NEW YORK — More than half of American adults taking prescription drugs misused their medications last year, according to a new study by Quest Diagnostics.

Quest believes that the study, “Prescription Drug Monitoring Report 2016,” is the largest-ever examination of drug misuse based on physician-ordered lab tests. The misuse included potentially dangerous combinations with other drugs.

The multiyear analysis of 3.14 million de-identified test results excluded patients in drug rehabilitation or addiction treatment centers, where unusually high rates of drug misuse can be expected, but did include patients under the care of primary care clinicians or undergoing pain management in 49 states and the District of Columbia between 2011 and 2015.

For the purposes of the study, drug misuse was defined as evidence based on laboratory test results that a patient is using or combining nonprescribed drugs or skipping doses in ways that are inconsistent with the directions of the prescribing ­physician.

Evidence of drug misuse showed up in 54% of patient results tested in 2015, a slight increase over the 53% rate in 2014. On a positive note, though, the rate represented a marked decrease from the 63% registered in 2011.

Moreover, although results indicated misuse in 44% of results for children ages 10 to 17, that figure marked a steep decline from the 70% reported for 2011. The study suggests that the improvement might reflect closer oversight by parents or ­guardians.

Rates of misuse were highest among patients ages 18 to 64, exceeding 50%, while 46% of results for patients age 65 and older showed evidence of misuse. Regionally, the rate of abuse was highest — 66% — in the Western states of Colorado, Montana, North Dakota, South Dakota, Utah and Wyoming. The lowest rate, about 51%, occurred in the Southern states of Alabama, Florida, Georgia, Kentucky, Mississippi, North Carolina, South Carolina and Tennessee.

“The key takeaway from this massive, nationally representative analysis is that, despite some gains, a large number of patients use prescription drugs inappropriately and even dangerously,” says co-researcher Dr. Harvey Kaufman, senior medical director of medical informatics for Quest Diagnostics.

Perhaps the most alarming trend revealed by the Quest Diagnostics report is the sharp increase in the percentage of test results that indicated that prescription drugs were combined with other drugs without the physician’s knowledge. That percentage jumped to 45% last year from 35% in both 2014 and 2013. The rates for 2012 and 2011 were 33% and 32%, respectively.