Today when a patient comes with memory problems, doctors might say that the person has a chance of developing Alzheimer’s in the next decade, a chance of not getting much worse for several years, and a chance of actually getting better. Tests like brain scans, Dr. Petersen said, “will allow us to be much more definitive.” If the tests show changes characteristic of Alzheimer’s disease, a doctor can say, “I think you are on the Alzheimer’s road.” That can be a difficult conversation, but it can allow patients and their families to plan. “At least it’s a conversation the physician can have with the patient,” Dr. Petersen said.