One in three women with breast cancer detected by a mammogram is treated unnecessarily, because screening tests found tumors that are so slow-growing that they're essentially harmless, according to a Danish study published Monday in Annals of Internal Medicine, which has renewed debate over the value of early detection.

The study raises the uncomfortable possibility that some women who believe their lives were saved by mammograms were actually harmed by cancer screenings that led to surgery, radiation and even chemotherapy that they didn't need, said Dr. Otis Brawley, chief medical officer of the American Cancer Society, who wrote an accompanying editorial but was not involved in the study.

Researchers increasingly recognize that not all breast cancers pose the same risk, even if they look the same under a microscope, Brawley said. While some early tumors turn into deadly monsters, others stop growing or even shrink. But assuming that all small breast lesions have the potential to turn deadly is akin to "racial profiling," Brawley wrote in his editorial.

"By treating all the cancers that we see, we are clearly saving some lives," Brawley said in an interview. "But we're also 'curing' some women who don't need to be cured."

Although experts such as Brawley have long discussed the risks posed by "overdiagnosis," relatively few women who undergo cancer screenings are even aware of the debate.

The American College of Radiology, which strongly supports breast cancer screenings, acknowledges that mammograms lead some women to be treated unnecessarily, but said the problem is much less common than the new study suggests. Another study from Denmark -- whose national health program keeps detailed records -- estimated the overdiagnosis rates at only 2.3 percent.

"The amount of overdiagnosis really is small," said Dr. Debra Monticciolo, chair of the American College of Radiology's Commission on Breast Imaging. "Articles like this aren't very helpful," she said, because they leave women confused about how to be screened for breast cancer.

Yet treating women for cancer unnecessarily can endanger their health, said Fran Visco, president of the National Breast Cancer Coalition, an advocacy group. Radiation can damage the heart or even cause new cancers . Visco notes that breast cancer activist Carolina Hinestrosa , a vice president at the coalition, died at age 50 from soft-tissue sarcoma, a tumor caused by radiation used to treat an early breast cancer.

Women should understand these risks, Visco said. Instead, women often hear only about mammograms' benefits.

"Women have been inundated with the early detection message for decades," Visco said.

The risks of overdiagnosis and false positives, which can lead women with benign growths to undergo biopsies and other follow-up tests, have caused some experts to reevaluate breast cancer screenings. Although mammograms don't find all tumors, they reduce the risk of dying from breast cancer by 25 percent to 31 percent for women ages 40 to 69, according to the Agency for Healthcare Research and Quality , part of the Department of Health and Human Services.

Medical groups now offer differing advice on mammograms:

The American College of Radiology takes the most aggressive stance, recommending annual mammograms beginning at age 40. Tumors should be found when they're "smaller and easier to treat," Monticciolo said.

The U.S. Preventive Services Task Force, an independent expert panel that advises the federal government on health, provoked a firestorm of criticism in 2009 when it bucked that advice, recommending that women get mammograms every other year beginning at age 50. The group noted that breast cancer risk rises with age, so mammograms are more likely to discover cancer -- as opposed to benign growths -- after age 50.

The American Cancer Society also scaled back its screening advice in 2015, recommending women get annual mammograms from 45 to 54, followed by screenings every other year after that.

In the new study, Danish researchers estimated the rate of overdiagnosis by comparing the number of early-stage and advanced breast tumors before and after the country started offering mammograms. If screenings work as intended, the number of small, curable breast tumors should increase, while reducing the number of large cancers by about the same amount.

Although mammograms in Denmark detected a lot more breast cancers, these were mostly small, early-stage tumors, said study coauthor Dr. Karsten Jorgensen, a researcher at the Nordic Cochrane Center in Copenhagen, Denmark. The number of advanced cancers did not fall.

The debate about overdiagnosis illustrates the limits of medical technology, Brawley said.

Although researchers can estimate the statistical rate of overdiagnosis, doctors treating actual patients can't definitively tell which breast tumors need treatment and which might be safely ignored, Brawley said. So doctors tend to err on the side of caution and treat all breast cancers with surgery and, in many cases, radiation and chemotherapy.

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An estimated 253,000 new cases of breast cancer will be diagnosed in the U.S. women this year, with nearly 41,000 deaths, according to the American Cancer Society

An additional 63,000 women will be diagnosed with ductal carcinoma in situ, also known as DCIS, which has some, but not all, of the typical traits of cancer. Although DCIS cells have changed to appear malignant under the microscope, they haven't invaded surrounding tissue.

The American Cancer Society defines DCIS as the earliest stage of breast cancer, and women with the condition typically undergo the same treatment given to women with early invasive cancers. Although DCIS isn't life-threatening, doctors recommend treating it to prevent it from becoming invasive.