Supplementary data are available at Bioinformatics online.

This chapter covers the state-of-the-art multivariate statistical methods designed for high-dimensional multiset omics data analysis. Recent biotechnological developments have enabled large-scale measurement of various biomolecular data, such as genotypic and phenotypic data, dispersed over various omics domains. An emergent research direction is to analyze these data sources using an integrated approach to better model and understand the underlying biology of complex disease conditions. However, comprehensive analysis techniques that can handle both the size and complexity, and at the same time can account for the hierarchical structure of such data, are lacking. An overview of some of the developments in multivariate techniques for high-dimensional omics data analysis, highlighting two well-known multivariate methods, canonical correlation analysis (CCA) and redundancy analysis (RDA), is provided in this chapter. Penalized versions of CCA are widespread in the omics data analysis field, and there is recent work on multiset penalized RDA that is applicable to multiset omics data. How these methods meet the statistical challenges that come with high-dimensional multiset omics data analysis and help to further our understanding of the human condition in terms of health and disease are presented. Additionally, the current challenges to be resolved in the field of omics data analysis are discussed.

Background: Recent technological developments have enabled the measurement of a plethora of biomolecular data from various omics domains, and research is ongoing on statistical methods to leverage these omics data to better model and understand biological pathways and genetic architectures of complex phenotypes. Current reviews report that the simultaneous analysis of multiple (i.e. three or more) high dimensional omics data sources is still challenging and suitable statistical methods are unavailable. Often mentioned challenges are the lack of accounting for the hierarchical structure between omics domains and the difficulty of interpretation of genomewide results. This study is motivated to address these challenges. We propose multiset sparse Partial Least Squares path modeling (msPLS), a generalized penalized form of Partial Least Squares path modeling, for the simultaneous modeling of biological pathways across multiple omics domains. msPLS simultaneously models the effect of multiple molecular markers, from multiple omics domains, on the variation of multiple phenotypic variables, while accounting for the relationships between data sources, and provides sparse results. The sparsity in the model helps to provide interpretable results from analyses of hundreds of thousands of biomolecular variables. Results: With simulation studies, we quantified the ability of msPLS to discover associated variables among high dimensional data sources. Furthermore, we analysed high dimensional omics datasets to explore biological pathways associated with Marfan syndrome and with Chronic Lymphocytic Leukaemia. Additionally, we compared the results of msPLS to the results of Multi-Omics Factor Analysis (MOFA), which is an alternative method to analyse this type of data. Conclusions: msPLS is an multiset multivariate method for the integrative analysis of multiple high dimensional omics data sources. It accounts for the relationship between multiple high dimensional data sources while it provides interpretable results through its sparse solutions. The biomarkers found by msPLS in the omics datasets can be interpreted in terms of biological pathways associated with the pathophysiology of Marfan syndrome and of Chronic Lymphocytic Leukaemia. Additionally, msPLS outperforms MOFA in terms of variation explained in the chronic lymphocytic leukaemia dataset while it identifies the two most important clinical markers for Chronic Lymphocytic Leukaemia

Redundancy Analysis (RDA) is a well‐known method used to describe the directional relationship between related data sets. Recently, we proposed sparse Redundancy Analysis (sRDA) for high‐dimensional genomic data analysis to find explanatory variables that explain the most variance of the response variables. As more and more biomolecular data become available from different biological levels, such as genotypic and phenotypic data from different omics domains, a natural research direction is to apply an integrated analysis approach in order to explore the underlying biological mechanism of certain phenotypes of the given organism. We show that the multiset sparse Redundancy Analysis (multi‐sRDA) framework is a prominent candidate for high‐dimensional omics data analysis since it accounts for the directional information transfer between omics sets, and, through its sparse solutions, the interpretability of the result is improved. In this paper, we also describe a software implementation for multi‐sRDA, based on the Partial Least Squares Path Modeling algorithm. We test our method through simulation and real omics data analysis with data sets of 364,134 methylation markers, 18,424 gene expression markers, and 47 cytokine markers measured on 37 patients with Marfan syndrome.

Quantum computing is a field that aims to exploit the principles of superposition and entanglement to perform computations. By using quantum bits (qubits) a quantum computer is able to perform certain tasks more efficiently when compared to classical computers. While applied quantum computing is still in its early stages, quantum algorithms on simulated quantum computers have already been applied to certain problems in epidemics modeling and image processing. Furthermore, companies like Google and IBM continue to develop new quantum computers with an increasing number of qubits. While much progress has been made in the recent years, the so called ”quantum supremacy”has not yet been achieved, and quantum computing appears to be still unsuitable for most applications in biomedical sciences.