When Alicia was diagnosed, Mr Steenson became suspicious. He looked under their Ohauiti house, in an area near where Alicia often played, and found old, empty containers of paint thinners had been dumped there.
He contacted police who told him the house had been raided in 2011 and the people there charged with methamphetamine offences.
Preliminary testing of the house by Auckland-based company Meth Solutions revealed there was a high level of the drug still present.
A spokeswoman said detailed testing of the property was now being undertaken.
Mr Steenson believed Alicia's sickness could be related to the chemicals under the house and the contamination.
"It started in her mouth and she's the only one in the house who's a thumb sucker," he said.
"We were definitely all quite lethargic."
Ms Steenson said he was concerned the landlord did not notify him.
Tauranga medical oncologist Richard North said it was unlikely, but not impossible, Alicia's cancer had been caused by living in the contaminated home.
Dr North said leukaemia could be caused by prolonged exposure to chemicals, but thought it unlikely that living in a meth home would cause it.
"What is impossible is to prove it," he said. The Steenson's property manager, Afra van der Velden, said neither herself nor the owners of the property were aware the house had methamphetamine contamination. She said the owners were never told of any police raid on the property and were talking to police to establish what had happened.
"We are very concerned about this and we are looking into it. We don't actually know who was renting the house in 2011."
According to the New Zealand Drug Detection Agency, children are particularly vulnerable to the health risks associated with meth labs because they had immature organ systems, faster metabolic rates, and weaker immune systems.
Nina Harland, a work colleague of Mr Steenson who is fundraising for the family, said the family was concerned they had nowhere to live.
"They had to leave everything in their house their furniture, everything," she said.
Mr Steenson said Alicia's body was "riddled" with cancer by the time they found it and while it was an aggressive type it also responded well to treatment.
Doctors expected she would make a full recovery but would likely be in hospital until August, he said.
Alicia's blonde hair had now fallen out and the chemotherapy was tiring her out but she was putting on a brave face, Mr Steenson said.
Ms Harland started fundraising at work and soon extended her efforts further afield by setting up a page on givealittle.co.nz
"They are a lovely family. They are very family-oriented. Everything's for their kids. They don't have a lot. It's been a really big hit for them."
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Can you help?
Visit www.givealittle.co.nz/cause/aliciakade or phone Nina Harland on 021 209 5128 if you would like to help.