The longest study yet to examine women who undergo mammography shows that it reduces death from breast cancer by at least 30 percent, a finding that many doctors say may help ease the recent controversy surrounding the procedure.

The three-decade study in Sweden showed that a breast cancer death is prevented for every 414 to 519 women who are screened, a much lower number than the 1,000 to 1,500 that had been projected in previous studies.

“What this tells us is that, in the long term, screening for breast cancer is a very good investment,” said epidemiologist Robert A. Smith, director of cancer screening at the American Cancer Society and a co-author of the paper appearing in the journal Radiology.

Critics had argued that overuse of the procedure produced too many false positives, requiring many women to undergo unnecessary invasive procedures — which have risks of their own — to rule out the presence of a tumor.

“There is little question that there is some overdiagnosis,” Smith said, “but the number we have identified is really quite small. We estimated it is less than half the number of lives saved, so it is really pretty low.”

The findings are “a really big deal,” said Dr. Loretta Lawrence, chief of breast imaging at North Shore University Hospital in Manhasset, N.Y. “A 30 percent reduction in mortality translates to 15,000 to 20,000 lives saved by mammography screening each year.”