Thread by @ProfColinDavis

My TL is absolutely full of people who look at this graph and *still* want to say “the link is broken” or “the link has weakened” or “the jury is out”. So let me have another go at explaining a distinction that confuses some people (and is wilfully abused by others). [THREAD]

Of course vaccines have reduced the proportion of cases that lead to hospitalisation. I'm not denying that. I've published research about how important it is that we talk about the high efficacy of COVID vaccines, because this could increase vaccine uptake.bpspsychub.onlinelibrary.wiley.com/doi/full/10.11…

That research is published in the British Journal of Health Psychology (it's open access, so you can read it). bpspsychub.onlinelibrary.wiley.com/doi/full/10.11…

There's a short summary in the @ConversationUK . theconversation.com/vaccines-for-c…

So yes -- VACCINES WORK!

It’s hard for me to assign a charitable explanation to those who look at a graph titled “The link between cases and hospitalisation hasn’t been broken” and then say “he’s misrepresenting the data (he wants to deny the vaccine effect)”. But this is Twitter, I guess.

When we talk about the “link” between variables, we're talking about their correlation. We might also be talking about whether there's a causal relationship between the variables. Although correlation is not causation, there’s no doubt what we’re observing here IS a causal link.

In statistical terms, the link between two variables is measured by a correlation coefficient. The correlation between cases and hospitalisation is very close to 1 (which would be a perfect correlation). That is, the link HAS NOT been broken or even weakened.

A *different* metric, the regression coefficient, measures how big a change you expect to see in one variable, given a fixed change in the other. Some people who say the link has weakened mean that the regression coefficient has been reduced.

Both coefficients are relevant, but the correlation coefficient – the measure of the link – is especially critical when we’re dealing with exponential growth (it's frustrating to be so far into the pandemic and still having to explain exponential growth, but there we are).

Here's why the correlation is so important. It's very simple.

Cases double. Hospitalizations double.

Cases double. Hospitalizations double.

Cases double. Hospitalizations double.

etc. You can see the pattern.

“Yeah, yeah, but the ratio is so much lower”. Yes, it's lower (that’s the regression coefficient I mentioned above). Vaccines work. It’s also lower because a larger proportion of cases are in younger people (as a result of government policy).

Anyway, I am not at all dismissing the fact that a given rate of cases leads to fewer hospitalisations now than in January. The rate is currently running at 2% of cases. It’s varied a lot, but it’s reasonable to say that it's lower by a factor of about 4, relative to January.

(Watch out, BTW, for those who compute larger factors by ignoring the time lag between cases and hospitalisation, or claiming we’re currently at 600 admissions - it was 870 today).

“But hospitalisation rates are four times lower. That's massive!” A four-fold improvement is brilliant, and I’m grateful to the vaccine scientists. But beware of linear thinking. 4-fold is two doublings. Cases are doubling every 13 days, and have been for a couple of months.

A 4-fold reduction in the hospitalisation rate isn't much use if we just allow infections to reach 4x the previous peak.

Was the whole point of developing vaccines and jabbing most adults simply to allow us to have a few extra weeks of clubbing before the NHS is overwhelmed?

“Yeah but how do you know cases are going to keep rising?” One comment I’ve had today is that this kind of extrapolation is “no better than a horoscope”. Really??? Is the virus going to get tired?

“He’s a professor of psychology, he doesn’t understand statistics”. Oh dear. You’re going to upset a lot of people with that kind of talk. But I’m not going to take the time now to educate you about psychological science. psychologicalscience.org/members/apssc/…

But I might as well mention that I’m also a mathematical/computational modeller, and I’ve spent more time than any sensible person would looking at graphs showing exponential growth and decay. I literally wrote a PhD thesis about this.

While I’m being self-indulgent, here’s something I’ve thought about recently when reflecting on looking ahead. I used to play a lot of chess. I was what they call a child prodigy: Australian junior champion, state champ etc. Here’s me in Moscow playing Gary Kasparov when I was 17

Playing so much chess when I was a kid probably amplified some of my eccentricities. But one positive thing about it is that I got used to looking ahead. Or is that a positive? I'm not entirely sure.
#Covid #ClimateEmergency #SixthMassExtinction

It’s kind of amusing when you’re playing a rank amateur at chess, and you know that if you offer them your queen, they’ll snap it up, You watch them unable to contain their glee as they grab the queen, not realising that checkmate will inevitably follow in three moves time.

But it’s hard to feel the same way about Boris Johnson staring uncomprehendingly at the data and saying, “I don’t see any problem”. Yes, it’s laughable that he’s such a buffoon. But the huge human cost that we suffer, over and over again is just so heartbreaking.

Apologies for the long thread, which veered slightly away from where I'd originally intended.

In summary:

- the hospitalisation rate has decreased, but
- the link b/w cases and hospitalisation is still strong
- if we don't control transmission, the NHS will be overwhelmed