Cardiovascular diseases continue to be the leading cause of mortality worldwide, claiming a significant number of lives each year. Despite the advancements in predictive models, including logistic regression, neural networks, and random forests, these techniques often lack transparency and interpretability, limiting their practical application in clinical settings. To address this challenge, this research introduces EPFHD-RARMING, an innovative approach designed to enhance the understanding and predictability of heart disease through the discovery of rare and meaningful patterns. EPFHD-RARMING utilizes rare association rule mining to uncover hidden and unexpected rules that identify critical factors contributing to heart disease. This method is particularly adept at identifying high-risk patterns in individuals who appear healthy but may develop heart disease under certain conditions, thus facilitating early intervention and preventive measures. By integrating these insights with established feature engineering techniques, EPFHD-RARMING enhances its practical utility, enabling medical professionals to proactively manage patient care and tailor interventions to individual risk profiles. This study demonstrates the effectiveness of EPFHD-RARMING in providing a deeper, actionable understanding of the complex dynamics of heart disease. The model's ability to identify and interpret rare patterns holds significant promise for advancing medical analytics and improving patient outcomes. Moreover, the applicability of EPFHD-RARMING extends beyond the healthcare domain, offering valuable insights in various fields where the discovery of rare patterns is critical, such as finance, marketing, and cybersecurity. This study conducts a comprehensive evaluation, which demonstrates the superior performance of EPFHD-RARMING compared to traditional predictive models in identifying key factors contributing to heart disease, in terms of interestingness, explainability, and comprehensiveness of insights. The results underscore the potential of this innovative approach to revolutionize our understanding and prediction of heart disease, ultimately contributing to more effective and personalized healthcare solutions. This research emphasizes the importance of rare association rule mining in medical analytics and paves the way for future studies to explore and utilize these techniques across diverse domains.