Privacy-Preserving Multivariate Bayesian Regression Models for Overcoming Data Sharing Barriers in Health and Genomics

Abstract We present multivariate Bayesian regression models specifically designed to over-come data-sharing barriers in health and genomics. These multi-response models are well suited for scenarios where data must remain decentralized due to privacy, intellectual property, or regulatory constraints. In extensive simulation studies, our approach consistently outperformed traditional single-response models trained on individual datasets, particularly under real-world conditions such as low signal, unbalanced cohorts, and high-dimensional feature spaces. For the first time, we demonstrate that multivariate Bayesian regression can be implemented using or-thogonal transformations of sufficient statistics, enabling fully privacy-preserving analysis without sharing individual-level data. The models are scalable, inter-pretable, and applicable to predictive tasks across diverse collaborators, supporting secure data-driven research in domains such as clinical trials, biomarker discovery, and precision health. Competing Interest Statement The authors have declared no competing interest. Funding Statement PS obtained funding from Novo Nordisk Foundation through the drug discovery platform, Open Discovery Innovation Network (ODIN) under grant number NNF20SA0061466. This funding aims to foster collaboration between universities and companies promoting long-term benefits of innovation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability All data produced in the present study are available upon reasonable request to the authors.