CHICAGO — Drug overdose deaths rose for the 11th straight year, federal data show, and most of them were accidents involving addictive painkillers despite growing attention to risks from these medicines.

“The big picture is that this is a big problem that has gotten much worse quickly,” said Dr. Thomas Frieden, head of the Centers for Disease Control and Prevention, which gathered and analyzed the data.

In 2010, the CDC reported, there were 38,329 drug overdose deaths nationwide. Medicines, mostly prescription drugs, were involved in nearly 60 percent of overdose deaths that year, overshadowing deaths from illicit narcotics.

The report appears in Tuesday’s Journal of the American Medical Association.

It details which drugs were at play in most of the fatalities. As in previous recent years, opioid drugs — which include OxyContin and Vicodin — were the biggest problem, contributing to 3 out of 4 medication overdose deaths.

Frieden said many doctors and patients don’t realize how addictive these drugs can be, and that they’re too often prescribed for pain that can be managed with less risky drugs.

Medication-related deaths accounted for 22,134 of the drug overdose deaths in 2010.

Anti-anxiety drugs including Valium were among common causes of medication-related deaths, involved in almost 30 percent of them. Among the medication-related deaths, 17 percent were suicides.