Scientists in the UK have figured out the exact ingredient in the Pfizer-BioNTech COVID-19 vaccine behind a few rare cases of anaphylaxis.

They're stressing the risk of the taking the vaccine is far outweighed by the dangers of contracting the virus, which has killed more than 3 million people worldwide in the past 14 months. 

There were three cases of anaphylaxis - a severe allergic reaction - on the first day of the UK vaccination campaign.

"This was alarming, as anaphylaxis to vaccines is rare - in the order of one case per million doses," according to a new case study published in journal Clinical & Experimental Allergy. Around 130,000 doses were given in the first week of the UK's rollout, according to government data. 

A study in March suggested anaphylaxis was far more common with mRNA vaccines - like those made by Pfizer and US company Moderna - than those based on older technology, but still nowhere near as dangerous as COVID-19 itself. 

Now scientists think they've worked out what's causing it - polyethylene glycol, or PEG.

"Allergy to PEG is rare but reactions can be severe or even fatal," they said.

PEG is commonly used in medications, laxatives and pharmaceutical products. Its link to anaphylaxis rests on the case of a 52-year-old woman who "developed throat constriction, cough then loss of consciousness immediately after receiving the Pfizer/BioNTech COVID-19 vaccine".

The woman had a history of allergies to "multiple products", including developing urticaria - red, itchy welts - after using shampoos, conditioners and shower gels containing PEG - though she never put two and two together before, not realising she was allergic. 

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Skin prick tests confirmed it was PEG causing the reaction. 

"COVID-19 vaccine anaphylaxis and PEG allergy are both rare, so proof of PEG as the cause in one case of vaccine anaphylaxis is important. However, it is important to emphasise that PEG allergy is rare and that COVID-19 vaccines remain safe."

There are no reports yet of any dying from anaphylaxis triggered by either mRNA vaccine. Those with a known allergy to PEG should avoid mRNA vaccines, the scientists said - noting both the AstraZeneca vaccine and Janssen/Johnson & Johnson vaccines don't contain it. 

The Pfizer vaccine is the one being rolled out in New Zealand. The Janssen vaccine is expected to be approved soon, and is currently with Medsafe. 

In separate research, another group of scientists say they've stumbled on a way people who had an allergic reaction to the first dose of an mRNA vaccine could still get a second.

Two US women with a history of allergies had a reaction to the first dose, but got the second in five smaller doses, delivered 15 minutes apart.

"Both patients responded well to the graded dosing protocol and reported no additional symptoms over the following 24 hours," the American College of Physicians said in a statement. 

Four weeks later both patients had antibodies against the virus, "suggesting vaccination was efficacious despite the graded dosing protocol". 

Their findings were published in journal Annals of Internal Medicine this week.