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For women with a high risk of breast cancer because of genetic mutations or family history, yearly M.R.I. scans in addition to mammograms and breast exams may save lives, a new study finds.

The study, the first to measure survival in a large number of high-risk women receiving M.R.I.’s, found that after six years of follow-up, 93 percent of mutation carriers with cancer were still alive, compared with 74 percent alive at five years in earlier studies. In the new study, all of the women at high risk because of family history were still alive after six years.