This is one of medicine's major problems: such a study is considered to be required, yet no one with enough funds (read: big pharma) will execute a study of the enormous size required to control for all these variables (because there is nothing to be gained for them). For all we know, every mental illness is cured in 80% of the cases by changing to -- and adhering to -- a healthy lifestyle. As the situation is, there will never be a study that proves it.