About 1 in 10 doctors reported that they had made a major medical error in the prior three months in a national survey of over 6,000 American doctors just published in Mayo Clinic Proceedings. Just over half of the doctors surveyed reported being burned-out, and the study authors found that those doctors were twice as likely to report errors.

Medicine has taken a page from aviation over the last decade or so, adopting practices such as checklists and flattening the hierarchies among doctors, nurses, and other clinicians in an effort to reduce medical errors. That approach may be neglecting the well-being of doctors themselves, however, says study author Tait Shanafelt at Stanford University—with consequences for the rest of us.

Medical errors are the third-leading cause of death in the United States, behind only heart disease and cancer, according to a BMJ study. The direct economic costs may be over $20 billion and the opportunity costs of losing over 250,000 workers a year could be around $200 billion a year.

In their analysis of the survey, Shanafelt and his colleagues checked to see if they could attribute the errors to a few bad apples. Instead, they found that error rates rose in line with fatigue levels. So even doctors who are only a little more tired are more dangerous to their patients.

Better leadership could be part of the solution.

A 2015 Mayo Clinic study found that doctors who rated their leaders favorably were less likely to report burnout. And medicine is already borrowing from business, with some institutions bringing in executive coaches and offering doctors sessions on mindfulness and positive psychology. And last year, a meta-analysis of studies in the Journal of the American Medical Association found that organizational revamps could make a small, but noticeable difference in reducing physician burnout.