Artificial Intelligence (AI), Machine Learning (ML), and Internet of Things (IoT) technologies have rapidly advanced, bringing drastic positive changes to modern healthcare by enhancing data driven decision-making, real time patient monitoring, and predictive diagnostics. Predictive analytics utilized within fog computing is one of the most promising developments in this field, as fog computing is a decentralized computing architecture that can process data from the source nearer as opposed to using only cloud based infrastructures. It enables healthcare institutions to improve clinical decision support continuity, optimize resource allocation, increase response time for emergencies and early disease detection at a low latency. Served by AI and ML, the predictive analytics utilizes complex computational models like the decision trees, random forests, support vector machines, deep learning, and reinforcement learning to examine large medical datasets to predict disease risks, to form the best possible treatment plans for patients and ultimately enhance patient outcomes in critical situations like detection of sepsis in Intensive Care Units (ICUs) and AI-based stroke prediction through real time imaging analysis. On the other hand, fog computing processes healthcare data at the edge of the network to reduce the dependency on cloud infrastructure, decrease the data transmission delay and appraise healthcare data at the edge of the network in real time to facilitate real time AI driven diagnostics and remote health monitoring especially in areas where there is no network coverage. Although the advantages of predictive analytics in the fog-based healthcare system, however, the implementation of predictive analytics in fog based healthcare system faces many challenges such as data privacy issues, computational resource limitations, and the issues of interoperability as well as biases in AI based medical predictions. For the success of the implementation of AI powered predictive analytics inside the fog computing environment, the main problem to resolve is to ensure the compliance with data protection regulations such as HIPAA and GDPR and address the constraints of Computing Devices at the edge, as well as the development of standard frameworks for secure healthcare data management in fog computing environments. Although these obstacles have to be overcome, further research into privacy protecting AI models, federated learning techniques, and modalities of blockchain based health data management systems are necessary to achieve that goal. Ultimately, the fusion of predictive analytics with fog computing has the potential to revolutionize healthcare by enhancing diagnostic accuracy, reducing hospital readmissions, and improving overall healthcare efficiency, making it a crucial innovation in the future of medical technology. Looking ahead, emerging technologies such as 5G connectivity, federated learning, blockchain-based secure data exchanges, and edge AI acceleration will further enhance the capabilities of predictive healthcare analytics in fog computing. These advancements will enable seamless remote diagnostics, privacy-preserving AI model training, and intelligent real-time health monitoring systems. As healthcare systems continue to evolve toward AI-driven, decentralized computing paradigms, the integration of predictive analytics with fog computing will play a pivotal role in shaping the future of precision medicine, telehealth, and smart hospital infrastructures. By addressing existing challenges and harnessing cutting-edge technological innovations, predictive analytics in fog-based healthcare has the potential to revolutionize patient care, streamline clinical workflows, and establish an intelligent, real-time, and data-driven healthcare ecosystem. This paper aims to provide a deep, technical, and practical understanding of how predictive analytics supports fog computing deployment in healthcare, offering valuable insights into its applications, benefits, limitations, and future directions in advancing medical AI and digital health transformation.