A Trial of 177Lu-PSMA617 Theranostic Versus Cabazitaxel in Progressive Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: 1. Male aged 18 or older with metastatic adenocarcinoma of the prostate defined by: * Documented histopathology of prostate adenocarcinoma OR * Metastatic disease typical of prostate cancer (i.e. involving bone or pelvic lymph nodes or para-aortic lymph nodes) 2. Castration-resistant prostate cancer (defined as disease progressing despite castration by orchiectomy or ongoing Luteinizing Hormone-Releasing Hormone (LHRH) analog 3. Progressive disease with rising PSA on 3 consecutive measurements, and PSA ≥ 20 ng/mL 4. Target or non-target lesions according to RECIST 1.1 5. Prior treatment with docetaxel 6. Significant PSMA avidity on 68Ga-PSMA PET/CT, defined as a minimum uptake of SUVmax 20 at a site of disease, and SUVmax \> 10 at sites of measurable disease ≥10mm (unless subject to factors explaining a lower uptake, e.g. respiratory motion, reconstruction artefact) 7. ECOG Performance status 0 to 2 8. Assessed by a medical oncologist as suitable for chemotherapy with cabazitaxel 9. Adequate renal function: • Cr Cl ≥ 40mL/min (Cockcroft-Gault formula) 10. Adequate bone marrow function: * Platelets ≥ 100 x10 billion /L * Hb ≥ 90g/L (no red blood cell transfusion in last 4 weeks) * Neutrophils \> 1.5 x10 billion/L 11. Adequate liver function: * Bilirubin \< 1.5 x upper limit of normal (ULN) (or if bilirubin is between 1.5-2x ULN, must have a normal conjugated bilirubin) * AST or ALT ≤ 2.0 x ULN (or ≤ 5.0 x ULN in the presence of liver metastases) 12. Estimated life expectancy \> 12 weeks 13. Study treatment both planned and able to start within 21 days of randomisation 14. Willing and able to comply with all study requirements, including all treatments (cabazitaxel or Lu-PSMA); and, the timing and nature of all required assessments 15. Signed, written informed consent Exclusion Criteria: 1. Prostate cancer with significant sarcomatoid or spindle cell or neuroendocrine small cell components 2. Site(s) of disease that are FDG positive with minimal PSMA expression defined as FDG intensity \> 68Ga-PSMA activity OR 68Ga-PSMA SUVmax \< 10 3. Sjogren's syndrome 4. Prior treatment with cabazitaxel or Lu-PSMA 5. Contraindications to the use of corticosteroid treatment 6. Active malignancy other than prostate cancer 7. Concurrent illness, including severe infection that may jeopardise the ability of the participant to undergo the procedures outlined in this protocol with reasonable safety 8. Presence of any psychological, familial, sociological or geographical condition potentially hampering compliance with the study protocol and follow-up schedule, including alcohol dependence or drug abuse 9. Patients who are sexually active and not willing/able to use medically acceptable forms of barrier contraception