A sign that the treatment is working is that the patient becomes terribly ill, with raging fevers and chills — a reaction that oncologists call “shake and bake,” Dr. June said. Its medical name is cytokine-release syndrome, or cytokine storm, referring to the natural chemicals that pour out of cells in the immune system as they are being activated, causing fevers and other symptoms. The storm can also flood the lungs and cause perilous drops in blood pressure — effects that nearly killed Emma.

Steroids sometimes ease the reaction, but they did not help Emma. Her temperature hit 105. She wound up on a ventilator, unconscious and swollen almost beyond recognition, surrounded by friends and family who had come to say goodbye.

But at the 11th hour, a battery of blood tests gave the researchers a clue as to what might help save Emma: her level of one of the cytokines, interleukin-6 or IL-6, had shot up a thousandfold. Doctors had never seen such a spike before and thought it might be what was making her so sick.

Dr. June knew that a drug could lower IL-6 — his daughter takes it for rheumatoid arthritis. It had never been used for a crisis like Emma’s, but there was little to lose. Her oncologist, Dr. Stephan A. Grupp, ordered the drug. The response, he said, was “amazing.”

Within hours, Emma began to stabilize. She woke up a week later, on May 2, the day she turned 7; the intensive-care staff sang “Happy Birthday.”

Since then, the research team has used the same drug, tocilizumab, in several other patients.

In patients with lasting remissions after the treatment, the altered T-cells persist in the bloodstream, though in smaller numbers than when they were fighting the disease. Some patients have had the cells for years.

Dr. Michel Sadelain, who conducts similar studies at the Sloan-Kettering Institute, said: “These T-cells are living drugs. With a pill, you take it, it’s eliminated from your body and you have to take it again.” But T-cells, he said, “could potentially be given only once, maybe only once or twice or three times.”