We introduce a new approach for topic modeling that is supervised by survival analysis. Specifically, we build on recent work on unsupervised topic modeling with so-called anchor words by providing supervision through an elastic-net regularized Cox proportional hazards model. In short, an anchor word being present in a document provides strong indication that the document is partially about a specific topic. For example, by seeing "gallstones" in a document, we are fairly certain that the document is partially about medicine. Our proposed method alternates between learning a topic model and learning a survival model to find a local minimum of a block convex optimization problem. We apply our proposed approach to predicting how long patients with pancreatitis admitted to an intensive care unit (ICU) will stay in the ICU. Our approach is as accurate as the best of a variety of baselines while being more interpretable than any of the baselines.