Abstract: This proposal requests research funding for the development of two papers that propose novel methods for leveraging large amounts of imprecise information along with small amounts of specific information to improve the efficacy of medical treatment. Both papers posit novel strategies to help companies innovate more easily, and show under what conditions it is most economically beneficial to use these strategies. The first paper posits a clinical trial design that leverages information from previous clinical trials in order to more efficiently predict the true impact of a new treatment. The paper also determines under which conditions this design is most useful, and analyzes its performance based on data from Metastatic Breast Cancer clinical trials. The second paper will present a method of combining large amounts of image data from a well-studied population with limited data from a previously under-represented population to more accurately pre-screen the under-represented patient pool, and analyzes its performance when applied to predicting the occurrence of skin cancer. Both papers use adaptive methods that update predictions as more information becomes available.