"Over about a period of a year of her treating me and seeing me in clinic every two weeks and hospital visits and stuff we became very friendly," Downs said.
Downs' treatment then took him to the United States, which he joked was when the pair were "allowed" to become friends.
Elinder-Camburn decided to shave her hair to raise money for Leukemia & Blood Cancer New Zealand, a charity that helps blood cancer patients and their support networks. A charity she said is very close to her heart.
"Just watching what they have done over the past few years made me think I would like to support them and also raise awareness," she said.
During the country's Covid-19 lockdowns, she said the work from Leukemia & Blood Cancer New Zealand was extremely important since patients could not be supported by loved ones when attending appointments or treatment.
But during this time, she said the charity ensured patients were cared for.
"They can contact patients, they can provide material and make people feel they are supported virtually."
When Downs heard his friend was going to shave her hair, he jumped at the opportunity to be the one to do it.
"The thing about when you get chemotherapy, your hair falls out so I like to say Anna gave me a really bad haircut so it's my turn to give her one," he joked.
While the fundraising aspect of Shave for a Cure is important, Downs said Elinder-Camburn has shown incredible support for her patients.
"She's going to see patients now and over the next year or so who are going to be asking her why her hair is short and she's going to be able to say I am doing it in support of you and people like you."
Leukemia & Blood Cancer New Zealand CEO Peter Fergusson said Shave for a Cure is a "lifeline as it's one of the few events that can still happen during the pandemic".
"It's been a lifeline in terms of finance. Most of our events in the last 12 months, four of our events have been either postponed or cancelled altogether which is roughly $2 million worth of income."
However, he said as income has dropped the need for support has risen between 20 and 30 per cent since Christmas.
"We've got this conundrum going on, where we have less income coming in to provide the support and more need."
In the past few years, Fergusson said he was only aware of three haematologists including Elinder-Camburn who had shaved their hair for support.
"The wonderful thing for us is that they are a walking billboard. In a DHB they are a specialist in that area, the patient sees they are doing something on their behalf."