177 LuPSMA-617 vs Docetaxel in Metastatic Castration Resistant and PSMA-Positive Prostate Cancer

Inclusion Criteria: * Histological evidence of prostate cancer with no evidence of small cell component * Patients must have castration resistance and metastatic disease with evidence of biochemical or imaging progression in the setting of surgical/medical castration * Progression on treatment with abiraterone and/or enzalutamide, or similar next-generation androgen receptor (AR) targeted therapy * Evidence of PSMA positive metastatic disease, as assessed on PSMA-PET imaging studies obtained as part of other clinical trial protocols are mandated, provided they are obtained within a timeframe that meets the requirements of this study. The radiopharmaceuticals must be based on a lysine-urea-glutamate backbone, with a 18F or 68Ga radionuclide label. * Prior orchiectomy, or if on LHRH agonist/antagonist then testosterone \< 1.7 nmol/L * Adequate organ function * Recover from all previous cancer treatment toxicities to grade ≤ 2 (as per CTCAE v5.0) * Male subject ≥ 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 Exclusion Criteria: * Prior treatment with chemotherapy for castration-resistant disease or prior chemotherapy in the castration-sensitive (hormone-sensitive) setting ≤ 1 year prior to enrollment. * Prior treatment with 177Lu-PSMA (including other radiolabeled therapeutic PSMA-ligands) or radio-immunotherapy. Prior treatment with radium-223 is allowed but requires a minimum of a 6-month interval between the last dose of radium-223 and enrollment. * Radiotherapy to target lesions (measurable disease) ≤ 12 weeks prior to enrolment. * Presence of majority (\> 50% of extra-osseous lesions) or large (\> 5 cm) soft tissue lesions that are negative on PSMA-Ligand PET/CT or PSMA-Ligand PET/MR * Known parenchymal brain metastases * Active epidural disease (treated epidural disease is permitted) * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Clinically significant cardiac disease * Major surgery within 4 weeks of starting study treatment * Patients with a history of hypersensitivity to the study drug or components * Patients with a clinically significant medical condition which, in the opinion of the treating physician, makes it undesirable for the patient to participate in the study or which could jeopardize compliance with study requirements including, but not limited to: ongoing or active infection, significant uncontrolled hypertension, or sever psychiatric illness/social situations.