Zainab’s parents estimated that their daughter’s illness began more than 10 months ago when they noticed that her temperament changed and her appetite waned. She developed fevers and constipation, and she wasn’t urinating normally.

Zainab was once an active, chubby child, but she lost weight and preferred to be on the bed instead of running around. Her condition seemed to worsen over the summer. The family recalled visiting relatives in Atlanta and attending a barbecue where Zainab was quiet and withdrawn.

“Everybody wanted to play with her,” Mr. Mughal said. “So there were a lot of other kids there. But she would not play with anybody. My wife kept telling me, she said, ‘She is not O.K. She is not O.K.’”

They brought Zainab to the pediatrician.

“I went to the doctor and I said to her over and over, ‘She is not eating,’” Zainab’s mother, Mariam Mehmood, recalled during the interview.

When they learned that Zainab had cancer, it was “devastating,” Mr. Mughal said. “At that time we were completely destroyed.”

Zainab had a tumor growing in her stomach, Mr. Mughal said, and a biopsy revealed that it was cancer. Doctors have characterized Zainab’s neuroblastoma as high risk. Children in that category have a five-year survival rate of around 40 to 50 percent, according to the American Cancer Society.

Soon after Zainab received her first blood transfusion, doctors realized that she was missing the Indian-B antigen, meaning that if her body receives blood that does have the antigen, her immune system will attack it.