Thread by @ProfDFrancis

As a distraction from Corona stress, let's have a short tweetorial.

OK I lied. Corona may sneak in a bit.

We see lots of arguing back and forth about

(a) Why are WHO lying about mortality rates?

(b) Why is rate higher in country X than Y?

(c) What is the real truth?

Freya will remember that when she was with us at ORBITA HQ she asked me about this graph, which is the most commonly shown graph in talks about Aortic Stenosis. "It's a bit funny, isn't it? Or am I going mad?"

What is the mortality of this condition, as shown on this graph?

Why?

Mortality of a condition depends far more on the denominator than you think.

If we recruited for a study of dandruff in the same place that Ross & Braunwald did their recruitment, that too would be confirmed as universally fatal.

Korea has an unusually low mortality rate from COVID.

Glad to know that angiography cures aortic stenosis. This takes the sting out of ISCHEMIA and ORBITA.

Glad to know that angiography cures aortic stenosis. This takes the sting out of ISCHEMIA and ORBITA.

Meanwhile in Iran, the disease seems far more deadly.

Could this be a contributor to higher mortality?

Does having kissing as part of routine social greeting increase the case fatality rate of Covid?

Does having kissing as part of routine social greeting, during an outbreak of Covid, cause a larger number of people to die from Covid?

I'll give it some time for people to catch up to here. Back later today!

OK there are three things.

On top, the number of people who die

On the bottom, the denominator number of people.

Which could be:

All the people in the country

All the people who show up at hospital with suspected COVID

All the people who get tested for COVID and are positive

or many other possibilities

Side-bar.

Someone just sent me this. I've never seen this presenter before but apparently it was an impromptu reaction to the Genius-in-Chief.

I vote for this guy to be President. Or that Doctor chappie. Or indeed anyone else.

mediamatters.org/jake-tapper/cn…

Top divided by bottom, gives the ratio.

If the bottom is "all the cases of Covid", then the ratio is the "case fatality rate of Covid".

What do you need to have to be a case of Covid?

Exactly. I don't know either.

Poor Matt Daniels. MD and PhD. But yet so trusting.

(going back to aortic stenosis)

At the average age at death, roughly what proportion of people should be dead?

In the words of David Brown, "Let's go through this again."

If I was average height, and everyone got ranked by height, where would I expect to be in the line of people?

.

OK good. Sorry I feel like this Fauci guy. Biting his own tongue off, to stop himself berating the Dear Leader as an imbecile.

https://twitter.com/i/status/1241164801235181568

Anyway, back to top-numbers and bottom-numbers in the fraction.

The answer to the question of "what does it take to be a case of Covid" is ....

I don't know.

Use what you like, but bear in mind that you have used what you like.

Thanks to the thousands of people who paid up enthusiastically to volunteer for the wonderful Diamond Princess experiment, where large numbers of people travelled together on an ocean liner with Covid, we have some systematic data.

There is this beautiful paper, which is a preprint that they have printed on Github! Amazing.

Which contains this wonderful table of all-you-can-eat data

EVERYONE on the cruiseliner was tested.

This is a unique dataset.

In the Cruseliner, in the under 30's, what proportion of people WITH the VIRUS, had SYMPTOMS?

You can see why the world is going to hell in a handbasket.

A 7 votes, the MAJORITY are unable to make sense of a table.

No wonder the Great Covfefe is the leader of the free world. It's not his fault. He is just a random loon. It is our fault for electing him.

OK at 9 votes, the people with a brain have squeaked into a marginal majority position. Maybe there is yet hope.

Now look at the "deaths" column.

Note that scientists are careful people. If someone left the ship and then dropped dead, they wouldn't know. That's why they entitled that column "Observed deaths on ship".

If you were 70-79 years old, and you had the virus while on the ship, what is the probability that would die?

Sorry. Erratum for sticklers who will object that if I am addressing a person, that person must necessarily not have died.

"For a random 70-79 year old from the ship who had the virus, what was the probability that they would die on that ship?"

What about for an under-40 year old?

Meanwhile, if you HAVE the virus, what is the probability that you will show symptoms (assuming you were drawn at random from all people on the ship).

Pick the closest to the correct answer.

Assuming that this is probability of being symptomatic applies broadly across everyone, by what scale factor will the "number of people with Covid" vary by whether you count only symptomatic people or asymptomatic too?

Now an admission. I ignored this chappie @GlennGalen, thinking he was making some subtle wisecrack about Instant Flow Reserve versus Coronary Flow Reserve.

But in a flash of insight, which I am famous for having when my research fellows Whatsapp me a Wikipedia link, I have realised that he is saying that CASE and INFECTION are different.

CASE means you have symptoms of some sort at least.

INFECTION just means virus present.

There is an Infection Fatality Rate, where the denominator (bottom number) is everyone who has the virus. You can only tell that if you can capture everyone with it, i.e. test asymptomatic people systematically.

Generally, we can't. There aren't enough test kits.

We have the Diamond Princess data of 7 deaths amongst 619 people (from the tablet above), who were typically in the 60-80 age range, which comes to about

That was for just anyone who has the Covid VIRUS: the INFECTION fatality rate.

Now for the CASE fatality rate, we use only the people who has symptoms, i.e. Covid DISEASE.

(Yes I know that the "vi" in means Virus and "d" means Disease, so it is redundant. But it is clear.)

In the Diamond Princess analysis, using only those who have the DISEASE, i.e. Cases, what is the Case Fatality Rate?

And of course we could be even more restrictive if we wanted.

In this Lancet paper, for example ...

thelancet.com/action/showPdf…

... is this Table 2, pointed out to me by my colleague Dr Prapa Kanagaratnam,

It covers all patients ADMITTED TO HOSPITAL with Covid disease. What proportion died?

Why is that?

So there you have it. Thanks to Glenn Galen for straightening me out ... I mean coincidentally mentioning something that immediately preceded my own brilliant flash of insight.

Even in a broad age group, you can get fractions from as low as 1% (by testing absolutely everyone) or as high as 28% (by only counting people so sick they have to be hospitalized even in a crisis of bed shortage).

The denominator matters. Bigly.

Moreover the age matters a great deal too. In the Diamond Princess ...

.. the upper HALF of the patients by age had what proportion of the deaths?

Also thanks to @TheSuperHak my statistical friend, and others, for pointing out that the numerator is uncertain too.

Do we count only people who die within X days?

Do we count people who die with Covid + (say) ST elevation myocardial infarction?

Do we count people who die *ever*? (In which case it is 100%, but is also 100% for dandruff)

Fortunately this is an acute infectious disease and so there is a natural duration of followup, i.e. "until they seem to be back to normal".

HOWEVER

If you stand in a hospital and count all the people you have ever seen with Covid, and all the people that have died with Covid, that is not quite a fair comparison:

The people still in hospital with Covid might still die, so if we put them in the bottom of the fraction, they are guaranteed to not contribute fairly to the top number, i.e. we will get a falsely low result.

So the answer is to look back in time.

... by longer than a fairly long hospital admission with covid, and then say, "Of the people we had seen up to that time point, what proportion have now died?"

Obviously this has a weakness:

So to counter that weakness, the clever epidemiologists have a way of allowing for the people that have been in hospital for only limited time, to contribute to our knowledge of the early part of the disease.

By this and other manoeuvres, they can get less-biased answers.

Thank you, it's lunch time here in UK.

I leave you with a pic of the author of the Github preprint, Tim Russell of London School of Hygiene & Tropical Medicine.

Looks like a fun group to work in! They don't have @rallamee saying "no" to cholesterol, carbs, and other good stuff

If your thread stops here, click this link:

https://twitter.com/ProfDFrancis/status/1241342683018338307

Appendix, some answers to questions that people seem to find a bit hard. Look at what people said here.

I was making a simple point.

The NUMBER of people infected, and the PROBABILITY OF DYING FOR THE PEOPLE WHO DO GET INFECTED, are different things.

In principle they are independent.

In other words, if I could halve the number of people with coronavirus in the UK today, I would decrease the NUMBER of cases but not change the FATALITY RATE.

So the answer I was looking for is that:

Kissing increases the NUMBER of cases, but does not increase the CASE FATALITY RATE.

Similarly it increases the number of infections, but does not increase the infection fatality rate.

However people have pointed out something more subtle, that is not a mathematical feature but a (very important) real-world feature.

If we have too many people ill *at the same time* we exceed the peak capacity of healthcare resources, which means some people may die not because the disease was too severe to be survivable, but because it was too severe to be survivable _without sophisticated care_.

So if you picked "Iranians kissing increased their case fatality rate", I will forgive you, as I will generously assume you were making the subtle point about what happens if we don't Flatten The Curve.

Now a genuine question to which I don't know the answer. I have been telling off the ORBITA-HQ fellows when they talk about the "Normal distribution" of the infection time course.

I of course ridicule them. However I am starting to find myself thinking it *does* look like a Normal distribution.

This is curious. Normal distributions arise when we randomly and independently add/subtract things.

So this appearance of the graph must be a coincidence.

I suppose the rising phase has to have an exponential rise and then a plateau, i.e. a sigmoid, so that explains the left half.

But I can't work out why the right half has any obligation to be sigmoid.

And I *definitely* don't know why the right half can know how to be a mirror of the left half [i.e. to be spread over a similar time period].

Maybe I am overthinking. Maybe it's just that we mentally try to map any shape that looks like that onto a Normal.

Comments welcome.

Yes, vaguely.

Aha! The ORBITA-HQ PhD Panel has sent me the answer.

Apparently they have this thing called "Google", and it has all the answers for everything.

Short answer:

It isn't a Normal distribution, it just looks like it.

In an epidemic, one can model the population as three groups.

Susceptible people (everyone starts here)
Infected/infectious people
Recovered-or-died people

You can only move forward through the groups. (i.e. this model assumes you can only get it once.)

"OK here comes the science bit. Concentrate."

How many people move from "Susceptible" to "Infected" is roughly proportional to the number of infected people, and to the number of susceptible people.

i.e. you need to have someone with it, bumping in to someone susceptible.

And how many people move from "Infected" to "Recovered/dead" today is roughly proportional to the number of people in the "Infected" category today.

It's not really a random decay like this, but because the disease lasts varying durations in different people, it is a bit like it

And when you run a simulation with two features:

Move people from S to I in proportion to S and I,

Move people from I to R in proportion to I,

... you get this:

The green thing is the number of cases CURRENTLY infected.

Meanwhile plots of countries' NEW cases are in effect the slope of the first curve (blue). Because the blue curve is vaguely sigmoidal, its slope *vaguely* Normal.

But the blue curve is not a symmetrical shape: it's slope eases away more slowly than it develops.

So that, in short, is why numbers of NEW cases tend to look vaguely Normal.

It's not really Normal. Our brains are so used to looking for normality that we squish things mentally into a Normal template.

It's like the Badlands Indian, a rock formation that from a satellite looks like a Native-American wearing iPhone earphones.

No i did not photo shop it.

google.com/maps/place/50%…

Stefan Harb is completely right.

I was only saying "subtle" to cover up my failure to recognise it!

And @MrWBond is wise to point out that the Diamond Princess may not be the *only* confined group that had systematic testing and scientific publication of results.

3 reservations on relying on Kirkland

1. Was it selected for the headlines because of an unusually high death rate?

2. People were already needing nursing home.

3. Has anyone seen a scientific publication of it? Especially age stratification?

Comments welcome.