As a physician who treats a lot of prostate cancer patients, I think I am qualified to answer this question

Let’s start from what we know:

Joe Biden has a Stage 4 (metastatic into bones), high Grade (Gleason 9 score), castrate sensitive (he hasn’t received androgen deprivation yet) adenocarcinoma of the prostate.

it is very treatable and he will get an immediate response

The initial treatment will always involve androgen deprivation therapy which essentially means injecting a substance like leuprolide to eliminate testosterone out of his bloodstream. This treatment may be augmented by an oral anti-androgen therapy like Xtandi or Zytiga to improve outcomes.

Biden will likely not get any type of surgery due to his advanced age and metastatic condition. Radiation therapy may be recommended to treat either the primary site of malignancy (prostate) and/or metastatic sites as an adjunct to the systemic treatment of adrogen deprivation. This will depend on several factors including voiding symptoms.

How long does he have to live? I hate making those type of predictions because everyone responds differently with treatment based on the tumor genetics and overall health of the patient. However, it is reasonable to expect at least 5 years life expectancy given the state of the art treatment that he will receive.

Another issue is that some of the treatments may affect his cognitive function which appears to be already impaired.