This study explores the integration of Differential Privacy (DP) in healthcare analytics, particularly focusing on enhancing data privacy in Machine Learning (ML) applications. We examine the effectiveness of differential private ML in managing sensitive medical data and the trade-offs between privacy and model performance. We use data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to develop a predictive ML model that classify patients into different stages in the progression of Alzheimer’s disease whilst maintaining privacy in patient data. We contribute to growing literature of healthcare analytics and privacy by demonstrating the feasibility of implementing privacy preserving models on healthcare data whilst maintaining an acceptable prediction accuracy. We anticipate that our findings will help boost clinician trust in ML-based DSSs and subsequently promote their adoption in medical practices. Our research emphasizes the importance of balancing data utility and privacy in healthcare, offering insights for policymaking, clinical practices, and future technological advancements in health information systems.