There's an entire, and fascinating, book on psychosomatic illnesses that goes into this topic called It's All in Your Head by Suzanne O'Sullivan, an Irish neurologist.

Most people seem to write off psychosomatic illnesses as they don't fit into their models of how the world should work, but their existence and ways to resolve them are well documented and doctors frequently find psychological or neurological ways to resolve or alleviate them (e.g. prescribing antidepressants to chronic pain sufferers).

The book also goes into how cancer can, in some circumstances, be hugely affected by the mental outlook of the patient, but for some reason this continues to be controversial in a way that 'dying of a broken heart' is not.