Measuring Circulating Tumor Deoxyribonucleic Acid Tumor Fraction to Guide Early 177Lu-PSMA-617 Treatment Discontinuation in Patients With Metastatic Castration-Resistant Prostate Cancer, DYNAMO Trial

Inclusion Criteria: * Willing and able to provide informed consent * Adult males ≥ 18 years age * History of histologically confirmed adenocarcinoma of the prostate without evidence of neuroendocrine or small cell differentiation. If histology is not available, patients must have metastatic disease typical of prostate cancer (i.e., involving bone or pelvic lymph nodes or para-aortic lymph nodes) * Evidence of metastatic disease on bone scan or CT scan * Patient must have evidence of castration- resistant prostate cancer as evidenced by PSA progression (per Prostate Cancer Working Group 3 \[PCWG3\] criteria) and a castrate serum testosterone level (i.e., ≤ 50 mg/dL) * Serum/plasma PSA progression defined as 2 consecutive increases in PSA over a previous reference value measured at least 1 week prior. The minimal start value is 2.0 ng/mL * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Prior treatment and progression on at least one androgen receptor pathway inhibitor (ARPI), in either castration-sensitive or castration-resistant setting * Eligible for treatment with either 177Lu-PSMA-617 or docetaxel as per their respective Food and Drug Administration (FDA) labels * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Platelet count ≥ 100 x 10\^9/L * Hemoglobin ≥ 9 g/dL * Creatinine clearance ≥ 50 ml/min (calculated by Cockcroft-Gault formula) * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) except for patients with known Gilbert's syndrome (direct bilirubin ≤ 1.5 x ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN, unless liver metastases are present in which case they must be ≤ 5 x ULN. For patients with known Gilbert's Syndrome they must be ≤ 3 x ULN * Able to comply with study requirements including provision of peripheral blood samples at specified time points for correlative studies Exclusion Criteria: * Evidence of serious and/or unstable pre-existing medical, psychiatric or other condition that could interfere with patient safety or provision of informed consent to participate in this study * Evidence of metastatic neuroendocrine/small cell prostate cancer (NEPC). Note: baseline biopsy is not required * Patients receiving any systemic therapy (aside from a luteinizing hormone-releasing hormone \[LHRH\] analogue) or radiotherapy within 2 weeks prior to study treatment * Persistent toxicities (CTCAE grade \> 2) from prior cancer therapy, excluding alopecia and stable neuropathy * Patients considered a poor medical risk due to a serious, uncontrolled medical disorder or active, uncontrolled infection. Examples include, but are not limited to uncontrolled seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining informed consent * Patients who are known to be serologically positive for human immunodeficiency virus (HIV) and a CD4 count \< 200 * Patients with known active hepatitis (i.e. hepatitis B or C). Prior hepatitis C infection is allowed as long as polymerase chain reaction (PCR) is negative * Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery * Serious cardiac disorder, including but not limited to uncontrolled ventricular arrhythmia, recent (within 12 months) myocardial infarction, resting electrocardiogram (ECG) indicating Fridericia's corrected QT interval prolongation \> 500ms, or congenital long QT syndrome * Prior systemic chemotherapy with taxane chemotherapy, including in hormone sensitive setting (e.g. docetaxel or cabazitaxel) * Brain metastases or active epidural disease (treated epidural disease is permitted) * Note: baseline brain imaging is not required * Contraindication to prednisone therapy including poorly controlled diabetes mellitus