Passersby write messages to sexual assault victims during an event held at UCLA in 2015 to pay respect to students who have experienced sexual violence. (Evelyn Hockstein for The Washington Post)

Startled by data suggesting that sexual assault is common and underreported on campuses across the country, university leaders have increased staffing, training and support for students in recent years, according to a new survey of leading universities.

Schools have increased spending and hiring to combat sexual assault on campus, the survey found, adding an average of five new full-time employees in the past few years. At the University of Virginia, those efforts have cost $1.6 million since 2014.

That’s just one sign of what the Association of American Universities says is a sweeping response by top schools.

The AAU report, released Wednesday, comes in the early months of the Trump administration. Some have wondered how the new president and Education Secretary Betsy DeVos will handle campus sexual assault.

Two years ago, a landmark AAU survey found that more than 20 percent of female undergraduates were victims of sexual assault or misconduct, a report that many university leaders called alarming and a call to action. Some 150,000 students at 27 schools, including most of the Ivy League, had responded to the survey, providing extensive data on the scope of a problem that activists had been demanding be confronted head-on.

That data compounded the sense of urgency that scrutiny from the Obama administration and student activists had brought to the issue. Under President Barack Obama, the Education Department conducted hundreds of investigations of colleges for their handling of sexual violence complaints. And universities responded, with town hall meetings, new classes, skits for incoming freshmen, complete overhauls of their policies around the issue and more.

It was a big wake-up call, said Mary Sue Coleman, president of the AAU. “We understood the problem in a way we didn’t before,” she told The Washington Post. The AAU is a group of 62 prominent research universities in the United States and Canada.

The new report details the scope of that response, with an array of efforts aimed at improving education, prevention, investigations and support for students affected. All of the 55 universities surveyed added training as well as efforts to better support victims of sexual misconduct. The vast majority worked to improve and streamline the way complaints are handled, sharing information confidentially across departments.

“There is no magic bullet,” the report concludes, “or one-size-fits-all approach: universities have undertaken a wide variety of actions including increased and targeted training, greater awareness-building, better coordinated data collection, . . . and greater levels of collaboration within institutions and their communities.”

One of the biggest changes, several university presidents said Tuesday, was the response from students: At the University of Wisconsin at Madison, Chancellor Rebecca Blank said that more than 200 students in the Greek community voluntarily convened around the issue, crafting a set of bylaws for their own organizations to require training and oversight, and designating people to look for ways to minimize risk.

“If anything will make a difference, it’s not what I or other people around this table say about this,” Blank said. “It’s what students say to each other.”

David Leebron, president of Rice University, noted that students had helped design a mandatory course on the issue.

“There has been a transition from the question of ‘What are you going to do about this?’ to ‘What can we do about it?’ ” Leebron said.

One “critical area” that the AAU report indicates universities are dedicating more attention to is bystander-intervention training, or making sure students, staff and others in the academic community know how to step in when situations seem troubling.

Carol Folt, chancellor of the University of North Carolina at Chapel Hill, compared bystander-intervention training to the impact the idea of “designated drivers” had on the way people planned for parties. Students who might have looked the other way in the past now see it as admirable to intervene if needed. “That is a very large cultural shift we’re seeing,” Folt said.

Among other findings in the report:

●Since 2013, all of the schools that responded had surveyed their students on sexual assault and misconduct issues at least one time.

●In the past three academic years, all the schools that responded had changed or are working to change their education and training, aimed at the student body and faculty members.

●S. Daniel Carter of the advocacy group SurvJustice said the survey was a reflection of many of the changes he has seen in recent years, including greater efforts by individual schools to document the scope of the problem. He said he was troubled, though, that the report did not pay more attention to disciplinary procedures.

Folt and others said adjudication of sexual assault allegations remained a challenge for institutions — and one with no easy answers. Campuses must deal with privacy concerns and consider disclosure, they explained, and try to find a balance.

Several university presidents said they think sexual assault prevention efforts will be lasting no matter what shifts may occur in federal policy.

“This has been institutionalized as an issue on campus,” Leebron said.