The medical team grasped for a scientific explanation. Because Andrew had received no treatment over the summer, the answer had to lie in the bone-marrow transplant of Wills’s cells. Their main theory was that the infection that nearly killed Andrew in July had triggered a huge increase in his new white blood cells — and that heightened immune response had attacked not only the infection but the cancer cells as well.

The doctors theorized that the response was partly a product of timing: The cancer had returned just as Andrew’s new immune system grew strong enough to destroy the cancer cells. A critical part of why transplants work is that some of the white blood cells, the T cells, that grow from the transplanted bone marrow will attack any lingering cancer cells, an effect known as graft versus leukemia. Chemotherapy rarely kills every last cancer cell, so it is believed that without graft versus leukemia, the cancer will eventually grow back. This is often spoken of as a model of so-called immunotherapy — stimulating the patient’s own immune system to attack cancer cells — which is widely regarded as one of the most promising avenues for cancer treatment.

Willert had made a key decision to depart from Stanford’s protocol to increase Andrew’s chances of getting a robust graft versus leukemia effect. Typically, a leukemia patient receives immune-suppressing drugs for at least 100 days (and often much longer) in order to avoid a serious side effect called graft versus host disease, in which new T cells attack not only the cancer cells but also the patient’s skin, liver and gastrointestinal tract. The art of a transplant is said to be maximizing graft versus leukemia while minimizing graft versus host.

Willert, who is now at the University of California, San Francisco, Benioff Children’s Hospital, had advocated a rapid early taper of Andrew’s immune-suppressing drugs on Day 60, as is the practice at U.C.S.F. and other places, because she felt that the benefits outweighed the risk of graft versus host. “I fought for it because I have seen the power of getting rid of immune suppressants and letting the cells do their job,” she says. “After all, that’s the whole point of a transplant!”

The final, critical decision was made against medical advice: Esther and Dan’s resolution to stop treatment and let Andrew die. Had they permitted more chemotherapy, the treatment would have killed Wills’s cells, which were what ultimately enabled Andrew to live.

“When you have a child with a life-threatening illness, you have an irrevocably altered existence,” Barbara Sourkes had told the Levys, and Esther feels that is true. She had always felt in control of her fate, but now she believes this to be a fiction. She finds it difficult to reconcile bitterness over the blight of Andrew’s illness with gratitude for the reprieve. “We are the luckiest of the unluckiest people in the world,” she says. “I truly believe that.” The story presents itself to her as a riddle that cannot be resolved. She recalls her anger when others told them to hope. Is the lesson that their friends were right and there is always hope? Yet it was only by letting go of hope and accepting Andrew’s death that he lived.

She has not returned to work. “My full-time job is to help the kids feel safe again,” she says. But it is hard for her to feel safe. The two years after a transplant are the riskiest time for a relapse; after two years that likelihood plummets, and after five years, a patient is considered cured. The two-year mark is still nine months away.