Medical Cyber-physical Systems (MCPS) are vulnerable to accidental or malicious faults that can target their controllers and cause safety hazards and harm to patients. This paper proposes a combined model and data-driven approach for designing context-aware monitors that can detect early signs of hazards and mitigate them in MCPS. We present a framework for formal specification of unsafe system context using Signal Temporal Logic (STL) combined with an optimization method for patient-specific refinement of STL formulas based on real or simulated faulty data from the closed-loop system for the generation of monitor logic. We evaluate our approach in simulation using two state-of-the-art closed-loop Artificial Pancreas Systems (APS). The results show the context-aware monitor achieves up to 1.4 times increase in average hazard prediction accuracy (F1-score) over several baseline monitors, reduces false-positive and false-negative rates, and enables hazard mitigation with a 54% success rate while decreasing the average risk for patients.