I have had cats and the neighbors have cats - and I have rats. BIG rats. Norweign Roof Rats that no cat would dare mess with - unless it was a mane coon cat or another huge hunter cat. I had a Siamese who used to kill and eat them - but that was years ago and she was taught how to kill them. My dog will kill them if she can catch them - but she has to shake the big ones to kill them before they bite her. Regular puddy cats run for the hills when these things come out - I had one I caught by the face in the big tomcat rat traps and when I went to dispose of it my mother saw it from a distance and wanted to know what happened to that poor kitty... it was probably 18" long (without the tail) and I would guess about 2 lbs...
If you have warf rats you will need to get a ratter dog - or a really big cat... those things are nasty too and will gang up and kill cats.