Given those odds, the little girl's parents, Jalal and Shaheda Hoque, decided not to let doctors operate, and instead started taking her to a Montreal homeopath for herbal and nutritional treatments in hopes of curing her.
But now Michigan prosecutors have taken the Hoques to court to force them to go ahead with the surgery in a case that revisits the question of who should decide what is best for the child when it comes to lifesaving medical treatment.
"There's no other outcome but death, without surgery," said David Gorcyca, prosecutor in suburban Detroit's Oakland County. "I think if I'm a parent given a 30 percent fighting chance of survival, I'm taking that shot every time."
On Friday, Circuit Judge Martha Anderson ordered the parents to allow a state social worker to see Noshin and gauge her condition, after the Hoques turned away the last one who came to their home. The couple were also ordered to provide prosecutors with complete records of their daughter's treatments.
A hearing was set for May 12, when the judge will receive the results of a court-ordered brain scan on Noshin to determine the effectiveness of the homeopathic treatment.
The walnut-size cancerous tumor lies against several important arteries and affects Noshin's speech, vision and gait. But the location of the mass could make surgery risky.
Two pediatric neurosurgeons told the couple that there was a 70 percent to 80 percent chance that their daughter would emerge either dead or with severe complications. If Noshin survived the initial surgery, she would then have to undergo chemotherapy and follow-up operations to have any chance at living, said the couple's lawyer, Charles Cooper.
The couple, an electrician and his homemaker wife, are from Bangladesh, where homeopathy is more widely accepted. The Hoques (pronounced HOKE) fear surgery would kill Noshin or leave her in a vegetative state, Cooper said.
"They didn't want her to be going into the hospital and having the top of her head removed and then all of these different surgeries and having her go through all of this," Cooper said.
Cooper said Noshin is doing much better now that she is receiving alternative medicine; her left eye does not roam anymore, and her left arm is stronger than it has been for a while.
Noshin's pediatrician at Children's Hospital of Michigan in Detroit contacted the state after her parents, who live in Royal Oak, stopped bringing her to appointments. Prosecutors filed an emergency petition to intervene.
Such disputes occur from time to time around the country, and judges have generally ruled that parents cannot withhold lifesaving medical care from a seriously ill child.
Parents often cite religious beliefs when rejecting medical treatment for their ill children. Christian Scientists believe in prayer instead of conventional medicine, while Jehovah's Witnesses oppose blood transfusions.
But that is not the case with the Hoques.
Lawrence Schneiderman, a doctor of internal medicine and a medical ethicist who teaches at the University of California at San Diego, said the Hoques' situation is also different because surgery in this case is so risky.
"The clinical condition of the child is so serious that quality-of-life considerations should take precedence over a prolongation of life. Therefore, the parents have a right to decide what they think is in the best interest of their child," he said.
But Schneiderman warned that any suggestion that homeopathic treatment can cure or ease cancer is quackery. He suggested that the Hoques instead concentrate on making their daughter as comfortable as possible.
"There are nicer, easier, better things you can do for her than take her up to Canada for this foolishness," he said.