Those facts lead Dr. Narod to a blunt view. After a surgeon has removed the aberrant cells for the biopsy, he said, “I think the best way to treat D.C.I.S. is to do nothing.”

Others drew back from that advice.

Dr. Monica Morrow, chief breast cancer surgeon at Memorial Sloan Kettering Cancer Center, said it made more sense to view D.C.I.S. as a cancer precursor that should be treated the way it is now, with a lumpectomy or mastectomy. She questioned whether those women who were treated and ended up dying of breast cancer anyway had been misdiagnosed.

In some cases, pathologists look at only a small amount of tumor, Dr. Morrow said, and could have missed areas of invasive cancer. Even the best mastectomy leaves cells behind, she added, which could explain why a small number of women with D.C.I.S. who had mastectomies, even double mastectomies, died of breast cancer.

Dr. Brawley said the new study, by showing which D.C.I.S. patients were at highest risk, would help enormously in defining who might benefit from treatment. It could not show that the high-risk women — young, black or with tumors with ominous molecular markers — were helped by treatment because there were too few of them, and pretty much every one of them was treated. But Dr. Brawley said he would like to see clinical trials that addressed that question, as well as whether the rest of the women with D.C.I.S., 80 percent of them, would be fine without treatment or with anti-estrogen drugs like tamoxifen or raloxifene that can reduce overall breast cancer risk.

The notion that most women with D.C.I.S. might not need mastectomies or lumpectomies can be agonizing for those, like Therese Taylor of Mississauga, Ontario, who have already gone through such treatment. Four years ago, when she was 51, a doctor sent her for a mammogram, telling her he felt a lump in her right breast. That breast was fine, but it turned out she had D.C.I.S. in her left breast. A surgeon, she said, told her that “it was consistent with cancer” and that she should have a mastectomy.

“I went into a state of shock and fear,” Ms. Taylor said. She had the surgery.

She regrets it. “It takes away your feeling of attractiveness,” she said. “Compared to women who really have cancer, it is nothing. But the mastectomy was for no reason, and that’s why it bothers me.”

But if D.C.I.S. is actually a risk factor for invasive cancer, rather than a precursor, it might be possible to help women reduce their risk, perhaps with hormonal or immunological therapies to change the breast environment, making it less hospitable to cancer cells, Dr. Esserman said.