Durvalumab With or Without Tremelimumab in Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: * Patients must have histologically confirmed adenocarcinoma of the prostate that is castrate resistant. * Disease progression as defined as one or both of the following: PSA Progression: A rising PSA with 2 subsequent rises over a reference value (not necessarily consecutively), measured a minimum of one week apart. The PSA that confirms progression must have a value of ≥ 2 ng/ml (ug/L). OR Objective Progression: * RECIST 1.1 * PCWG 3 Criteria for bone progression * Patients must be surgically or medically castrated, with testosterone levels of \< 50 ng/dL (\< 1.7 nM). Patients who have not undergone orchiectomy must continue (or restart if previously discontinued) LHRH therapy throughout the study. * All patients must have a tumour block from their primary or metastatic tumour available and consent to release the block/recently cut slides for correlative analyses and the centre/pathologist must have agreed to the submission of the specimen(s). The site of planned biopsy must not be the measurable lesion. * Presence of clinically and/or radiologically documented disease. All radiology studies must be performed within 28 days prior to randomization (within 35 days if negative). * All patients must have at least one measurable lesion as defined by RECIST 1.1 that has not been the site of the protocol mandated biopsy. The criteria for defining measurable disease are as follows: CT scan (with slice thickness of 5 mm) ≥ 10 mm --\> longest diameter; Lymph nodes by CT scan ≥ 15 mm --\> measured in short axis * Patients must be ≥ 18 years of age. * ECOG performance status 0 or 1. * Prior Therapy Systemic Therapy: 0-1 prior regimen of cytotoxic chemotherapy in the CRPC setting is permitted. Hormonal Therapy: * Patients must be castrate resistant. * Have failed/progressed on prior abiraterone and/or enzalutamide. * Patients must have discontinued anti-androgens for at least 4 weeks prior to study entry (at least 6 weeks for bicalutamide). Other therapy: Prior treatment with other agents, such as tyrosine kinase or other targeted agents is permissible. * Systemic corticosteroids are permitted at a dose equivalent to ≤10 mg prednisone daily and are only permitted for reasons other than prostate cancer treatment (ex: fatigue, anorexia, etc); topical applications (e.g. rash), inhaled sprays (e.g. obstructive airways diseases), eye drops or local injections (e.g. intra-articular) are permitted. * Bisphosphonates/denosumab are permitted for treatment of hypercalcemia, osteoporosis and skeletal-related events. Immunotherapy: Patients may not have received prior immune check point inhibitors (anti PDL1 and anti CTL-4). Vaccines and treatment with oncolytic viruses is permissible. Patients must have recovered from all reversible toxicity related to prior systemic therapy (chemotherapy and hormone) and have adequate washout as follows: Longest of one of the following: * Two weeks; * The longer of 30 days or 5 half-lives for investigational agents; * Standard cycle length of standard therapies. Radiation: Prior external beam radiation or radium-223 is permitted provided a minimum of 28 days (4 weeks) have elapsed between the last dose of radiation and the date of randomization. Exceptions may be made for low-dose non-myelosuppressive radiotherapy after consultation with CCTG. Concurrent radiotherapy is not permitted. Prior strontium-89 at any time is not permitted Prior Surgery: Prior major surgery is permitted provided that a minimum of 28 days (4 weeks) have elapsed between any major surgery and date of randomization, and that wound healing has occurred. * Laboratory Requirements (Must be done within 7 days prior to randomization): Abs Neutrophils ≥ 1.5 x 10\^9/L Platelets ≥ 100 x 10\^9/L Hemoglobin ≥ 90 g/L Bilirubin ≤ 1.5 x ULN AST and ALT ≤ 2.5 x ULN ≤ 5.0 ULN (if patient has liver mets) Serum Creatinine \< 1.25 x ULN or Creatinine clearance ≥ 40mL/min * Non-sterilized male patients who are sexually active with a female partner of childbearing potential must use male condom plus spermicide while on study and for 6 months after the last dose of durvalumab and tremelimumab, or for 3 months after the last dose of durvalumab alone. Female partners of a male subject must use a highly effective method of contraception throughout this period. * Male patients should also refrain from donating sperm during the study and for 6 months after the last dose of durvalumab and tremelimumab or for 3 months after the last dose of durvalumab alone. * Subjects should not donate blood while participating in this study, or for at least 90 days following the last infusion of durvalumab or tremelimumab. * Patient consent must be appropriately obtained in accordance with applicable local and regulatory requirements. Each patient must sign a consent form prior to enrollment in the trial to document their willingness to participate. Patients who cannot give informed consent (i.e. mentally incompetent patients, or those physically incapacitated such as comatose patients) are not to be recruited into the study. Patients competent but physically unable to sign the consent form may have the document signed by their nearest relative or legal guardian. Each patient will be provided with a full explanation of the study before consent is requested. * Patients must be accessible for treatment and follow up. Patients registered on this trial must be treated and followed at the participating centre. This implies there must be reasonable geographical limits (for example: 1 ½ hour's driving distance) placed on patients being considered for this trial. The patient's city of residence may be required to verify their geographical proximity. Investigators must assure themselves the patients registered on this trial will be available for complete documentation of the tretment, adverse events, and follow-up. * Patients must agree to return to their primary care facility for any adverse events which may occur through the course of the trial. * In accordance with CCTG policy, protocol treatment is to begin within 5 working days of patient randomization. Exclusion Criteria: * Patients with a history of other malignancies requiring concurrent anticancer therapy. * Patients with brain metastases are not eligible. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease (e.g. colitis or Crohn's disease), diverticulitis with the exception of diverticulosis, celiac disease or other serious gastrointestinal chronic conditions associated with diarrhea), systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome (granulomatosis with polyangiitis), rheumatoid arthritis, hypophysitis, uveitis, etc., within the past 3 years prior to the start of treatment. The following are exceptions to this criterion: * Patients with alopecia. * Patients with Grave's disease, vitiligo or psoriasis not requiring systemic treatment (within the last 2 years). * Patients with hypothyroidism (e.g. following Hashimoto syndrome) stable on hormone replacement. * History of primary immunodeficiency, history of allogenic organ transplant that requires therapeutic immunosuppression and the use of immunosuppressive agents within 28 days of randomization or a prior history of severe (grade 3 or 4) immune mediated toxicity from other immune therapy or grade ≥ 3 infusion reaction. * Live attenuated vaccination administered within 30 days prior to randomization or within 30 days of receiving durvalumab. * History of hypersensitivity to durvalumab or tremelimumab or any excipient. Any previous treatment with a PD1 or PD-L1 inhibitor, including durvalumab or an anti-CTLA4, including tremelimumab. * Patients who have experienced untreated and/or uncontrolled cardiovascular conditions and/or have symptomatic cardiac dysfunction (unstable angina, congestive heart failure, myocardial infarction within the previous year or cardiac ventricular arrhythmias requiring medication, history of 2nd or 3rd degree atrioventricular conduction defects). Patients with a significant cardiac history, even if controlled, should have a LVEF ≥ 50%. * Concurrent treatment with other investigational drugs or anti-cancer therapy (except LHRH in patients not surgically castrated). * Patients with serious illnesses or medical conditions which would not permit the patient to be managed according to the protocol (including corticosteroid administration), or would put the patient at risk. This includes but is not limited to: * History of significant neurologic or psychiatric disorder which would impair the ability to obtain consent or limit compliance with study requirements. * Active infection requiring systemic therapy; (including any patient known to have active hepatitis B, hepatitis C or human immunodeficiency virus (HIV) or tuberculosis or any infection requiring systemic therapy). * Active peptic ulcer disease or gastritis. * Pneumonitis.