Patient-centered health care information systems (PHSs) on peer-to-peer (P2P) networks (e.g., decentralized personal health records) enable storing data locally at the edge to enhance data sovereignty and resilience to single points of failure. Nonetheless, these systems raise concerns on trust and adoption in medical workflow due to non-alignment to current health care processes and stakeholders’ needs. The distributed nature of the data makes it more challenging to train and deploy machine learning models (using traditional methods) at the edge, for instance, for disease prediction. Federated learning (FL) has been proposed as a possible solution to these limitations. However, the P2P PHS architecture challenges current FL solutions because they use centralized engines (or random entities that could pose privacy concerns) for model update aggregation. Consequently, we propose a novel conceptual FL framework, CareNetFL, that is suitable for P2P PHS multi-tier and hybrid architecture and leverages existing trust structures in health care systems to ensure scalability, trust, and security. Entrusted parties (practitioners’ nodes) are used in CareNetFL to aggregate local model updates in the network hierarchy for their patients instead of random entities that could actively become malicious. Involving practitioners in their patients’ FL model training increases trust and eases access to medical data. The proposed concepts mitigate communication latency and improve FL performance through patient–practitioner clustering, reducing skewed and imbalanced data distributions and system heterogeneity challenges of FL at the edge. The framework also ensures end-to-end security and accountability through leveraging identity-based systems and privacy-preserving techniques that only guarantee security during training.