The purpose of this study is to test ways to personalize treatment for patients with prostate cancer that has returned after prostatectomy. The study will assess if the use of PET scans can help identify patients for whom more therapy may lead to better outcomes. All participants will receive the usual treatment (radiation therapy and short-term hormone therapy). In addition:
- Some patients will receive additional PET imaging, depending on the results of their initial PET
- Some patients will also receive a newer type of hormone therapy called apalutamide, which is already approved by the FDA for some prostate cancers
- Some patients, depending on the results of their initial PET scan, will receive metastasis-directed radiation therapy