ONDSA: a testing framework based on Gaussian graphical models for differential and similarity analysis of multiple omics networks

The Gaussian graphical model (GGM) is a statistical network approach that represents conditional dependencies among components, enabling a comprehensive exploration of disease mechanisms using high-throughput multi-omics data. Analyzing differential and similar structures in biological networks across multiple clinical conditions can reveal significant biological pathways and interactions associated with disease onset and progression. However, most existing methods for estimating group differences in sparse GGMs only apply to comparisons between two groups, and the challenging problem of multiple testing across multiple GGMs persists. This limitation hinders the ability to uncover complex biological insights that arise from comparing multiple conditions simultaneously. To address these challenges, we propose the Omics Networks Differential and Similarity Analysis (ONDSA) framework, specifically designed for continuous omics data. ONDSA tests for structural differences and similarities across multiple groups, effectively controlling the false discovery rate (FDR) at a desired level. Our approach focuses on entry-wise comparisons of precision matrices across groups, introducing two test statistics to sequentially estimate structural differences and similarities while adjusting for correlated effects in FDR control procedures. We show via comprehensive simulations that ONDSA outperforms existing methods under a range of graph structures and is a valuable tool for joint comparisons of multiple GGMs. We also illustrate our method through the detection of neuroinflammatory pathways in a multi-omics dataset from the Framingham Heart Study Offspring cohort, involving three apolipoprotein E genotype groups. It highlights ONDSA's ability to provide a more holistic view of biological interactions and disease mechanisms through multi-omics data integration.