Study of Olaparib Maintenance Following Cabazitaxel-Carbo in Men With AVPC

Study Groups: If you are found to be eligible to take part in this study, you will be randomly assigned (as in a roll of dice) to 1 of 2 study groups. This is done because no one knows if one study group is better, the same, or worse than the other group. You will have a 2 in 3 chance of being assigned to Group 1 and a 1 in 3 chance of being assigned to Group 2: * If you are in Group 1, you will receive olaparib. * If you are in Group 2, you will not receive olaparib. All participants will receive cabazitaxel and carboplatin. You and the study staff will know to which group you have been assigned. Study Drug Administration: Each study cycle is 21 days. You will receive cabazitaxel by vein over 60 minutes on Day 1 of Cycles 1-6. You will then receive carboplatin by vein over 60 minutes on Day 1 of Cycles 1-6. You will take 1 tablet of prednisone by mouth 2 times each day of Cycles 1-6. You will be given standard drugs to help decrease the risk of side effects (for example, filgrastim) before and/or after each dose of cabazitaxel and continuing through several days. Your doctor will describe these drugs to you in more detail, including how they are given and any side effects you may expect. If you are in Group 1, you will take tablets of olaparib 2 times by mouth each day starting on Day 1 of Cycle 7. Swallow the whole tablet or tablets. Do not chew, crush, divide, or dissolve the tablets. If you vomit shortly after taking your olaparib tablet you can retake a new dose as long as you can see that the tablet came out whole. You should take the doses at the same time each day (or within 2 hours of the scheduled times). Do not take the dose if you forget and it is more than 2 hours since your scheduled time. Take olaparib at least 1 hour after and 2 hours before eating. If you are in Group 2, you will receive standard of care treatment and follow-up after Cycle 6. The study doctor will tell you more about what this may mean for you. Length of Treatment: You will receive carboplatin and cabazitaxel for up to 6 cycles. If you are in Group 1, you may continue receiving olaparib for as long as the doctor thinks it is in your best interest. You may no longer be able to take the study drugs if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over after the follow-up visits. Study Visits: On Day 1 of Cycles 1-6: * You will have a physical exam. * Blood (up to 5 tablespoons) will be drawn for routine tests, biomarker testing, tumor marker testing, and to measure your PSA level. At some of these visits, this sample will also be used for CTC testing. You must fast for up to 12 hours before the Cycle 4 visit. * Urine will be collected for tumor marker testing. * At Cycle 4 only, you will have a bone scan and either MRIs or CT scans to check the status of the disease. After Cycle 6, you will have a second tumor biopsy for biomarker testing to compare to the one taken at screening. The type of biopsy you have will depend on where the disease has spread and/or what the doctor thinks is in your best interest. The doctor will discuss with you the type of biopsy you will have. On Day 1 of Cycle 7: * Blood (up to 5 tablespoons) will be drawn to check your testosterone levels, biomarker testing, and for tumor marker testing. * You will have an EKG. * You will have a bone scan and either MRIs or CT scans. On Day 1 of Cycles 8-10: * You will have a physical exam. * Blood (up to 5 tablespoons) will be drawn for routine tests, tumor marker testing, biomarker testing, and to measure your PSA level. At some of these visits, this sample will also be used for CTC testing. * Urine will be collected for tumor marker testing. After Cycle 10, you will only have study visits every 3 cycles. Beginning on Day 1 of Cycle 13, every 3 cycles (Cycles 13, 16, 19, and so on): * You will have a physical exam. * Blood (up to 5 tablespoons) will be drawn for routine tests, tumor marker testing, biomarker testing, and to measure your PSA level. At some of these visits, this sample will also be used for CTC testing. You must fast for up to 12 hours before the visits at Cycle 10 and every 3 cycles after that. * Urine will be collected for tumor marker testing. * You will have a bone scan and either MRIs or CT scans to check the status of the disease. * You will have an EKG. If you have severe side effects, you may return to the clinic more often so the study doctor can check on your health. End of Study Visit: When you leave the study, the following tests and procedures will be performed: * You will have a physical exam. * You will have a bone scan and either MRIs or CT scans to check the status of the disease. * You will have an EKG. * Blood (about 3 tablespoons) will be drawn for routine tests, tumor marker testing, and to measure your PSA level. You must fast for up to 12 hours before this visit. * Urine will be collected for tumor marker testing. Follow-Up: About every 6 months after the end-of-study visit, the study staff will check your health. This will be done either by a chart review or a phone call. If you are called, this call will last about 5 minutes. These calls will stop if you withdraw from the study.