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Many disease processes are extremely complex and characterized by multiple stochastic processes interacting simultaneously. Current analytical approaches have included mechanistic models and machine learning (ML), which are often treated as orthogonal viewpoints. However, to facilitate truly personalized medicine, new perspectives may be required. This paper reviews the use of both mechanistic models and ML in healthcare as well as emerging hybrid methods, which are an exciting and promising approach for biologically based, yet data-driven advanced intelligent systems.