Co-Inertia analysis for multi-omics data with FDR control via SLOPE

Co-inertia analysis (CIA) is a multivariate analysis method that assesses relationships and trends in two sets of data. It has been effectively employed in the integrative analysis of high-dimensional multi-omics datasets. Recently, penalized CIA methods have been introduced to enhance the interpretability by inducing sparsity in the loading vectors. However, challenges persist in ensuring that non-zero elements in the estimated vector genuinely represent significant features. To address these challenges, we propose a penalized CIA method that controls the false discovery rate (FDR) using sorted l-1 penalized estimation (SLOPE). This approach allows for simultaneous FDR control and sparsity induction in the estimated vectors. Extensive simulation studies demonstrate the performance compared to the existing CIA method. Additionally, we apply our methods to the integrative analysis of NCI60 data to show its effectiveness in real-world scenarios.