They say the positive trend for Pacific and Maori children and those living in the most deprived areas began in the early 2000s, when there was a big increase in primary health care funding to reduce patient charges.
"Successive policy initiatives, particularly very low-cost access, zero fees for under-6s and free after-hours care, are likely to have strengthened this trend, and with the imminent introduction of free care to those under 13, this trend should continue.
"Reducing cost barriers to primary care works to reduce avoidable hospital admissions ... "
But the researchers linked the negative trend for Pacific adults in part to the continuation - despite the increased state money for the primary sector - of financial barriers to health care. They also blamed social and economic factors.
Dr Matheson told the Herald: "We know from Health Survey data there are still barriers to low-income Maori and Pacific access to primary care, particularly due to the cost of going to the doctor, and also in some areas not being able to get an appointment when they want it."
The researchers said more GPs were needed, and there was evidence that greater use of nurse practitioners could reduce preventable hospital admissions.
Avoidable admission rates
2002: Adults aged 45-64
Pacific - 6918
Maori - 6703
Other - 3133
2014: Adults aged 45-64
Pacific - 8754
Maori - 6312
Other - 2821