Thread by @JamesWard73

It’s even better than that: it’s brilliant news. By my calcs, Hancock’s statistic (10% of people in hospital have had 2 doses of vaccine) implies the vaccine is having at least a 95% protective effect – and probably more like 98%, or maybe even higher. Let me explain… 1/n

https://twitter.com/BristOliver/status/1397868946234167297

To start with, we have to recognise that for this calculation, not all people are equal – some have more hospitalisation risk than others. So vaxxing those people will have more of an effect. Fortunately, we have targeted our vaccines on those with highest risk. 2/n

By applying some broad weighting factors to different JCVI categories, I can estimate that c. 71% of the (pre-vaccine) hospitalisation risk is in people who have now had a second dose of the vaccine, and a further 22% is in people who have had a first dose. 3/n

Let’s just focus on the 71% for a second, and assume (wrongly) that the other 29% haven’t had their risk reduced at all. Now for every 9 people hospitalised from that 29%, we’re seeing 1 person hospitalised from the 71%. So the relative risk is (1/71)/(9/29) = 4.5%. 4/n

So that means the vaccine is reducing the risk of hospitalisation by over 95%. Wow. But we ignored the effect of 1st doses, which will also be reducing the risk of hospitalisation to some extent – let’s assume that is ~80% reduction, consistent with previous PHE/PHS data. 5/n

This means that instead of the 9 patients without 2nd doses being split roughly as 7 with a first dose and 2 with no vaccine (which is what you’d expect if 1st doses had no effect), they will more likely be split roughly 3.5 with a first dose, and 5.5 with no vaccine. 6/n

(I should pause here to note here my sincere apologies to the patient that we just split in half). 7/n

But now we can recalculate our relative risk for second doses, comparing them to just those with no vaccine at all, and it works out to (1/71)/(5.5/7)= 1.8%. So a better estimate is that 2 doses of vaccine reduces risk of hospitalisation by 98%. 8/n

That’s not even the end. If some of the people in hospital only got their second dose in the last week or two, they may not have been fully protected. Which means that the observed risk reduction will be an under-estimate of the full effect, a few weeks after 2nd dose. 9/n

But hey, 98% protection against hospitalisation is still pretty good, I think we’d take that result. 10/end

@BristOliver @PaulMainwood @AdamJKucharski you might like this one