Keith Negley

Mammography has become a fighting word in recent years, with some researchers questioning its value and others staunchly defending it.

One especially disturbing criticism is that screening mammography may lead to “overtreatment,” in which some women go through grueling therapies — surgery, radiation, chemotherapy — that they do not need. Indeed, some studies estimate that 19 percent or more of women whose breast cancers are found by mammography wind up being overtreated.

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This problem occurs, researchers say, because mammography can “overdiagnose” breast cancer, meaning that some of the tiny cancers it finds would probably never progress or threaten the patient’s life. But they are treated anyway.

So where are these overtreated women? Nobody knows.

They are out there somewhere, studies suggest. But the figures on overtreatment are based on theory and calculations, not on counting the heads of actual patients known to have experienced it. No one can point to a particular woman and say, “Here’s a patient who went through the wringer for nothing.”

Overdiagnosis is not the same as a false positive result, in which a test like a mammogram initially suggests a problem but is proved wrong. False positives are frightening and expensive, but overtreatment is the potential harm of mammography that worries doctors most, according to an article published last week in The Journal of the American Medical Association.

But the authors also say that estimates of how often overdiagnosis and overtreatment occur are among the least reliable and most controversial of all the data on mammography.

In the past, overdiagnosis was thought to apply mainly to ductal carcinoma in situ, or D.C.I.S., a breast growth that may or may not turn cancerous. Now, researchers think that invasive cancers are also being overdiagnosed and overtreated by mammography.

The concept of overtreatment is based on the belief that not all breast cancers are deadly. Some never progress, researchers suspect, and some progress so slowly that the patient will probably die of something else, particularly if she is older or has other health problems.

But mammography can find all of these tumors, even those too small to feel. And doctors and patients rarely watch and wait — once a tumor is found, it is treated, because nobody knows how to tell the dangerous ones from those that could be safely left alone.

“Everyone has an anecdote of a small spot on mammography year after year that was finally biopsied and turned out to be positive — invasive, low grade,” said Dr. Constance Lehman, a radiologist at the Fred Hutchinson Cancer Center and the director of breast imaging at the University of Washington in Seattle.

Where do the numerical estimates of overdiagnosis come from? In several large studies of mammography screening, women judged to have the same risk of breast cancer were picked at random to have the test or to skip it. Early on, more cancers were expected in the mammogram group, because the test can find small tumors.

Over time, the groups should have equalized, because if small tumors in the unscreened group were really life-threatening, they would have grown big enough to be felt or caused other symptoms.

But in several studies, the number of cancers in the unscreened group never caught up with the number in the mammography group. The reason for the difference, researchers assume, is that there must have been women in the unscreened group who had cancers that were never diagnosed and never progressed — and therefore did not need treatment.

The next step is to subtract the number of cancers in the unscreened group from the number in the mammography group. The result is the estimate of how many women in the mammography group were overtreated.

“We don’t know which individual women those were,” said Dr. Lydia E. Pace, of Brigham and Women’s Hospital, an author of the new paper. “All we know is the proportion, and a lot of people would argue that we don’t really know the proportion.”

This kind of calculation was used in a Canadian study of about 90,000 women, published in February in the journal BMJ. The authors found that after 15 years there was a “residual excess” of 106 invasive cancers in the mammography group. The authors attributed that to overdiagnosis, and said that it amounted to 22 percent of the 484 invasive cancers found by mammography. They concluded that for every 424 women who had mammography in the study, one was overdiagnosed.

Other studies have estimated overdiagnosis in different ways, with huge variations in the results, reporting that 5 percent to 50 percent of cancers found on mammograms are overdiagnosed. To make it clear that the numbers are uncertain, some offer ranges: For example, one says that if 10,000 50-year-old women have annual mammograms for 10 years, 30 to 137 women will be overdiagnosed.

It is frightening to consider the prospect that mammography could be leading some down a slippery slope to unneeded surgery, chemotherapy and radiation, with all their risks and side effects. But the numbers on overdiagnosis are all over the map, a shaky foundation on which to base important decisions.

The best hope for resolving the confusion may lie in molecular tests that can tell the difference between dangerous tumors and those unlikely to progress — but those tests are in the future.

A version of this article appears in print on 04/08/2014, on page D6 of the NewYork edition with the headline: Look for Cancer, and Find It.