Metabolomics deals with multiple and complex chemical reactions within living organisms and how these are influenced by external or internal perturbations. It lies at the heart of omics profiling technologies not only as the underlying biochemical layer that reflects information expressed by the genome, the transcriptome and the proteome, but also as the closest layer to the phenome. The combination of metabolomics data with the information available from genomics, transcriptomics, and proteomics offers unprecedented possibilities to enhance current understanding of biological functions, elucidate their underlying mechanisms and uncover hidden associations between omics variables. As a result, a vast array of computational tools have been developed to assist with integrative analysis of metabolomics data with different omics. Here, we review and propose five criteria — hypothesis, data types, strategies, study design and study focus — to classify statistical multi-omics data integration approaches into state-of-the-art classes under which all existing statistical methods fall. The purpose of this review is to look at various aspects that lead the choice of the statistical integrative analysis pipeline in terms of the different classes. We will draw particular attention to metabolomics and genomics data to assist those new to this field in the choice of the integrative analysis pipeline.

BackgroundCanonical correlation analysis (CCA) is a classic statistical tool for investigating complex multivariate data. Correspondingly, it has found many diverse applications, ranging from molecular biology and medicine to social science and finance. Intriguingly, despite the importance and pervasiveness of CCA, only recently a probabilistic understanding of CCA is developing, moving from an algorithmic to a model-based perspective and enabling its application to large-scale settings.ResultsHere, we revisit CCA from the perspective of statistical whitening of random variables and propose a simple yet flexible probabilistic model for CCA in the form of a two-layer latent variable generative model. The advantages of this variant of probabilistic CCA include non-ambiguity of the latent variables, provisions for negative canonical correlations, possibility of non-normal generative variables, as well as ease of interpretation on all levels of the model. In addition, we show that it lends itself to computationally efficient estimation in high-dimensional settings using regularized inference. We test our approach to CCA analysis in simulations and apply it to two omics data sets illustrating the integration of gene expression data, lipid concentrations and methylation levels.ConclusionsOur whitening approach to CCA provides a unifying perspective on CCA, linking together sphering procedures, multivariate regression and corresponding probabilistic generative models. Furthermore, we offer an efficient computer implementation in the “whitening” R package available at https://CRAN.R-project.org/package=whitening.

Metabolomics time-course experiments provide the opportunity to understand the changes to an organism by observing the evolution of metabolic profiles in response to internal or external stimuli. Along with other omic longitudinal profiling technologies, these techniques have great potential to complement the analysis of complex relations between variations across diverse omic variables and provide unique insights into the underlying biology of the system. However, many statistical methods currently used to analyse short time-series omic data are i) prone to overfitting or ii) do not take into account the experimental design or iii) do not make full use of the multivariate information intrinsic to the data or iv) unable to uncover multiple associations between different omic data. The model we propose is an attempt to i) overcome overfitting by using a weakly informative Bayesian model, ii) capture experimental design conditions through a mixed-effects model, iii) model interdependencies between variables by augmenting the mixed-effects model with a conditional autoregressive (CAR) component and iv) identify potential associations between heterogeneous omic variables by using a horseshoe prior. Results: We assess the performance of our model on synthetic and real datasets and show that it outperforms existing models for metabolomic longitudinal data analysis. Our proposed method is able to identify metabolic biomarkers related to treatment, infer perturbed pathways as a result of treatment and find significant associations with additional omic variables. We also show through simulation that an informative beta like prior compares better than a non-informative uniform prior in inferring significant pathways. On real data, we investigate how the number of profiled metabolites can affect the predictive ability of the model. Supplementary material for this article are available online.

Metabolomics deals with multiple and complex chemical reactions within living organisms and how these are influenced by external or internal perturbations. It lies at the heart of omics profiling technologies not only as the underlying biochemical layer that reflects information expressed by the genome, the transcriptome and the proteome, but also as the closest layer to the phenome. The combination of metabolomics data with the information available from genomics, transcriptomics, and proteomics offers unprecedented possibilities to enhance current understanding of biological functions, elucidate their underlying mechanisms and uncover hidden associations between omics variables. As a result, a vast array of computational tools have been developed to assist with integrative analysis of metabolomics data with different omics. Here, we review and propose five criteria – hypothesis, data types, strategies, study design and study focus – to classify statistical multi-omics data integration approaches into state-of-the-art classes under which all existing statistical methods fall. The purpose of this review is to look at various aspects that lead the choice of the statistical integrative analysis pipeline in terms of the different classes. We will draw a particular attention to metabolomics and genomics data to assist those new to this field in the choice of the integrative analysis pipeline.

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