(CNN) If there's anything both sides of America's heated and polarizing gun debate may agree on, it's the need to keep firearms out of the hands of people with serious mental illness.

That is not the same as saying gun violence is a mental health issue, which has become a renewed area of contention since President Obama announced new actions earlier this month to reduce gun violence, including increased funding for mental health treatment and enhanced background checks.

Mental health advocates say media reports of mass shootings by disturbed individuals galvanize public attention and reinforce the impression that severe mental illness leads to violence. But various epidemiologic studies over the past two decades show that the vast majority of people with severe mental illnesses, such as schizophrenia, bipolar disorder or severe depression, are never violent toward others.

People with serious mental illness are three times more likely than those who are not mentally ill to commit violent acts again themselves or others, but that is still a very small number of people, about 2.9% of people with serious mental illness within a year. And the impact on gun violence statistics is marginal, amounting to about 4% of all firearm homicides, according to research as recent as last year

When talking about gun deaths from suicide, however, epidemiologists say mental illness legitimately becomes an area of concern. Suicides accounted for 61% of all firearm fatalities in the United States in 2014, or 21,384 of 33,599 gun deaths recorded by the Centers for Disease Control and Prevention.

Finding new indicators of risk

Gun violence and mental illness are public health problems "that intersect at the edges" but have very little overlap, said Jeffrey Swanson, a professor in psychiatry and behavioral sciences at Duke University who specializes in gun violence and mental illness.

It's a phrase that frequently appears in his research and journal articles to emphasize the point that fixing the mental health system is not a silver bullet for reducing gun violence, he said. It takes multiple approaches, many of which have nothing to do with the mentally ill.

"Mental health stakeholders are loath to have this conversation about improving mental health care in a context driven by violence prevention, because that's not why we need mental health reform per se," Swanson said. "We need it because people are struggling with illnesses and they don't have access to care."

Instead of policies that restrict gun access based solely on mental illness diagnoses, or because a person has made contact with the judicial system or health care agencies due to mental illness, the American Psychological Association , the National Alliance on Mental Illness and other advocacy groups have called for criteria based on more subtle indicators of potentially dangerous behavior, largely informed by the work of Swanson and others.

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The difficulty is that policies intended to keep guns away from mentally ill people who are likely to be violent depend on clinicians' ability to accurately identify them.

Research shows that risk prediction, especially for statistically rare events like mass shootings, is an inexact science, "only slightly more accurate than flipping a coin."

How, then, can policymakers strike a balance, and will Obama's executive orders address these concerns?

Identifying "evidence of dangerousness"

Obama put mental health stakeholders in a tough spot when he announced on January 5 new actions to reduce gun violence. He acknowledged the underfunded needs of a struggling population and proposed a $500 million investment toward improving access to care and treatment services.

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But some balked at the inclusion of mental health reform in a bundle of orders aimed at reducing gun violence.

"The mental health community and stakeholders are very concerned about reinforcing the false association in the public's mind between mental illness and violence, because that is a source of a great deal of discrimination," Swanson said.

As Swanson and his colleagues see it, gun ownership restrictions related to mental health are too broad and too narrow all at once. They capture a lot of people because of some contact with the courts or health care system, in some cases minor or a long time ago, who are actually at low risk of perpetrating gun violence. At the same time, they miss people who have yet to be diagnosed, adjudicated mentally ill or involuntarily committed, including people who are suicidal or have pathological anger, he said.

Swanson supports intervention at the point of purchase through comprehensive background checks. But to make background checks work, criteria for inclusion on the database should be based on other indicators of risk besides mental health history, such as pending charges or convictions for violent assault, domestic violence restraining orders or multiple DUIs. These are indicators of aggressive, impulsive or risky behavior, Swanson said.

"Criteria for becoming a prohibited person needs to map onto risk," he said. "We need to mix criteria to make it more about contemporaneous indicators of risk."

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The American Psychiatric Association also recommends firearms restriction based on "evidence of dangerousness."

The APA has called for the development and testing of better methods to identify high-risk individuals who should be denied gun access, implying that current criteria under federal law related to mental illness are inadequate to serve as a basis for gun disqualification. On the other hand, the APA points out in its position statement that while research shows most people diagnosed with serious mental health conditions are never violent toward others, and most violent individuals do not suffer from these major mental disorders, merely having a diagnosis of a psychiatric disorder should not be the only basis for disqualification from firearms.

A number of common mental health conditions -- including personality disorders, post-traumatic stress disorder and alcohol use disorder -- tend to be associated with the risky mix of pathological anger with gun access, according to the APA.

"However, only a small proportion of angry people with guns has ever been hospitalized for a mental health problem -- voluntarily or involuntarily -- and thus most would not be prohibited from firearms under the involuntary commitment exclusion."

Who are the 'pathologically angry'?

To find out the proportion of angry people in the United States who own or carry guns and have a diagnosable mental illness, Swanson and colleagues conducted household surveys with 9,282 people from February 2001 to April 2003, excluding people who carried guns for work, resulting in a response rate of 70.9%.

An analysis of survey results estimated that nearly 1 in 10 adults has access to firearms and also has a problem with anger and impulsive aggressive behavior.

These people were more likely to be male, younger, married, and to live in outlying areas around metropolitan centers rather than in central cities, Swanson and his colleagues wrote in their report.

They were significantly more likely to meet diagnostic criteria for a wide range of mental disorders, including depression, bipolar and anxiety disorders, PTSD, intermittent explosive disorder, pathological gambling, eating disorder, alcohol and illicit drug use disorders, and a range of personality disorders.

What's more, despite evidence of "considerable psychopathology" in many of these respondents, only a very small proportion, 8% to 10%, were ever hospitalized for a mental health problem.

"Because a minority of psychiatric hospitalizations are involuntary, only a small fraction of these respondents could have had a potentially gun-disqualifying involuntary commitment," Swanson and his colleagues said in their report.

Suicide prevention could have the biggest impact

While mass shootings often grab the headlines, the reality is that guns are also used by thousands of individuals to end their own lives, often with little or no media attention.

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Some observers say that talking more about suicides will change the focus of the gun control debate, in part by bringing a new demographic of victims into the discussion. Where often the victims of firearm-related homicide are young black or Hispanic males, nearly 80% of those who use guns to take their own lives are white men, according to the CDC.

Across the population, many studies have shown that suicide risk is substantially higher in persons with mental disorders. And a growing body of research suggests that having guns in the home contributes to increased suicide risk above and beyond other risk factors such as substance abuse, a history of self-harm, hopelessness or depression.

While access to mental health treatment can help alleviate risk factors for suicide, so can keeping guns out of homes of people at risk of using them to harm themselves, epidemiologists say.

Limited research has been conducted in the United States evaluating state gun restrictions on rates of violence and suicide. Swanson and his colleagues noted this in the 2015 Annals of Epidemiology article, " Mental illness and reduction of gun violence and suicide: Bringing epidemiologic research to policy ." But a growing body of research points to similar conclusions regarding the effectiveness of background checks and firearms restrictions.

2011 study of the impact of state firearm regulations from 1995 to 2004 found that gun permit and licensing requirements significantly lowered suicide rates among males. The findings support earlier studies of the effects of the Brady Law , which found that gun background checks and waiting periods significantly reduced suicide in the older population. Another frequently cited study from 1991 looked at the effects of restrictive handgun licensing in the District of Columbia from 1968 to 1987. The study found that a handgun ban signed into law in 1976 was followed by an abrupt decline in gun suicides. No similar reductions were seen in suicides by other means, and no reductions were seen in neighboring jurisdictions that were not subject to the law. There were also no increases in suicides by other means, suggesting that people did not substitute other methods for firearms.

Testing solutions on the state level

State laws restricting access to guns by requiring permits to purchase firearms also show promise for reducing suicide rates. Researchers examined suicide rates in Connecticut and Missouri, two states that recently changed their permit-to-purchase handgun laws in recent decades.

Connecticut passed a law in 1995 that requires people to apply for a permit with local law enforcement and take eight hours of gun safety training before they can buy a firearm. In the 10 years after its passage, the rate of gun-related suicide in Connecticut was 15% lower than what researchers predict it would have been had the law not been passed.

In contrast, Missouri repealed a law in 2007 that required people to apply with the local police for permission to buy a gun. The gun-related suicide rate in Missouri was 16% higher from 2007 to 2011 than researchers predict it would have been, based on the rates in the comparable states of North Carolina and Nebraska.

None of those interventions can do anything about guns already in the home. Researchers are keeping a close eye on the effect of laws in Connecticut, Indiana and California allowing the temporary seizure of guns from people who pose an immediate threat of harm, known as gun violence restraining orders or pre-emptive gun seizure laws. While such policies could help address suicides, researchers hope they will flag so-called "lone wolf terrorists" or "pseudo-commando killers" behind mass shootings who may not be prohibited from owning a gun under current laws.

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Obama's proposed $500 million investment toward improving access to mental health treatment could very well catch the Loughners and the Rodgers out there. Balancing the desire to snag them upstream with the rights enshrined in the Second Amendment will continue to be a challenge for policymakers.

"Recent tragedies have focused attention on the fact that most people with serious mental illness do not have access to mental health treatment," NAMI executive director Michael Fitzpatrick said in an open letter in 2013

"Misguided policies that have the effect of further limiting access to care would be ill-advised and counterproductive to the goal of improving mental health treatment."