The media have again become fixated on the higher number of COVID-19 fully-vaccinated people in Irish hospitals and ICUs – but when you apply a little mathematics, it’s clear that it’s still the unvaccinated who are much more likely to end up needing a hospital than the vaccinated.
Mainstream and social media have been busy suggesting that the COVID-19 vaccine isn’t working because Ireland is seeing more vaccinated people in hospital than unvaccinated people.
Does this mean that the vaccine is not effective? Well, actually it doesn’t mean that – in fact, the numbers show the opposite – as we’d expect, the highest proportion of people needing advanced healthcare because of SARS-CoV-2 infection are unvaccinated.
But it does look a bit weird on the surface. Numbers never lie right? Well, they don’t, but they can mislead. Sometimes there’s more to the story than just the numbers. So let’s take a look at this particular story.
SIDENOTE: This pattern was also seen in Israel back in September. I highly recommend Professor Jeffrey S Morris’s breakdown of that event and his clarification the Simpson’s Paradox.
The claim that 54% of hospital patients are vaccinated
One article noted that 54% of 311 (168) hospitalised COVID-19 cases had been fully vaccinated. This leaves 143 (46%) who weren’t vaccinated. At face value, over half those in the hospital with COVID-19 were fully vaccinated. Why so many? Is this evidence that the vaccine isn’t working? Well, no it’s not because face value doesn’t work in this instance – it’s about some percentages.
We also know that as I write this 89% of the 5,011,500 Irish population  over the age of 12 years is fully vaccinated, meaning that 11% are not.
So using those population percentages – we’d expect that 89% of 311 people (~276) would be vaccinated – just by very crude maths and assuming no effect from vaccination. That would leave 35 people (which is 11% of 311) to be unvaccinated.
But hang on. That’s not how the numbers fell out in reality. What mathematical trickery are you trying to pull here Ian? It turns out this isn’t trickery – it’s a sign that there was some kind of an effect from vaccination. But what kind? A bad kind or a good kind?
There were 0.61 times as many vaccinated people in hospitals as we’d expect based on the percentage vaccinated. That’s fewer than expected.
But also, there were 4.0 times as many unvaccinated people in hospitals as we’d expect. That’s a lot more than expected if the vaccine isn’t working.
Extrapolating from this group, if you’re unvaccinated in Ireland you are 6.6 times more likely to be hospitalised with COVID-19 than your vaccinated friend. The vaccine protects from severe disease.
Only 6.6X times?
Frankly, I’d have expected to see an even bigger difference towards less representation by vaccinated people in hospitals. But there could be a couple of reasons why that isn’t so.
Vaccinations started taking off in Ireland in April. That’s now over six months ago and the combination of time plus the SARS-CoV-2 Delta variant of concern (and its subsequent “children”) may be important among those vaccinated who are now ending up in hospital. Boosters – or third doses – very much improve the immediate strength of the immune response to SARS-CoV-2.
The elderly – who make up the majority of those in hospitals in Ireland – may not develop as strong an immune response for as long as younger people.
It’s also important to keep expectations real – the vaccines do prevent a sizable chunk of transmission – but not all.
And trials show that they don’t prevent 100% of symptoms.
Assumptions and Limitations
I assumed this means the person had passed two weeks since their final vaccine dose. I included unvaccinated as those who had had no vaccine, had not completed their entire vaccine schedule or those for whom <14 days had passed since their final dose.
I’ve very crudely assumed that those in hospital with COVID-19 are a cross-section of the entire Irish population but they aren’t. About 60% of those in hospital were over 65 years of age. But this age group comprises only 15% of the total Irish population. 50% of all hospitalisations due to COVID-19 have been aged over 65 years. Vaccination in those aged over 65 years is at 94% and lower in younger age bands down to 78% in 18-44-year-old males. Those in the hospital will also likely be comprised of a higher proportion of people with underlying conditions.
- Israeli data: How can efficacy vs. severe disease be strong when 60% of hospitalized are vaccinated?
- Covid: 54% of hospital patients with virus are fully vaccinated
- Population and Migration Estimates, April 2021. Central Statistics Office, Ireland
- Surge in number of Covid-19 patients being treated in hospital
- Detailed Profile of Total Cases, Government of Ireland
- COVID-19 Vaccination Statistics Series 1
- Daily Vaccination Headline Figures, Government of Ireland
- Effectiveness of Covid-19 Vaccines against the B.1.617.2 (Delta) Variant
- COVID vaccine immunity is waning — how much does that matter?
- Protection Across Age Groups of BNT162b2 Vaccine Booster against Covid-19
- Science Brief: COVID-19 Vaccines and Vaccination