Longitudinal Sparse Single-Omics Factor Analysis for High-Dimensional Blood Biomarkers in Alzheimer's Disease

Alzheimer's disease (AD) is a progressive neurodegenerative disorder whose molecular mechanisms involve multiple biological pathways. Longitudinal blood-based omics data, such as lipidomics and metabolomics profiles, offer promising noninvasive biomarkers for early detection and prognosis, yet they are high-dimensional, sparse, and exhibit complex temporal and cross-feature correlations. The primary goal of this study is to identify which omics data types are most strongly associated with time to dementia onset in patients with mild cognitive impairment (MCI) at baseline. To address this, we propose a longitudinal sparse single-omics factor analysis (LS-SOFA) framework that models each omics view through view-specific latent factors and feature-weight matrices, with temporal dynamics captured by functional principal component analysis (FPCA). The resulting functional principal component (FPC) scores are incorporated into a survival model to test whether each omics view is associated with time to dementia onset. An efficient covariance-based estimation algorithm substantially reduces computational and memory cost, enabling large-scale application in the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. In simulations, LS-SOFA achieves higher longitudinal estimation accuracy and more stable hypothesis testing than competing methods. Applied to five blood-based omics views from ADNI, LS-SOFA identified plasma lipidomics and serum metabolomics from FIA and UPLC as significantly associated with dementia risk after FDR adjustment, with nominal evidence of association for gut microbial metabolomics from serum. The top features within each omics view reveal biologically interpretable metabolic pathways that may serve as blood-based biomarkers for AD progression.