Millions of women in 21 states will get an ominous note with their mammogram results this year. Even if everything seems fine, they’ll be informed that they have dense breast tissue, which can raise their risk for cancer and hide abnormalities, making their mammograms less accurate.

The question is: now what?

A host of new breast-imaging technologies promise to detect more cancers in these women. But many of the methods bring more false alarms as well, subjecting women to additional tests and biopsies unnecessarily. Some are also more expensive than mammograms and haven’t been widely studied yet.

Laws in 21 states require doctors to tell women they have dense tissue. Similar bills are pending in eight more states and a national bill was introduced in Congress earlier this month.

“It’s a very confusing time,” says Emily Conant, chief of breast imaging at the University of Pennsylvania Medical Center. “This legislation has happened before we have a medical consensus about what to tell women.”

Some experts say telling women they have dense breasts would make them anxious unnecessarily.

“Of course you might be anxious. But I’d trade a false positive for a false negative any day,” says Nancy Cappello, who started the campaign for density-notification laws and the organization Are You Dense? after numerous mammograms failed to spot her advanced breast cancer. Doctors had noted her dense breasts for years, but never told her that her mammograms might not be showing potential problems.

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