Well im pretty sure there are other ways to help with your depression. I find talking to my friends and listening to music a great way to cope with depression.
My kitties are perfect. All I have to do it make eye contact with my kitten and he purrs so hard I can see him vibrate from across the room. If that didn't make me happy, then I don't deserve that little bundle of happiness
One could also argue that it'd be more difficult to kill oneself if you knew you were going to leave your best buddy without you. Dogs are better people than humans most of the time.
These are all things that people find effective. It is also true that pets serve as a protective factor against suicide. Source: My Ph.D. In clinical psychology and current work with mood disorders and suicide prevention. {Sorry, when I see people casually talking about this stuff, I can turn into a bit of a dick. No offense meant. And yes, I know what I wrote sounds a bit arrogant :)} Though characterizing these as the "most" effective is not necessarily true.
Welp, Ima just deal with depression then.