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Hospitals seek to compare performance on operational metrics and quality indicators, but sharing granular patient-level, unit-level, or institution-level data raises privacy, legal, reputational, and competitive concerns. Privacy-preserving analytics has therefore become increasingly relevant for health systems that need collective insight without centralized pooling of sensitive data. This systematic review examines privacy-preserving models used for operational benchmarking, quality monitoring, resource planning, and multi-institutional performance comparison in healthcare. The review focuses on federated analytics, federated learning, secure multi-party computation, differential privacy, homomorphic encryption, and secure aggregation. A PRISMA 2020-compliant search was designed for PubMed, Scopus, IEEE Xplore, and Web of Science covering studies published from 2017 to 2025. Records were screened by two reviewers, and eligible studies were synthesized narratively by application domain, privacy-preserving method, implementation maturity, and operational relevance. Federated learning and secure aggregation dominated the literature, with more recent work increasingly combining federated workflows with differential privacy, homomorphic encryption, or governance frameworks. Most studies addressed clinical prediction or biomedical analytics, while fewer directly examined operational benchmarking, capacity planning, or routine multi-hospital performance comparison. The technical foundations for privacy-preserving federated analytics are increasingly mature, but their translation into routine healthcare operations remains early. Evidence is strongest for multi-site clinical modeling and weakest for sustained operational benchmarking, resource planning, and governance-tested deployment.