More Americans than ever before own firearms for protection, but the percentage of people who undergo formal training on how to use their weapons has flatlined, a new paper published in the journal Injury Prevention shows.

The research, conducted by Ali Rowhani-Rahbar and Vivian Lyons, epidemiologists at the University of Washington, along with public health experts at Northeastern and Harvard, finds that 61 percent of all gun owners reported receiving formal firearms training. The researchers say this a statistically insignificant increase over the 56 to 58 percent of gun owners who reported receiving training in 1994, the last time a comparable survey was conducted.

Of gun owners who said they own a handgun for the sole purpose of protection, 57 percent said they had received formal training. Only 14 percent of those who live with a gun owner, but who do not own guns themselves, have received safety training, which the authors say is a troubling finding considering how often accidental shootings or suicides involve guns that belong to a parent, spouse, or roommate.

“Despite the presence of training programs all around the country, it looks like they are not reaching a larger fraction of gun owners than they were 20 years ago,” said Rowhani-Rahbar. “I was surprised to see that.”

The researchers based their analysis on data from the National Firearms Survey, considered the first nationally representative investigation in more than two decades into how and why Americans keep weapons. The survey was conducted online in 2015 on behalf of a research team from Harvard and Northeastern universities by GfK, a market-research company. It surveyed nearly 4,000 Americans and oversampled for veterans and gun owners.

The survey asked respondents if they had received formal firearms training on safe handling and storage; accident or theft prevention; and the risk of suicide.

Just 15 percent of gun owners said they had received any training or materials that addressed suicide — even though roughly two-thirds of all gun deaths in the United States are self-inflicted.

Training requirements for gun owners are overwhelmingly popular. More than 80 percent of respondents said they agree or strongly agree that individuals should undergo training before owning their first firearm. (This finding is consistent with other surveys.) However, only seven states impose their own training requirements on firearms buyers.

The most-trained gun owners in America, statistically speaking, are people with concealed-carry permits. Eighty-three percent have undergone some formal training, the survey found.

But there’s a movement underway to eliminate permitting requirements altogether for carrying concealed weapons in public. Twelve states have lifted that obligation, including, this year, North Dakota and New Hampshire. The National Rifle Association has endorsed this effort — one article on the gun group’s website describes the wave of permitless carry bills as a “revolution” — even though the organization is often involved in conducting training for concealed-carry permits.

There’s evidence that as more states make permits optional, the number of residents who actually apply for them — and receive training in the process — declines. Kansas, for example, enacted permitless-carry legislation in 2015. Last week, the state’s attorney general’s office said that, in the fiscal year ending June 30, it had received only 5,119 applications for concealed-carry permits, the lowest number in more than a decade. A similar trend is apparent in Missouri, a state that dropped its training requirement earlier this year. According to local news reports, permit applications in some counties have fallen as much as 80 percent.

“I understand the politics of permitless carry, but it’s really a missed opportunity from the public-health perspective,” Rowhani-Rabhar said. “Training could have profound implications for reducing injury or death, especially suicide. Training could help reduce gun theft, and thus firearms-related crime.”