Most cervical cancers are caused by HPV, a sexually-transmitted infection that most people get at some point in their lives. The Government funds HPV vaccination for females and now males too - to age 26.
But Cox -of the Hugh Adam Cancer Epidemiology Unit, funded by the Director's Research Trust - said he believed the risks of the proposed testing regime were too great and could lead to cancer deaths.
"There's more opportunity for pre-invasive disease to develop into invasive disease between screening rounds," he said.
"It can be estimated that the new policy is likely to increase the incidence of cervical cancer by about 20 per cent."
He said mortality could rise by about the same proportion.
But both the Ministry of Health and its National Screening Unit have rejected Cox's fears.
"The change in New Zealand is expected to reduce cervical cancer incidence by around 12-15 per cent and to reduce cervical cancer mortality by 12-16 per cent," the unit's clinical director Dr Jane O'Hallahan said.
O'Hallahan said cell-testing of women's positive HPV samples would help to avoid over-referral and over-treatment.
Presently around 160 New Zealand women are newly diagnosed with cervical cancer each year and 60 die from the disease.
Our annual incidence and mortality rates from the disease have roughly halved since the programme began in 1990.
But Cox remains adamant the changes are the wrong move and is leading a challenge by cancer experts and women's health groups to the changes to the screening programme.
For his efforts was kicked off the ministry's National Screening Advisory Committee in late July for speaking out publicly against the changes after they had been endorsed by other committee members.
He advocates waiting and watching Australia's "experiment" with primary HPV testing for five years, or possibly using both tests together for primary screening.
He cites a study in Finland by Nea Malila and colleagues which concluded that the sensitivity of HPV testing and traditional Pap smears is similar for detecting abnormalities that will develop into cancer, but HPV leads to more "overdiagnosis" - the detection of abnormalities that don't develop into cancer.
"Therefore," the Malila group wrote in the International Journal of Cancer, "implementation of HPV testing needs to be reconsidered especially in countries with well organised programmes."
Cox's group also argues that primary HPV testing could result in many more women being referred unnecessarily for second level testing, by colposcopy - a magnifying instrument for looking at the cervix - and related testing/treatment by removal of a biopsy tissue sample. They say colposcopy services are already stressed.
In an email to the advisory committee, O'Hallahan and other health officials, Cox said the ministry and its advisers seemed to have misunderstood the concept of sensitivity and ignored the Malila study.
But Ministry calculations indicated the changes to the programme also would reduce the number of colposcopies.
O'Hallahan said Malila's "is not the only trial of HPV-based screening, and therefore its results should not form the sole guide for policy.
"A pooled analysis of data from four other major European trials concluded that HPV screening offers substantially greater protection against cervical cancer.
"The overwhelming international opinion is that primary HPV testing will reduce cancer rates compared with current cytology-based screening programmes. Most countries with organised screening programmes are in the process of executing this change."
Colposcopy delays
The ministry said it could not release any 2016 data on colposcopy waiting times, sought by the Herald under the Official Information Act in November, until this year because an independent monitoring organisation was still compiling the data tables.
The latest publicly available data, for July to December 2014, shows targets being missed by a large margin.
The target is that 95 per cent of women in whom cancer is suspected will be seen within 10 working days of receipt of the referral, and 20 working days for women with high-grade abnormalities. In both groups nationally just 65 per cent were seen within the relevant time.
How cervical screening works
Now
• The cervical smear - cervical cells taken with a spatula or brush are put into a vial of special preservative
• The first test done by the lab - cytology, the analysis of cervical cells for abnormalities
• Age of eligibility - women aged 20-70
• Frequency of screening - every three years
From 2018
• The cervical smear - no change
• The first test done by the lab - human papilloma virus (HPV)
• Age of eligibility - women aged 25 to 69
• Frequency of screening - every five years