Covid 19 Omicron outbreak: Dr Andy Anglemyer - Demystifying maths behind vaccination status and hospitalisation

OPINION:

I have read a couple of recent articles questioning the effectiveness of the Covid-19 vaccine as the authors tried to make sense of reported cases and hospitalisations in light of what is known about vaccination status. Firstly, it is always a good idea to be cautious about our health decisions. And a healthy amount of scepticism about the information we receive from all sources is wise.

One of the primary goals of any immunisation programme is to reduce hospitalisation and death. With Covid-19, there is the added benefit of a reduction in transmission, but this varies greatly by time since vaccination, variant, number of doses received, etc. With Omicron, in addition to many infections we will see among unvaccinated individuals, there will be many, many breakthrough infections among vaccinated people, as well. But in the end, hospitalisations and death remain the main focus.

So, what do we know about hospitalisations and vaccination status in New Zealand at this point?

Currently in hospital in Auckland and Northland, 75 per cent of Covid-19 patients are fully vaccinated. This seems high especially considering only 22 per cent of Covid-19 hospitalisations are partially vaccinated or unvaccinated!

A vial of Pfizer vaccine. Photo / Sylvie Whinray

Why are so many more hospitalised Covid-19 patients fully vaccinated than unvaccinated if vaccines supposedly prevent hospitalisation?

This confuses a lot of people and it's very easy to misinterpret these data, which could lead to more scepticism among the already doubtful or untrusting. Perhaps we can sort out what's happening.

We know that only 5 per cent of the community (12 and over) is partially vaccinated or unvaccinated. If Covid-19 vaccinations didn't prevent any hospitalisations, then we'd expect only 5 per cent of the Covid-19 hospitalisations to be unvaccinated. But it's much higher, at least 22 per cent are partially vaccinated or unvaccinated. To quantify how much higher this 22 per cent is than expected (5 per cent), we divide the observed numbers by the expected, giving us 22 per cent divided by 5 per cent, which 4.4. This means Covid-19 hospitalisation rates among unvaccinated people are 4.4 times higher than expected if the vaccinations didn't prevent hospitalisation.

Similarly, we know that about 95 per cent of the community (12 and over) is fully vaccinated. If vaccinations didn't prevent hospitalisations at all, we'd expect 95 per cent of hospitalisations to be fully vaccinated. But the rate is much lower. Again, we divide the observed 75 per cent of hospitalisations that are fully vaccinated by the expected 95 per cent, which gives us 75 per cent divided by 95 per cent equals 0.79. That means Covid-19 hospitalisation rates among fully vaccinated are 0.79 times lower than expected if vaccination didn't prevent hospitalisation.

One of the primary goals of any immunisation programme is to reduce hospitalisation and death. Photo / NZME

And if want to compare the two groups, we simply take the ratio comparing unvaccinated with vaccinated: 4.4/0.79=5.6. That is, unvaccinated individuals have more than 5 times higher probability of Covid-19 hospitalisation than vaccinated individuals.

This exercise is not math magic or clever reinterpretation of data. It's standard maths. An honest scepticism is healthy, but perhaps understanding the standard maths behind the data can reassure us that vaccination is protecting us and our whānau from hospitalisation at a time when Omicron cases are increasing exponentially. Of course, the data are more nuanced as age, booster status, comorbidities can all have an impact on severe illness, and as the rate of boosters increases the differences in risk of hospitalisation between vaccinated and unvaccinated will widen. But without vaccinations at the levels we have, our healthcare system would already be under immense pressure, several weeks from Omicron's predicted peak.

• Dr Andy Anglemyer is an infectious diseases epidemiologist and senior research fellow at the University of Otago in the Department of Preventive and Social Medicine.