If populations are highly vaccinated, we'd expect a higher proportion of future cases to have been previously vaccinated (because by definition, there aren't as many non-vaccinated people around to be infected). But what sort of numbers should we expect? A short thread... 1/
In above question, there are a lot of things happening conditional on other things happening (e.g. probability cases have been vaccinated), which means we can use Bayes rule (en.wikipedia.org/wiki/Bayes%27_…) to work out the proportion of cases that we'd expect to have been vaccinated. 2/
If we want to know the probability of event A given event B, or P(A|B) for short, we can calculate this as

P(A|B) = P(B|A) P(A)/ P(B)

There are a couple more mathsy tweets coming up, so hold on as then we'll get back to the real-life implications. 3/
Applying the above to our vaccine question, we therefore have:

P(vaccinated | case) = P(case | vaccinated) x P(vaccinated) / P(case)

which is equivalent to

P(vaccinated | case) = (1–V) x P(vaccinated)/P(not protected)

where V is vaccine effectiveness. 4/
If we write out the ways in which we could get P(not protected), we end up with below equation (I've labelled the terms on the bottom of the fraction to make it clearer where these come from): 5/
Now we have something we can apply to real-life situations, because can measure many of these things. For example, if 60% of a population have been vaccinated, and vaccine is 80% effective, above means we'd expect (1-0.8)x0.6/(1-0.6x0.8)= 23% of cases to have been vaccinated. 6/
This is an important result, because if cases appear among vaccinated individuals, many people's intuitive response is to ask 'surely the vaccine can't be that effective?' The answer: it may well be effective, just in a highly vaccinated population e.g. 7/
We can also flip the above equation around, which allows us to use data on % cases vaccinated and % vaccinated to get a rough estimate of vaccine effectiveness:

In short: Bayes rule is very useful, and case/vaccine patterns in highly vaccinated populations don't always do what you may assume. 9/9

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More from @AdamJKucharski

6 Apr
The debate around tracking infection/vaccine status for events is reminiscent of last year’s debate around privacy & contact tracing apps. Ultimately, the better countries' ability to track where infection is/isn’t, the lower their COVID risk will be. 1/
If people don’t want to collect/use data in this way, they need to accept the trade off will be a higher COVID risk in the community (or more disruptive measures to prevent that risk). 2/
Many countries have implicitly chosen to introduce stay-at-home orders or live with higher numbers of cases rather than use detailed surveillance (e.g. to identify infections linked to superspreading events or enforce quarantine). 3/
Read 4 tweets
24 Mar
This is an interesting perspective on Taiwan (& glad it mentions data/privacy), although I'd like to see more references to what local officials were actually saying about approach in real-time, rather than what UK-based researchers later say it was: theguardian.com/world/2021/mar… 1/
E.g. from April 2020: "Covid-19 is becoming flu-like. It means that since it is highly contagious with many mild or asymptomatic cases, and can be transmitted through droplets and contaminated areas, we won’t get rid of this virus totally." telegraph.co.uk/global-health/… 2/
Taiwan has implemented several innovative, effective measures against COVID-19, but it will harm our ability to plan for the next pandemic if we don't look fully at how countries were interpreting - and acting on - available evidence in real-time. 3/
Read 4 tweets
16 Mar
Is “we couldn’t have predicted the emergence of B117” a scientifically accurate statement? 1/
I’d argue it depends whether statement is interpreted in general or specific terms. “We couldn’t have predicted the possibility of a phenotypically distinct SARS-CoV-2 variant” is clearly inaccurate (given some adapation would have been involved in its original emergence)... 2/
...but “we couldn’t have predicted a variant emerging when it did in autumn 2020 with B117’s specific characteristics” is entirely reasonable (especially as our knowledge of its characteristics is still developing). 3/
Read 4 tweets
11 Mar
Slogans aside, there are three broad approaches to COVID countries can take from now on:
A. An R<<1 approach
B. An R<1 approach
C. An R>1 approach

Let's break them down... 1/
A. An R<<1 approach means keeping R as low as possible with stringent measures until no local transmission. E.g. this is what Auckland and Melbourne did recently in response to a handful of new cases. 2/
B. An R<1 approach means keeping epidemic declining, although transmission may still continue for a long time as measures are relaxed. As coverage increases, vaccination could also 'buy' some additional reduction in R & allow more reopening under such an approach. 3/
Read 5 tweets
1 Mar
What could happen next with novel variants like P.1 in the UK? There are four possible scenarios. A short thread with some thoughts... 1/
Scenario A: R<1 for both dominant B.1.1.7 variant and other variants of concern like P.1. This is likely situation we're currently in, but staying there is conditional on slow relaxation of control & substantial reduction in infectiousness via vaccines. 2/
However, even if R<1 for a novel variant, there could still be a lot of cases to come before outbreak ends, depending on value of R: 3/
Read 9 tweets
14 Feb
I sometimes see people making the mistaken assumption that once a group that make up X% of COVID hospitalisations/deaths are vaccinated, it will reduce hospitalisations/deaths by the same %, even if control measures are lifted. There are two main problems with this... 1/
First, there is a trade off between level of infection in the population and risk reduction through vaccination. Disease outcomes (e.g. hospitalisations/deaths) can broken down into the following: new infections x average-risk-per-infection... 2/
If we remove 50% of the hospitalisation risk within a population through vaccination, for example, but have a large increase in level of infection, it could mean no reduction (or even an increase) in overall hospitalisations... 3/
Read 5 tweets

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