Imagine being told by a doctor that you have a high risk of breast cancer and that the only way to greatly reduce that risk is to have a double mastectomy. This is the awful choice some women are faced with, most famously Angelina Jolie .

But what’s even worse is not to have this choice at all. At present genetic tests can only identify a tiny fraction of the women at high risk, but there’s now a way to identify far more. Deciding what to do about …