For many clinical conditions, only a small number of patients experience adverse outcomes. Developing risk stratification algorithms for these conditions typically requires collecting large volumes of data to capture enough positive and negative for training. This process is slow, expensive, and may not be appropriate for new phenomena. In this paper, we explore different anomaly detection approaches to identify high-risk patients as cases that lie in sparse regions of the feature space. We study three broad categories of anomaly detection methods: classification-based, nearest neighbor-based, and clustering-based techniques. When evaluated on data from the National Surgical Quality Improvement Program (NSQIP), these methods were able to successfully identify patients at an elevated risk of mortality and rare morbidities following inpatient surgical procedures.