Thomas Eakins, The Agnew Clinic, 1889; oil on canvas.

It seems that every time researchers estimate how often a medical mistake contributes to a hospital patient’s death, the numbers come out worse.

In 1999, the Institute of Medicine published the famous To Err Is Human report, which dropped a bombshell on the medical community by reporting that up to 98,000 people a year die because of mistakes in hospitals. The number was initially disputed, but is now widely accepted by doctors and hospital officials — and quoted ubiquitously in the media.

In 2010, the Office of Inspector General for Health and Human Services said that bad hospital care contributed to the deaths of 180,000 patients in Medicare alone in a given year.

Now comes a study in the current issue of the Journal of Patient Safety that says the numbers may be much higher — between 210,000 and 440,000 patients each year who go to the hospital for care suffer some type of preventable harm that contributes to their death, the study says.

That would make medical errors the third-leading cause of death in America, behind heart disease, which is the first, and cancer, which is second.

The new estimates were developed by John T. James, a toxicologist at NASA’s space center in Houston who runs an advocacy organization called Patient Safety America. James has also written a book about the death of his 19-year-old son after what James maintains was negligent hospital care.

Asked about the higher estimates, a spokesman for the American Hospital Association said the group has more confidence in the IOM’s estimate of 98,000 deaths. ProPublica asked three prominent patient safety researchers to review James’ study, however, and all said his methods and findings were credible.

What’s the right number? Nobody knows for sure. There’s never been an actual count of how many patients experience preventable harm. So we’re left with approximations, which are imperfect in part because of inaccuracies in medical records and the reluctance of some providers to report mistakes.

Patient safety experts say measuring the problem is nonetheless important because estimates bring awareness and research dollars to a major public health problem that persists despite decades of improvement efforts.

“We need to get a sense of the magnitude of this,” James said in an interview.

James based his estimates on the findings of four recent studies that identified preventable harm suffered by patients – known as “adverse events” in the medical vernacular – using use a screening method called the Global Trigger Tool, which guides reviewers through medical records, searching for signs of infection, injury or error. Medical records flagged during the initial screening are reviewed by a doctor, who determines the extent of the harm.

In the four studies, which examined records of more than 4,200 patients hospitalized between 2002 and 2008, researchers found serious adverse events in as many as 21 percent of cases reviewed and rates of lethal adverse events as high as 1.4 percent of cases.

By combining the findings and extrapolating across 34 million hospitalizations in 2007, James concluded that preventable errors contribute to the deaths of 210,000 hospital patients annually.