You’ve heard those hospital horror stories where the surgeon removes the wrong body part or operates on the wrong patient or accidentally leaves medical equipment in the person they were operating on.

Even scarier, perhaps, is a new study in the latest edition of BMJ suggesting most medical errors go unobserved, at least in the official record.

In fact, the study, from doctors at Johns Hopkins, suggests medical errors may kill more people than lower respiratory diseases like emphysema and bronchitis do. That would make these medical mistakes the third leading cause of death in the United States. That would place medical errors right behind heart disease and cancer.

Through their analysis of four other studies examining death rate information, the doctors estimate there are at least 251,454 deaths due to medical errors annually in the United States. The authors believe the number is actually much higher, as home and nursing home deaths are not counted in that total.

This is a much greater number than a highly cited 1999 study from the Institute of Medicine that put the number in the 44,000 to 98,000 range. Other studies have put estimates closer to 195,000 deaths a year. The U.S. Department of Health and Human Services Office of the inspector general in 2008 reported 180,000 deaths by medical error among Medicare patients alone.

Dr. Martin Makary and Dr. Michael Daniel, who did the study, hope their analysis will lead to real reform in a health care system they argue is letting patients down.

“We have to make an improvement in patient safety a real priority,” said Makary, a professor of surgery and health policy and management at Johns Hopkins.

One reason there’s such a wide range of numbers is because accurate data on these kinds of deaths is surprisingly sparse. That’s in part because death certificates don’t ask for enough data, Makary said. Currently the cause of death listed on the certificate has to line up with an insurance billing code. Those codes do not adequately capture human error or system factors.

“Billing codes are designed to maximize billing rather than capture medical errors,” Makary said.

The study gives an example of exactly how limited the death certificates are when it comes to recording medical errors. One example involved a patient who had a successful organ transplant and seemed healthy, but had to go back to the hospital for a non-specific complaint. During tests to determine what was wrong, a doctor accidentally cut her liver and hadn’t realized it. The hospital sent her home, but she returned with internal bleeding and went into cardiac arrest and later died. It was the cut that led to her death, but her death certificate only listed a cardiovascular issue as the cause.