Empirical Bayes Estimation of Sample-Specific Correlation Networks for Cross-Sectional and Longitudinal Omics Data

Sample-specific molecular networks, which capture how an individual's gene regulatory structure may deviate from the population as a whole, are important tools for understanding heterogeneity in health and disease. However, most existing methods either do not accommodate uncertainty quantification or cannot handle missing data, non-Gaussian modalities, and longitudinal structure common in modern multi-omic studies. For example, copy number alterations in cancer genomic studies are non-Gaussian and often only partially observed, and their regulatory effects on gene expression may vary substantially across patients, variation that a single, population-averaged network cannot capture. To address these challenges, we propose PRISM (Personalized Relational Inference via Sample-specific Modeling), an empirical Bayes framework for estimating sample-specific covariance matrices from cross-sectional and longitudinal multi-omic data. PRISM models each individual sample's covariance matrix as drawn from an inverse-Wishart prior whose parameters are estimated from the data and allowed to vary across subpopulations or evolve over time, yielding a closed-form posterior and edge-level uncertainty quantification, ensuring scalability to high-dimensional omics data. In simulation experiments, PRISM achieves point-estimate accuracy comparable to or better than existing methods, substantially improved uncertainty calibration under non-Gaussian marginals, and lower computational cost, while maintaining robust coverage under moderate missingness. We apply PRISM to a yeast cell-cycle time course dataset, recovering time-varying biologically meaningful regulatory relationships independently documented in literature, and to paired copy number and gene expression data from ovarian cancer patients, identifying copy-number-expression interactions associated with survival, including TFs HNF4G and PAX8 which have independent evidence of clinical relevance in this cancer.