Why Boris Johnson's "moonshot" plan may not be a great idea.
A brief thread...

So our beloved PM has a vision of a "moonshot"; carrying out 10 million rapid COVID-19 tests per day, allowing those who test negative to resume "normal life" again. https://www.theguardian.com/world/2020/sep/09/boris-johnson-pinning-hopes-on-covid-testing-moonshot-leaked-papers-show

I'm going to leave aside the eye-watering cost, the practicalities of laboratory capacity, and the non-existence of the test; believe it or not, these are side issues.

Let's imagine that it's possible, using the tests that we have available today.

And for ease of maths (sorry, there may be some maths involved), let's say that we'll test 10 million people, with a population prevalence of 20 per 100,000 people.

Current swab testing is approximately 80% sensitive and 98% specific.

Roughly-speaking, the test will come back positive in 80% of true cases of COVID-19, whilst missing 20% of them.

Conversely, in healthy people the test will come back negative in 98% of cases, with 2% of healthy people getting a false positive result.

Not bad, right?

So in our population of 10 million people, we would expect there to be approximately 2000 people who have COVID-19, and 9,998,000 healthy people.

(That's our 0.02% prevalence, multiplied by 10 million people).

So how does our test fare?

2000 people have COVID-19.
The 80% sensitive test picks up 1600 of them, with 400 false negatives.

9,998,000 don't have COVID-19.
The 98% specific test correctly identifies about 9,800,000 as being clear. It gives a false positive result to almost 200,000 healthy people.

As you'll see, over 200,000 individuals will test positive, but with only 1600 of them being truly infected.

Of those with a positive result, 99.2% will be false-positives.

Nearly 200,000 healthy people being told to self-isolate unnecessarily. Don't forget, this is PER DAY.

(This is before we add in their households and family members, of course.)

Meanwhile, remember our false-negatives?

Every day, 400 people with COVID-19 are going to be falsely reassured, before being advised that it is safe, or even encouraged, to resume high-risk social contact. Go to the theatre, go on the Northern Line, go to Old Trafford.

So yeah, we can hope for a better test. But until a perfect test comes along, mass-testing our way back to normal life may not be as simple as it sounds.

I think that's the end.