However, the Herald can reveal serious concern about the programme, including the perverse possibility it could actually worsen inequality.
Auckland, Counties Manukau and Waitemata DHBs have jointly written to the ministry's chief advisor on child health, Dr Pat Tuohy, urging a review.
"Local data identifies the B4SC may be increasing inequities," states the October 2017 letter, released under the Official Information Act.
"The children at the highest risk of poor health outcomes are less likely to be identified and referred, and if they are referred, the families are less able to navigate the system to receive timely appropriate follow-up.
"Eligibility for publicly funded health services...is currently a barrier for some families and a national solution to this issue should be sought."
The timing of screening should be reviewed, the DHBs suggested, because currently there wasn't time to help children with some conditions before school. Conversely, four can be too young to assess hearing and vision.
The ministry has acknowledged the concerns, some of which were already identified, and says they will be fed into an upcoming review. No screening can identify all issues, it says, and checks run alongside regular nurse and GP visits.
The problems were discovered during research involving 126 children attending mostly decile 1A schools in Auckland's Glen Innes, Pt England and Panmure.
The Welcome To School study involved the Manaiakalani Kāhui Ako group of local schools, the Cure Kids research foundation and Starship community services.
Specialists and nurses checked new entrants.
The number of problems not picked up by before school checks was "very significant", said Russell Burt, study co-author, principal at Pt England School and Manaiakalani convenor.
There had been a misunderstanding about what checks covered, Burt said. For example, schools assumed eye testing was more comprehensive.
"But what in effect was being checked on was what lay people would call a lazy eye. The before school tests were vision test lite.
"If a parent doesn't notice there's something inhibiting their child...then you've got a kid who might struggle to interact with text, when their brains are perfectly alright but their eyes aren't doing what they ought to."
Aspects of the before school checks rely on parent perception. A strengths and difficulties questionnaire (SDQ) asks parents to rate their child on 25 statements related to emotions, peer relationships, hyperactivity and socialisation.
Burt said the most disadvantaged families - often Māori and Pacific - were more likely to say their child was okay, because their development was typical for the community.
"Middle classes and above tend to be far more in-advocacy for their children's needs - taking note of when other children walk, how early they are toilet trained, how well they speak - this view of developmental things being a competition."
In their letter to the ministry, the DHBs said "there remains a question about the validity" of the SDQ questionnaire in relation to Māori and Pacific families.
Ministry of Health-commissioned research in 2014 found Māori parents and teachers saw the questionnaire as a Pākehā approach to labelling their children. However, "the findings of that work have not been accepted by the ministry and this issue has not been resolved", the DHBs stated.
Burt said the Welcome to School research showed the challenge facing low decile schools was bigger than suspected.
Many children were starting at a language development age of 3-4 years. More than 30 per cent had a language proficiency in the bottom 2.5 per cent of the population.
The study, sent to ministers of health and education, concludes: "our current model of delivering health, education and social services equally is increasing inequity. We need to realign the current health and education systems".
A ministry spokesman said the concerns would feed into a planned review of the suite of Well Child Tamariki Ora services, offered from birth to 5-years-old. The B4SC programme was successful, he said, with coverage consistently above 90 per cent.
"No screening test identifies all children with problems. All screening tests exist in a context, which [for Tāmaki families] is regular visits by a well child nurse and intermittent consultations with a GP. Emerging health issues can be identified by these professionals.
"B4SC is not just about screening. However, we know all of the screens have limitations due to characteristics of the test, the way the tests are administered, or different levels of participation."
The SDQ questionnaire had been used in the national health survey without issue, the spokesman said, and was internationally recognised and one of limited options.
A spokeswoman for the three Auckland DHBs said the concerns had been acknowledged, and Dr Tuohy had since met with community paediatric teams.
When disadvantage is normal
Pt England School principal Russell Burt knew plenty of his students had bad teeth.
But it took a comprehensive check of new entrants at schools in the Tamaki area as part of the Welcome to School study to reveal the true picture.
By the time they were five-and-a-half, a quarter of new entrants either had or needed tooth extractions under general anaesthetic.
Burt said in a middle class family such a procedure would be considered extremely significant.
The fact it was so common in his school's area but not well understood showed how disadvantage "normalises things that ought not to be normal".
Other study findings included 36 per cent of new entrants being obese and a similar proportion overweight.
"It is normal in this community to be an unhealthy weight," the study's executive summary noted. "Many of these children are actually malnourished kids in big bodies."
Fair Care investigation
The Herald is investigating whether all New Zealanders are getting good healthcare when they really need it.
Our reports will uncover some of the worst problems in our health system and then look for solutions.
We also want to hear about your experience and ideas. Tell us your story: faircare@nzherald.co.nz
Stories published so far include:
• Very premature babies are less likely to be resuscitated if Māori, Pacific or Indian - and experts believe it likely that racial bias is partly to blame.
• Breast cancer patients are battling for access to life-prolonging drugs.
• A young girl lost sight while languishing on a waiting list, as the DHB involved warns pressure on services remains "very real and concerning".
• Half of South Auckland children sent for specialist care for serious skin conditions are declined an appointment.
• One in 10 people are now steered away from some Auckland emergency departments with a voucher for a nearby private clinic.