Leuprolide Acetate or Goserelin Acetate With or Without Vismodegib Followed by Surgery in Treating Patients With Locally Advanced Prostate Cancer

PRIMARY OBJECTIVES: I. To assess the difference in less than or equal to 5% tumor involvement between patients between the two arms. SECONDARY OBJECTIVES: I. To assess differences in hedgehog signaling, androgen signaling, markers linked to high grade prostate cancer (PCa) progression, proliferation, apoptosis, and the expression of androgen producing enzymes in the tumor microenvironment between the two arms. II. To assess safety of preoperative GDC-0449 (vismodegib) in combination with luteinizing hormone-releasing hormone (LHRH). III. To assess the difference in proportion of patients with negative disease surgical margins between the two arms. IV. To collect and archive tissue from the primary tumor, bone marrow and blood (serum, plasma), bone marrow aspirate for future study. V. To assess difference in relapse rate (biochemical, objective) and time to progression. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I (androgen-ablation therapy and vismodegib): Patients receive LHRH analogue comprising leuprolide acetate intramuscularly (IM) or goserelin acetate subcutaneously (SC) on day 1 and vismodegib orally (PO) once daily (QD) on days 1-28. Treatment repeats every 28 days for up to 16 weeks in the absence of disease progression or unacceptable toxicity. ARM II (androgen-ablation therapy): Patients receive LHRH analogue comprising leuprolide acetate or goserelin acetate as in Arm I. Treatment repeats every 28 days for up to 16 weeks in the absence of disease progression or unacceptable toxicity. After completion of study therapy, patients undergo radical prostatectomy. After completion of study therapy, patients are followed up every 6 months for up to 8 years.