Comprehensive 2D gas chromatography coupled with mass spectrometry (GC × GC-MS) is a powerful analytical technique. However, the complexity and volume of data generated pose significant challenges for data processing and interpretation, limiting a broader adoption. Chemometric approaches, particularly multiway models like Parallel Factor Analysis (PARAFAC), have proven effective in addressing these challenges by enabling the extraction of meaningful chemical information from multi-dimensional datasets. However, traditional PARAFAC is constrained by its assumption of data tri-linearity, which may not be valid in all cases, leading to potential inaccuracies. To overcome these limitations, we present GcDUO, an open-source software implemented in R, designed specifically for the processing and analysis of GC × GC-MS data. GcDUO integrates advanced chemometric methods, including both PARAFAC and PARAFAC2, for a more accurate and comprehensive analysis. PARAFAC is particularly useful for deconvoluting overlapping peaks and extracting pure chemical signals, while PARAFAC2 relaxes de tri-linearity constraint, allowing the alignment between samples. The software is structured into six modules-data import, region of interest (ROI) selection, deconvolution, peak annotation, data integration, and visualization-facilitating comprehensive and flexible data processing. GcDUO was validated against the gold-standard software for comprehensive GC, demonstrating a high correlation (R2 = 0.9) in peak area measurements, confirming its effectiveness and reliability. GcDUO provides a valuable, open-source platform for researchers in metabolomics and related fields, enabling more accessible and customizable GC × GC-MS 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.

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: Validation of variable selection and predictive performance is crucial in construction of robust multivariate models that generalize well, minimize overfitting and facilitate interpretation of results. Inappropriate variable selection leads instead to selection bias, thereby increasing the risk of model overfitting and false positive discoveries. Although several algorithms exist to identify a minimal set of most informative variables (i.e. the minimal-optimal problem), few can select all variables related to the research question (i.e. the all-relevant problem). Robust algorithms combining identification of both minimal-optimal and all-relevant variables with proper cross-validation are urgently needed. RESULTS: We developed the MUVR algorithm to improve predictive performance and minimize overfitting and false positives in multivariate analysis. In the MUVR algorithm, minimal variable selection is achieved by performing recursive variable elimination in a repeated double cross-validation (rdCV) procedure. The algorithm supports partial least squares and random forest modelling, and simultaneously identifies minimal-optimal and all-relevant variable sets for regression, classification and multilevel analyses. Using three authentic omics datasets, MUVR yielded parsimonious models with minimal overfitting and improved model performance compared with state-of-the-art rdCV. Moreover, MUVR showed advantages over other variable selection algorithms, i.e. Boruta and VSURF, including simultaneous variable selection and validation scheme and wider applicability. AVAILABILITY AND IMPLEMENTATION: Algorithms, data, scripts and tutorial are open source and available as an R package ('MUVR') at https://gitlab.com/CarlBrunius/MUVR.git. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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.

Motivation: Our society has become data-rich to the extent that research in many areas has become impossible without computational approaches. Educational programmes seem to be lagging behind this development. At the same time, there is a growing need not only for strong data science skills, but foremost for the ability to both translate between tools and methods on the one hand, and application and problems on the other. Results: Here we present our experiences with shaping and running a masters' programme in bioinformatics and systems biology in Amsterdam. From this, we have developed a comprehensive philosophy on how translation in training may be achieved in a dynamic and multidisciplinary research area, which is described here. We furthermore describe two requirements that enable translation, which we have found to be crucial: sufficient depth and focus on multidisciplinary topic areas, coupled with a balanced breadth from adjacent disciplines. Finally, we present concrete suggestions on how this may be implemented in practice, which may be relevant for the effectiveness of life science and data science curricula in general, and of particular interest to those who are in the process of setting up such curricula. Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: ERp is a variable selection and classification method for metabolomics data. ERp uses minimized classification error rates, based on data from a control and experimental group, to test the null hypothesis of no difference between the distributions of variables over the two groups. If the associated p-values are significant they indicate discriminatory variables (i.e. informative metabolites). The p-values are calculated assuming a common continuous strictly increasing cumulative distribution under the null hypothesis. This assumption is violated when zero-valued observations can occur with positive probability, a characteristic of GC-MS metabolomics data, disqualifying ERp in this context. This paper extends ERp to address two sources of zero-valued observations: (i) zeros reflecting the complete absence of a metabolite from a sample (true zeros); and (ii) zeros reflecting a measurement below the detection limit. This is achieved by allowing the null cumulative distribution function to take the form of a mixture between a jump at zero and a continuous strictly increasing function. The extended ERp approach is referred to as XERp. RESULTS: XERp is no longer non-parametric, but its null distributions depend only on one parameter, the true proportion of zeros. Under the null hypothesis this parameter can be estimated by the proportion of zeros in the available data. XERp is shown to perform well with regard to bias and power. To demonstrate the utility of XERp, it is applied to GC-MS data from a metabolomics study on tuberculosis meningitis in infants and children. We find that XERp is able to provide an informative shortlist of discriminatory variables, while attaining satisfactory classification accuracy for new subjects in a leave-one-out cross-validation context. CONCLUSION: XERp takes into account the distributional structure of data with a probability mass at zero without requiring any knowledge of the detection limit of the metabolomics platform. XERp is able to identify variables that discriminate between two groups by simultaneously extracting information from the difference in the proportion of zeros and shifts in the distributions of the non-zero observations. XERp uses simple rules to classify new subjects and a weight pair to adjust for unequal sample sizes or sensitivity and specificity requirements.

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.

BACKGROUND: Metabolomics datasets are often high-dimensional though only a limited number of variables are expected to be informative given a specific research question. The important task of selecting informative variables can therefore become complex. In this paper we look at discriminating between two groups. Two tasks need to be performed: (i) finding variables which differ between the two groups; and (ii) determining how the selected variables can be used to classify new subjects. We introduce an approach using minimum classification error rates as test statistics to find discriminatory and therefore informative variables. The thresholds resulting in the minimum error rates can be used to classify new subjects. This approach transforms error rates into p-values and is referred to as ERp. RESULTS: We show that non-parametric hypothesis testing, based on minimum classification error rates as test statistics, can find statistically significantly shifted variables. The discriminatory ability of variables becomes more apparent when error rates are evaluated based on their corresponding p-values, as relatively high error rates can still be statistically significant. ERp can handle unequal and small group sizes, as well as account for the cost of misclassification. ERp retains (if known) or reveals (if unknown) the shift direction, aiding in biological interpretation. The threshold resulting in the minimum error rate can immediately be used to classify new subjects. We use NMR generated metabolomics data to illustrate how ERp is able to discriminate subjects diagnosed with Mycobacterium tuberculosis infected meningitis from a control group. The list of discriminatory variables produced by ERp contains all biologically relevant variables with appropriate shift directions discussed in the original paper from which this data is taken. CONCLUSIONS: ERp performs variable selection and classification, is non-parametric and aids biological interpretation while handling unequal group sizes and misclassification costs. All this is achieved by a single approach which is easy to perform and interpret. ERp has the potential to address many other characteristics of metabolomics data. Future research aims to extend ERp to account for a large proportion of observations below the detection limit, as well as expand on interactions between variables.

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.