Medical research increasingly requires combining data from multiple hospitals and health systems to achieve meaningful sample sizes, but patient privacy laws and institutional policies create significant barriers to data sharing. The challenge becomes even more complex when institutions use different electronic health record systems, patient populations, or data collection methods. A breakthrough computational approach now enables researchers to conduct rigorous multi-institutional studies while keeping sensitive patient data completely within each participating organization. The COLA-GLM-H algorithm reconstructs global statistical models using only summary statistics from each institution, requiring just a single round of communication between sites. Validation studies involving over 840,000 patients demonstrated the method's effectiveness across diverse research questions, from pediatric cardiovascular outcomes following COVID-19 to international mortality risk assessments. The algorithm produced results identical to traditional pooled analyses while maintaining complete data privacy. This represents a significant advance over existing federated learning approaches that typically require multiple communication rounds and may introduce estimation errors. For health researchers, this methodology could unlock previously inaccessible research opportunities by enabling collaboration between institutions that cannot share raw patient data due to regulatory, ethical, or competitive constraints. The approach is particularly valuable for rare disease research, where no single institution has sufficient patient numbers, and for international studies where data transfer restrictions are prohibitive. While the current validation focused on generalized linear models, the underlying principles could potentially extend to more complex analytical frameworks.