"The evidence shows that the likely benefit that treatment would offer Sinead is minimal," Pharmac medical director Dr John Wyeth wrote to her specialist. He said the decision was "not made lightly".
"Since the treatment is so very expensive (around $350,000 per year), this means that the cost effectiveness of funding [Kalydeco] for Sinead would be poor."
Manufacturers Vertex gave it to Sinead for free on compassionate grounds.
After she started taking it on November 3, her lung function jumped from 38 per cent to 70-80 in two weeks, and she gained 2.1kg.
Dr Catherine Byrnes, a respiratory specialist at the Starship children's hospital, said Sinead's condition was "dramatically better" since she had gone on Kalydeco.
Dr Byrnes had been preparing to put Sinead on the list for a lung transplant but that was no longer on the cards. "If she remains as well as she is, certainly there is no way. She just doesn't need one."
Ms Neame said she understood Sinead's response to the drug was among the best in the world, and said Pharmac got it wrong in her daughter's case. "I feel that we really showed them that they made a mistake. We're feeling a little bit grateful for a miracle."
For the drug to keep working, Sinead has to be on it indefinitely. Although it's not a cure, she feels better than ever.
"One of the things I've noticed is that I've had a lot more energy. Mum doesn't like the new me because I'm jumping around too much!"
An advocacy group said Sinead's case showed New Zealand was getting it wrong around drugs for rare diseases and a new $5 million Pharmac fund kicking in next year doesn't go far enough.
The executive director of the New Zealand Organisation for Rare Diseases, John Forman, said the fund didn't take into account that most drugs for rare diseases were not cost-effective compared to drugs for common diseases.
That was because drug companies spent millions on research and development, but because they could be used by only a small number of people, the firms had to charge high prices to recoup their costs.
Pharmac said it couldn't comment on individual cases, for privacy reasons.
But operations director Sarah Fitt said the organisation had to look at the bigger picture and sometimes that meant making "difficult decisions".
"It isn't a bottomless pit, and that goes right across the healthcare sector. There's a limit to how much we can actually fund," she said.
Pharmac balanced how funding one very expensive drug would affect its ability to fund many less expensive drugs, Ms Fitt said.
Pharmac's combined pharmaceutical budget for the past financial year was $795 million.
According to New Zealand Medical Association chairman Dr Mark Peterson, any criticism of Pharmac around funding drugs for rare diseases should be political.
"They are given a budget by government, which says, 'This is the amount of money we will spend on pharmaceuticals', and they have to work within that."
What is cystic fibrosis?
•The most common life-threatening genetic disorder affecting New Zealand children. It is inherited and non-contagious. Cystic Fibrosis New Zealand estimates more than 500 Kiwis have it.
How does it affect human beings?
•It clogs organs, especially the lungs and pancreas, with thick, sticky mucus. This can cause shortness of breath, a chronic cough and repeated chest infections. There is no cure.
What is Kalydeco?
•The first drug that can address the defective gene rather than the symptoms.
Who can have it?
•It is targeted at those with the G551D mutation - about 4 per cent of patients.
Which countries fund it?
•From December 1, the drug became government-funded in Australia. It is also available in the UK, Republic of Ireland, France, Germany, Italy, the Netherlands, Switzerland, Austria, Denmark, Sweden, Norway, Greece, Spain, the United States and Canada.