.com/uvabda., Comment: 32 pages, 14 figures

Modern empirical science relies more and more on acquiring data. This has been accelerated by the developments in instrumental measurement methods allowing for collecting data in a high-throughput and relatively cheap way. Although this development has certainly created a big advantage for science, it has also created a big challenge: how to analyze such data? When multiple data blocks are measured on the same system, then it is worthwhile to analyze those data blocks simultaneously to arrive at a global view of that system. This problem analyzing multiple related data blocks simultaneously has already a long history in data analysis with many proposed methods but has experienced a revival in the last decade because of the reasons mentioned earlier. Depending on the specific field of data analysis, the methods to deal with this problem are called multiset methods, multiblock methods, data integration, or data fusion methods, to name a few. In this chapter, we present two frameworks for data fusion. The first framework includes a generic account of an important subset of the class of so-called low-level model-based data fusion methods. The second framework focuses on a subset of the methods subsumed by the first framework to separate the variation in multiblock data in common and distinct parts. We illustrate both frameworks with real-life examples from metabolomics.