A clinical research study for patients whose prostate cancer has not spread beyond the prostate is now enrolling. Aragon Pharmaceuticals is seeking men to participate in a clinical trial of an investigational drug for prostate cancer. The purpose of the SPARTAN study is to evaluate the safety and effectiveness of an investigational drug in delaying prostate cancer from spreading beyond the prostate. This study is enrolling patients with prostate cancer who, despite treatment, have rising blood prostate-specific antigen (PSA) levels. All participants will continue to receive their current treatment along with either the investigational medication or a placebo. The selections will be random, and the investigational medication will be given to 2 out of every 3 study participants.