I am sure that professionals do the best that they can. I see that you put several caveats in there. My question was not about the responsibilities of the professionals though it was simply about a statistical comparison of mass murderers who were under care vs. mass murderers who were not.
There are probably not enough mass murderers to run a statistically significant “large-N” study, especially after all the haggling that would take place about definitions (many types of mass murderers, you know) and exclusionary criteria. And then there is the usual need to run multiple independent studies before anything can be said with any certainty, and then a chorus of critics who will point to the need for prospective (rather than retrospective) double-blind studies that use sham/placebo therapy, in order to say anything with confidence about the preventive value of various treatments.
Hopefully, after a hundred years of ObamaCare and police-state totalitarianism, the NSA will have collected enough data on every citizen to be able to answer your question, though.