<p>Predictive analytics is transforming healthcare by enabling early disease detection and personalized treatment, yet the sensitive nature of medical data raises critical security and privacy concerns, especially in multi-institutional settings. This review addresses these challenges by investigating homomorphic encryption (HE) as a powerful solution that enables computations directly on encrypted data, thus safeguarding patient confidentiality during analysis. We systematically examine state-of-the-art HE schemes and evaluate their applicability to healthcare scenarios, including their integration with federated learning and blockchain to enhance scalability and transparency in decentralized ecosystems. To demonstrate practical feasibility, we present a case study applying Paillier encryption to logistic regression for heart disease prediction. The results show that encrypted inference can achieve 90.16% accuracy, identical to plaintext performance, thus preserving model utility. However, the study also highlights a significant computational overhead, with encrypted inference requiring minutes versus milliseconds for plaintext, underscoring a key privacy-performance trade-off. Our findings confirm that HE can effectively preserve both data privacy and model accuracy, while identifying computational efficiency as the primary barrier to real-world clinical deployment. The review concludes that hybrid frameworks combining HE with other privacy-enhancing technologies represent the most promising direction for secure and reproducible healthcare analytics.</p>