I found this human study (most of the ones I've seen are on animals or on other types of cancer). The government is doing another Keto/PCa one but results aren't expected until spring 2021.
pubmed.ncbi.nlm.nih.gov/321...
The study conclusion was that Keto was safe and the subjects lost a lot of weight on the diet vs. the control subjects ("normal" diet). The study was terminated because of "futility". However, a post hoc study that accounted for some variables concluded that "PSADT was significantly longer in LCD versus control (28 vs. 13 months, P = 0.021) arms."
I'm considering doing 4-6 weeks of my normal Mediterranean diet followed by a couple of weeks of Keto. Pain though because the Keto flu isn't fun and lasts a few days.