More than 20 percent of patients who sought a second opinion at one of the nation’s premier medical institutions had been misdiagnosed by their primary care providers, according to new research published Tuesday.

Twelve percent of the people who asked specialists at the Mayo Clinic in Rochester, Minn., to review their cases had received correct diagnoses, the study found. The rest were given diagnoses that were partly in line with the conclusions of the Mayo doctors who evaluated their conditions.

The results are generally similar to other research on diagnostic error but provide additional evidence for advocates who say such findings show that the health-care system still has room for improvement.

“Diagnosis is extremely hard,” said Mark L. Graber, a senior fellow at the research institute RTI International and founder of the Society to Improve Diagnosis in Medicine. “There are 10,000 diseases and only 200 to 300 symptoms.”

Graber was not involved in the Mayo Clinic research, which appears in the Journal of Evaluation in Clinical Practice.

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In 2015, the National Academy of Medicine reported that most people will receive an incorrect or late diagnosis at least once in their lives, sometimes with serious consequences. It cited one estimate that 12 million people — about 5 percent of adults who seek outpatient care — are misdiagnosed annually. The report also noted that diagnostic error is a relatively under-measured and understudied aspect of patient safety.

According to previous research cited in the new study, diagnostic errors “contribute to approximately 10 percent of patient deaths” and “account for 6 to 17 percent of adverse events in hospitals.” Graber estimates that the rate of misdiagnosis, although difficult to determine, occurs in 10 percent to 20 percent of cases.

“Diagnostic error is an area where we need more research, more study and more information,” said James M. Naessens, a professor of health services research at the Mayo Clinic, who led its study. “The second opinion is a good approach for certain patients to figure out what’s there and to keep costs down.”

The researchers looked retrospectively at 286 patients who had seen primary-care physicians, physician assistants and nurse practitioners in 2009 and 2010. Nearly two-thirds were younger than 64, and most were female.

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With or without the help of their initial provider, those people sought additional advice from the Mayo Clinic’s internal medicine department. That makes the group somewhat different from the general population, Naessens said, because their conditions were serious enough to merit another look by some of the best physicians in the country.

“It’s not going to be 20 percent wrong every time” a patient goes to see a doctor, Naessens said.

In 62 cases (21 percent), the second diagnosis was “distinctly different” from the first, the researchers reported. In 36 cases (12 percent), the diagnoses were the same. In the remaining 188 cases, the diagnoses were at least partly correct but were “better defined/refined” by the second opinion, according to the study.

Naessens and Graber said a second opinion is valuable any time a patient is told he or she has a serious condition, such as cancer, or needs surgery — even if an extra visit initially means more expense. In the long run, additional advice can save lives and money, they said.

“Doctors are humans, and they make the same cognitive mistakes we all make,” Graber said. “If you are given a serious diagnosis, or you’re not responding the way you should [to medication], a second opinion is a very good idea. Fresh eyes catch mistakes.”