We show how the analysis of very large amounts of drug prescription data make it possible to detect, on the day of hospital admission, patients at risk of developing complications during their hospital stay. We explore, for the first time, to which extent volume and variety of big prescription data help in constructing predictive models for the automatic detection of at-risk profiles. Our methodology is designed to validate our claims that: (1) drug prescription data on the day of admission contain rich information about the patient's situation and perspectives of evolution, and (2) the various perspectives of big medical data (such as veracity, volume, variety) help in extracting this information. We build binary classification models to identify at-risk patient profiles. We use a distributed architecture to ensure scalability of model construction with large volumes of medical records and clinical data. We report on practical experiments with real data of millions of patients and hundreds of hospitals. We demonstrate how the fine-grained analysis of such big data can improve the detection of at-risk patients, making it possible to construct more accurate predictive models that significantly benefit from volume and variety, while satisfying important criteria to be deployed in hospitals.