A new Health Affairs study followed 81,704 adults with schizophrenia, bipolar disorder or depression who were receiving treatment through the public behavioral health systems in two Florida counties to measure the effectiveness of such policies. About 12.8 percent were restricted from purchasing a firearm for mental-health reasons. Federal and state laws prohibit people from obtaining guns if they have been committed for mental-health treatment involuntarily, found not guilty of a crime due to insanity, been found incompetent to stand trial, or deemed mentally unable to manage their affairs.

The study's findings provide a snapshot of gun violence within a population of mentally ill people. Although people with mental illness were more likely to be arrested for violent crime than the general population over the study period, from 2002 to 2011, the study found they actually had a slightly lower arrest rate for gun-related crimes. And although the rate of suicide was about four times higher among people with such mental illnesses, they were half as likely to use a gun as the general population.

What the study can't tell is whether those lower rates were a product of gun control laws aimed at restricting access or might be explained by other factors — for example, poverty.

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The study did find that policies to restrict people from obtaining guns don't seem to be particularly effective — 62 percent of people in the study who committed gun-related violent crimes were not allowed to buy a gun. Those restrictions, however, largely stemmed from their criminal records, not their history of mental illness. Only 3 percent of the violent gun offenders were prohibited because of their mental illness alone. Ten percent were prohibited because of both their criminal record and mental-health history.

More than a quarter of firearm suicides were carried out by people not legally allowed to purchase guns.

There was also a flip side: People who were legally allowed to obtain a gun and went on to commit a violent crime or suicide. If the goal of gun control policy is to prevent people from causing harm to themselves or others, the current criteria seem to have some major gaps. Among those who committed suicide with a gun, 72 percent were allowed to buy them. And 38 percent of the people arrested for violent gun crimes weren't prohibited.

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Together, these results suggest that the quest to restrict access to guns by forecasting which people are likely to use one to cause harm — to themselves or others — needs more fine-tuning.

"We have a long way to go in terms of developing laws that would have more precise criteria for determining who is at risk for gun violence and who should have their guns removed," said Jeffrey Swanson, a professor of psychiatry and behavioral sciences at Duke University School of Medicine. "It also suggests that we need more than one kind of policy. People always ask me, 'What's the one thing we should do?' It’s not a one thing problem."