BACKGROUND: Multiple co-inertia analysis (mCIA) is a multivariate analysis method that can assess relationships and trends in multiple datasets. Recently it has been used for integrative analysis of multiple high-dimensional -omics datasets. However, its estimated loading vectors are non-sparse, which presents challenges for identifying important features and interpreting analysis results. We propose two new mCIA methods: 1) a sparse mCIA method that produces sparse loading estimates and 2) a structured sparse mCIA method that further enables incorporation of structural information among variables such as those from functional genomics. RESULTS: Our extensive simulation studies demonstrate the superior performance of the sparse mCIA and structured sparse mCIA methods compared to the existing mCIA in terms of feature selection and estimation accuracy. Application to the integrative analysis of transcriptomics data and proteomics data from a cancer study identified biomarkers that are suggested in the literature related with cancer disease. CONCLUSION: Proposed sparse mCIA achieves simultaneous model estimation and feature selection and yields analysis results that are more interpretable than the existing mCIA. Furthermore, proposed structured sparse mCIA can effectively incorporate prior network information among genes, resulting in improved feature selection and enhanced interpretability.

MOTIVATION: Co-inertia analysis (CIA) is a multivariate statistical analysis method that can assess relationships and trends in two sets of data. Recently CIA has been used for an integrative analysis of multiple high-dimensional omics data. However, for classical CIA, all elements in the loading vectors are nonzero, presenting a challenge for the interpretation when analyzing omics data. For other multivariate statistical methods such as canonical correlation analysis (CCA), penalized least squares (PLS), various approaches have been proposed to produce sparse loading vectors via l1-penalization/constraint. We propose a novel CIA method that uses l1-penalization to induce sparsity in estimators of loading vectors. Our method simultaneously conducts model fitting and variable selection. Also, we propose another CIA method that incorporates structure/network information such as those from functional genomics, besides using sparsity penalty so that one can get biologically meaningful and interpretable results. RESULTS: Extensive simulations demonstrate that our proposed penalized CIA methods achieve the best or close to the best performance compared to the existing CIA method in terms of feature selection and recovery of true loading vectors. Also, we apply our methods to the integrative analysis of gene expression data and protein abundance data from the NCI-60 cancer cell lines. Our analysis of the NCI-60 cancer cell line data reveals meaningful variables for cancer diseases and biologically meaningful results that are consistent with previous studies. AVAILABILITY AND IMPLEMENTATION: Our algorithms are implemented as an R package which is freely available at: https://www.med.upenn.edu/long-lab/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Integrative clustering is a clustering approach for multiple datasets, which provide different views of a common group of subjects. It enables analyzing multi-omics data jointly to, for example, identify the subtypes of diseases, cells, and so on, capturing the complex underlying biological processes more precisely. On the other hand, there has been a great deal of interest in incorporating the prior structural knowledge on the features into statistical analyses over the past decade. The knowledge on the gene regulatory network (pathways) can potentially be incorporated into many genomic studies. In this paper, we propose a novel integrative clustering method which can incorporate the prior graph knowledge. We first develop a generalized Bayesian factor analysis (GBFA) framework, a sparse Bayesian factor analysis which can take into account the graph information. Our GBFA framework employs the spike and slab lasso (SSL) prior to impose sparsity on the factor loadings and the Markov random field (MRF) prior to encourage smoothing over the adjacent factor loadings, which establishes a unified shrinkage adaptive to the loading size and the graph structure. Then, we use the framework to extend iCluster+, a factor analysis based integrative clustering approach. A novel variational EM algorithm is proposed to efficiently estimate the MAP estimator for the factor loadings. Extensive simulation studies and the application to the NCI60 cell line dataset demonstrate that the propose method is superior and delivers more biologically meaningful outcomes.