WASHINGTON -- Defense Department health care providers do a good job of screening for suicide risk, but they fail to provide critical and effective follow-up treatment to servicemembers identified as suicidal, according to a Rand Corp. report released Monday.

Rand researchers found appropriate follow-up care was given to only 30 percent of servicemembers with depression and 54 percent of servicemembers with post-traumatic stress disorder who were at risk of suicide. The rest did not receive follow-up care or got medication and psychotherapy that has not been proven to help.

The report is based on observations of nearly 39,000 servicemembers with diagnosed PTSD or depression over a one-year period. It's one of the largest evaluations of military mental health care, said Kimberly Hepner, a behavioral scientist and the lead researcher.

"The military health system did quite well in screening for suicide risk," Hepner said. "Where we found they could do better was how the providers responded to servicemembers with suicide risk identified."

The Pentagon asked Rand for an independent report on the care it provides to servicemembers with PTSD and depression.

It's difficult to know how many active-duty servicemembers suffer from PTSD or depression, Hepner said. The report cites between 4 and 20 percent of the more than 2.6 million people who deployed to Afghanistan or Iraq during Operation Enduring Freedom or Operation Iraqi Freedom.

The Department of Veterans Affairs analyzed millions of veterans' records and reported last year an average of 20 veterans died from suicide each day in 2014. While veterans made up about 8.5 percent of the U.S. population in 2014, they accounted for 18 percent of suicides.

Capt. Mike Colston, a psychiatrist and director of Mental Health Programs for the Office of Health Affairs, said the Military Health System has grown exponentially since 9/11, in numbers of providers and patients. Pentagon officials first asked for the review in 2012, he said.

"You don't want to engage an intervention without measuring it," Colston said. "They thought, 'Let's get a real nuts-and-bolts measurement of how we're doing.'"