Multiset sparse partial least squares path modeling for high dimensional omics data analysis

“…from analyses of hundreds of thousands of MVs is addressed through sparse variable selection. msPLS enforces sparse variable selection through penalization methods, such as through the Least Absolute Shrinkage and Selection Operator (LASSO), Ridge, and Elastic Net (ENet) penalization methods [27].”

“…Partial Least Squares path modeling distinguishes between these two types of relationships between data sources (i.e. symmetric or asymmetric relationships) the same way as the two well known multivariate statistical methods Canonical Correlation Analysis [8] and Redundancy Analysis [10] do.”

“Detailed reviews and discussions on multi-variate methods for omics data analysis can be found in [3, 12–18].”

“The two most important clinical markers for CLL, namely the immunoglobulin heavy chain gene (IGHV) and the trisomy of chromosome 12 (trisomy12) were extracted as the first and second LV, respectively (Table 6) [11].”

“In addition, it has been reported that the activity of transforming growth factor beta (TGF-beta, associated pathway “ TGF-beta receptor signaling in EMT ”), is increased in aneurysmal vascular walls [31, 44– 46].”

“Abbreviations CCA: Canonical correlation analysis; CCL: Chronic lymphocytic leukaemia; CI: Confidence interval; ENeT: Elastic net; LVs: Latent variables; LASSO: Least absolute shrinkage and selection operator; MVs: Manifest variables; MOFA: Multi-omics factor analysis; msPLS: Multiset sparse partial least squares path…”

“Among the challenges are the lack of accounting for the hierarchical structure between omics domains (i.e. relationship between data sources) and the difficulty of interpretation of genomewide results [2, 3, 19, 20].”

“The explanatory and response omics data source pairs can be determined through the hypothesised information transfer between data sources as follows [21].”

“78 ×10−3 Vascular inflammation through interleukins [35, 36]”

“Abbreviations CCA: Canonical correlation analysis; CCL: Chronic lymphocytic leukaemia; CI: Confidence interval; ENeT: Elastic net; LVs: Latent variables; LASSO: Least absolute shrinkage and selection operator; MVs: Manifest variables; MOFA: Multi-omics factor analysis; msPLS: Multiset sparse partial least squares path…”

“In addition, it has been reported that the activity of transforming growth factor beta (TGF-beta, associated pathway “ TGF-beta receptor signaling in EMT ”), is increased in aneurysmal vascular walls [31, 44– 46].”

“Among the challenges are the lack of accounting for the hierarchical structure between omics domains (i.e. relationship between data sources) and the difficulty of interpretation of genomewide results [2, 3, 19, 20].”

“…matrix 3.87 × 10 − 2 Extracellular matrix organization [31] RHO GTPases Activate Formins 3.92 × 10 − 2 Extracellular matrix organization [41] TGF-betareceptor signalinginEMT(epithelialtomesenchymal transition) 3.92 × 10 − 2 Signaling by TGF-beta receptor complex [31] Cell-extracellular…”

“Therefore, modeling biological pathways across multiple omics domains might help to better understand the underlying genetic architecture and biological processes of complex phenotypes, which in turn leads to improved diagnosis, prognosis and therapy [1].”

“We applied msPLS to genomewide epigenomic, transcriptomic and proteomic data sources measured in Marfan patients [28].”

“…for the integrated (i.e. simultaneous) analysis of multiple high dimensional omics datasets are generalizations of well known multivariate methods; e.g. sparse Canonical Correlation Analysis (CCA) [4–8], sparse Redundancy Analysis (RDA) [9, 10], and Multi-Omics Factor Analysis (MOFA) [11].”

“1 × 10−4) [47], “HDACs deacetylate histones” (p-value 8.”

“Although MFS2 is phenotypically not separable from classic Marfan syndrome, both disease types include thoracic aortic aneurysm, and more generally aortic risk as the main common feature of the disease [31, 43].”

“These assumptions are based on the special biological sequential information transfers of the central dogma of molecular biology and its elaborated versions [25, 26].”

“…in Cancer Signaling by TGF-beta receptor complex [31] RUNX3 regulates CDKN1A transcription 1.67 × 10 − 2 Signaling by TGF-beta receptor complex [37] Signaling by TGF-beta Receptor Complex in Cancer 1.88 × 10 − 2 Signaling by TGF-beta receptor complex [31] Collagen formation 2.02 × 10 − 2…”

“The descriptions of the objective functions of PLS-PM can be found in [22, 24] and the objective function for msPLS is given by Eq.”

“In addition, we applied msPLS to genomic, epigenomic, transcriptomic, and drug response data sources measured in Chronic Lymphocytic Leukaemia (CLL) patients [29].”

“Detailed reviews and discussions on multi-variate methods for omics data analysis can be found in [3, 12–18].”

“…NCAM signaling for neurite out-growth [33] Interleukin-4 and Interleukin-13 signaling 9.78 × 10 − 3 Vascular inflammation through interleukins [35, 36] Collagen biosynthesis and modifying enzymes 1.12 × 10 − 2 Collagene formation [31] TGFBR1 KD Mutants in Cancer 1.26 × 10 − 2 Signaling by…”

“…), “ TP53 Regulates Transcription of Cell Death Genes ” ( p -value 8.1 × 10 − 4 ) [47], “ HDACs deacetylate histones ” ( p -value 8.73 × 10 − 25 ) [48], “ HS-GAG degradation ” ( p -value 1.22 × 10 − 4 ), “ HS-GAG biosynthesis ” ( p -value 7.6 × 10 − 4 ), and “ Heparan sulfate/heparin (HS-GAG)…”

“Thegoal of this analysis was to explore biological pathways associated with Marfan disease based on epigenomic, transcriptomic and proteomic data measured in 37 Marfan patients [30].”

“…biogenesis 8.17 × 10 − 4 Possibly through reduced mitochondrial respiration [32] Crosslinking of collagen fibrils 1.20 × 10 − 3 Collagene formation [31] Laminin interactions 1.98 × 10 − 3 Extracellular matrix organization [31] Mitochondrial biogenesis 2.40 × 10 − 3 Possibly through reduced…”

“33 ×10−2 Possibly by proresolving lipid mediators [40]”

“…reduced mitochondrial respiration [32] Transfer of LPS from LBP carrier to CD14 6.30 × 10 − 3 Possibly through toll-like receptor-4 signaling [34] Transport of HA trimer, NA tetramer and M2 tetramer from the endoplasmic reticulum to the Golgi Apparatus Signaling by TGF-beta receptor complex…”

“…organization [31] Transcriptional regulation of white adipocyte differentiation 2.17 × 10 − 2 Possibly by depleted or abnormal adipose tissue [38] Aromatic amines can be N-hydroxylated or N-dealkylated by CYP1A2 Possibly by proresolving lipid mediators [40] Degradation of the extracellular…”

“Among the challenges are the lack of accounting for the hierarchical structure between omics domains (i.e. relationship between data sources) and the difficulty of interpretation of genomewide results [2, 3, 19, 20].”

“…× 10 − 3 Degradation of the extracellular matrix [31] NCAM signaling for neurite out-growth 9.58 × 10 − 3 NCAM signaling for neurite out-growth [33] Interleukin-4 and Interleukin-13 signaling 9.78 × 10 − 3 Vascular inflammation through interleukins [35, 36] Collagen biosynthesis and modifying…”

“…X q and X q (cid:4) is indicated as c qq (cid:4) = c q (cid:4) q = 1, in which case the OF of their pairwise analysis is to maximise the correlation between their LVs ζ q and ζ q (cid:4) , corresponding to the characteristic objective function of Canonical Correlation Analysis (CCA) [8, 22, 50].”

“In an asymmetric relationship, the OF of a pairwise analysis is to maximise the sum of squared correlation between the explanatory LV ζ q and the response MVs in X q (cid:4) , corresponding to the characteristic objective function of Redundancy Analysis (RDA) [10, 22, 51].”

“…Death Genes ” ( p -value 8.1 × 10 − 4 ) [47], “ HDACs deacetylate histones ” ( p -value 8.73 × 10 − 25 ) [48], “ HS-GAG degradation ” ( p -value 1.22 × 10 − 4 ), “ HS-GAG biosynthesis ” ( p -value 7.6 × 10 − 4 ), and “ Heparan sulfate/heparin (HS-GAG) metabolism ” ( p -value 5.66 × 10 − 3 ) [49].”

“…lipid mediators [40] Cytokine Signaling in Immune system 4.49 × 10 − 2 Cytokine signaling [31] Synthesis of epoxy (EET) and dihydroxyeicosatrienoic acids (DHET) 4.73 × 10 − 2 Arachidonic acid metabolism [42] Arachidonic acid metabolism 4.76 × 10 − 2 Arachidonic acid metabolism [42] The ).”

“Among the challenges are the lack of accounting for the hierarchical structure between omics domains (i.e. relationship between data sources) and the difficulty of interpretation of genomewide results [2, 3, 19, 20].”

“…1.98 × 10 − 3 Extracellular matrix organization [31] Mitochondrial biogenesis 2.40 × 10 − 3 Possibly through reduced mitochondrial respiration [32] NCAM1 interactions 3.92 × 10 − 3 NCAM signaling for neurite out-growth [33] Collagen chain trimerization 3.92 × 10 − 3 Collagene biosynthesis and…”

“…for the integrated (i.e. simultaneous) analysis of multiple high dimensional omics datasets are generalizations of well known multivariate methods; e.g. sparse Canonical Correlation Analysis (CCA) [4–8], sparse Redundancy Analysis (RDA) [9, 10], and Multi-Omics Factor Analysis (MOFA) [11].”

“Multiset sparse partial least squares path modeling (msPLS) for high-dimensional omics data analysis (https://doi.org/10.1186/s12859-019-3286-3) 29 is a novel statistical method that models and helps us understand biological pathways and genetic architectures of Table 2.”

“Notable approaches include joint non-negative matrix factorization (jNMF) methods [42], partial least square (PLS) [43], canonical correlation analysis (CCA) [44], and multiple kernel learning (MKL) [45].”

“In PLSPM, latent variables are used to consider all relationships between explanatory and manifest variables [71].”

“Unsupervised multi-omics methods, such as PLS structural equation modeling (PLS-SEM; Csala et al., 2020) or Multi-Omics Factor Analysis (MOFA, Argelaguet et al., 2018), constitute powerful alternatives to explore the relationships among omics levels, but are not appropriate for classification of…”

“Examples of alternative methods with different objective functions include JIVE (joint and individual variation explained) [35], GSVD (generalized singular value decomposition) [36], and msPLS (multiset sparse partial least squares path modelling) [37].”

“The assertion by scientists is that PLS models will outperform other models when high dimensional datasets are applicable (Csala et al. 2020; Mehmood et al. 2022).”

“FDR-adjusted p -value applied but threshold not specified (Benjamini–Hochbergprocedure)”