Two major data mining competitions in 2008 presented challenges in medical domains: KDD Cup 2008, which concerned cancer detection from mammography data; and Informs Data Mining Challenge 2008, dealing with diagnosis of pneumonia based on patient information from hospital files. Our team won both of these competitions, and in this paper we share our lessons learned and insights. We emphasize the aspects that pertain to the general practice and methodology of medical data mining, rather than to the specifics of each modeling competition. We concentrate on three topics: information leakage, its effect on competitions and proof-of-concept projects; consideration of real-life model performance measures in model construction and evaluation; and relational learning approaches to medical data mining tasks.