And for those who demand more details than just a “yes,” “no” or “maybe,” Dr. de Leon refuses.

“We say, ‘It is a statistical exercise, it is a proof of concept, it is a baby test,’ ” Dr. de Leon said. “Some say: ‘That’s not good enough. I come back to you every year, and if you want me to continue I need more than that.’ ”

But Dr. de Leon said he was constrained by his hospital’s ethics board, which has to approve his studies. It is extremely difficult, he says, to convince the board that giving out uncertain information about risk can help people, given that there is no effective treatment. And so, he says, he tells patients, “You are here to do an experiment.”

Others, like Dr. Lawrence Honig of Columbia University, say they sometimes see patients with no symptoms of memory loss who are nonetheless worried about their risk. Some of them have already gotten one of the early diagnostic tests, like a spinal tap or brain scan, from a neurologist in private practice, and have been told they were on their way to developing Alzheimer’s. They come to Dr. Honig, hoping he will say it is not true.

That situation, Dr. Honig says, “has become more and more common over the last few years.” He says that when test results are consistent with Alzheimer’s, he is honest about it, telling patients that the results are “suggestive of Alzheimer’s” but adding that all he can say for sure is “at some point in the future, you might be faced with that condition.”

He agonizes, though, over telling people news like that.

“I think it’s pretty terrible,” Dr. Honig said. “It is psychologically invasive.”

But for neurologists like Dr. de Leon, the future is fast approaching, as patients increasingly demand to know.

“The floodgate is about to open,” Dr. de Leon said.

Information’s Burden

At Boston University, Dr. Robert Green faced an ethical dilemma. He wanted to test people for a gene, APOE, that has three variants. People with two copies of one of the variants, APO e4, have a 12- to 15-fold increased risk of Alzheimer’s disease. People with even one copy of the gene variant have about a threefold increased risk.