Most existing algorithms for clinical risk stratification rely on labeled training data. Collecting this data is challenging for clinical conditions where only a small percentage of patients experience adverse outcomes. We propose an unsupervised anomaly detection approach to risk stratify patients without the need of positively and negatively labeled training examples. High-risk patients are identified without any expert knowledge using a minimum enclosing ball to find cases that lie in sparse regions of the feature space. When evaluated on data from patients admitted with acute coronary syndrome and on patients undergoing inpatient surgical procedures, our approach successfully identified individuals at increased risk of adverse endpoints in both populations. In some cases, unsupervised anomaly detection outperformed other machine learning methods that used additional knowledge in the form of labeled examples.