“We realized we had never reported that,” Dr. Martínez-González said.

Image Dr. Miguel A. Martínez-González Credit... via Wikimedia Commons

An omission like that erodes the randomized nature of the trial. Family members are likely to share more than just a diet: If a husband and wife both dodge heart disease, it’s difficult to say that their diet is the only reason.

In their re-analysis, the investigators statistically adjusted data on 390 people who happened to be household members but whose diets were not randomly assigned.

Then the investigators discovered another problem.

A researcher at one of the 11 clinical centers in the trial worked in small villages. Participants there complained that some neighbors were receiving free olive oil, while they got only nuts or inexpensive gifts.

So the investigator decided to give everyone in each village the same diet. He never told the leaders of the study what he had done.

“He did not think it was important,” Dr. Martínez-González said.

But the decision meant that participants were not truly randomized and forced Dr. Martínez-González and his colleagues to make another statistical adjustment to data on 652 people in the trial.

The investigators spent a year working on the re-analysis in collaboration with Dr. Miguel Hernan of the Harvard T.H. Chan School of Public Health.

In the end, they concluded that the original findings were still accurate.

“You cannot imagine what it has been like,” Dr. Martínez-González said, adding that he and his team worked through vacations and weekends — and swallowed considerable professional embarrassment.