Penalized co-inertia analysis with applications to-omics data

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 l ₁ -penalization/constraint. We propose a novel CIA method that uses l 1-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.