I'm not sure about studies, but many cancer patients go on a very strict keto (very low carb (sugar), moderate protein and high fat) diet in hopes of shrinking the cancer tumors. Being on a keto diet will cause your body to switch from using glucose as a fuel source to using ketones. It's also a diet used for epilepsy treatment and by diabetics who have claimed to reverse their diabetes by staying on the diet.

This research seems to suggest their experience isn't just anecdotal.