Scrutable

Zac Weinersmith (of the comic Saturday Morning Breakfast Cereal) with an explainer published on fivethirtyeight.com.

fivethirtyeight: A Comic Strip Tour Of The Wild World Of Pandemic Modeling

Thanks for this, it's an interesting overview.

Given the issues with data reliability and comparability, I'm surprised I've not seen more mention of hierarchical modelling.

For e.g. wildlife biologists, we might want to model a population in space and/or time. We do this by surveying, e.g. BoaF goes to the woods and counts all the birds he sees/hears.

But this data has inherent problems with reliability: I'll never count all the birds that are present, because I'll miss some. I might make an identification mistake, or double-count something, or whatever.

There are also comparability issues. For example, it's much easier to count all the birds in a grassy field than in a tangled thicket.

So you build a hierarchical model. Say you're interested in population size (N) at time t, and you have a bunch of counts (C) for the 10 previous time steps.

Now, you can model your counts directly, and get an estimate of C at time t, quite easily. You could then make an assumption about the (constant) relationship between C and N and call it a day.

But there might several variables influencing the relationship. As N goes up, the relative proportion counted might go down as detection facilities are overwhelmed. (This is true for birds - it's very hard to count flocks of 1000s of individuals accurately, and you typically underestimate. It also seems to be the case with COVID, as tests are limited and healthcare systems reach capacity). There's a variable lag between N and C, at least for deaths, with C depressed during the weekends. And so on.

So in hierarchical models you treat detection as a variable (p) to be estimated, and allow changes in C to be caused by either changes in N - the population of interest - or in p, the detection processes at play.

I've not seen this mentioned explicitly, but AFAICT people are mostly treating counts as if they were accurate reflections of N, and ignoring p. There may be good reasons for this (eg if the role of p is relatively small with an exponential increase in N), but given the importance of prioritising testing it seems to me that using the available data to understand what's going on with detection, and where the biggest uncertainties lie, might be valuable.

Disclaimer: I'm neither an epidemiologist nor a statistician.

I've seen yet another couple of preprints trying to model if the virus arrived in Italy some time before the official first cases, or trying to figure out how many cases are really circulating in the population.

This is probably a sign that there are actually a huge number of preprints being shared around a susceptible population on ResearchGate and medRxiv and we're only seeing a relatively small proportion of those on social media; it's clear a lot more testing is required but fairly early on the authorities couldn't keep up with "review and trace co-authors" and had to go to "let any moron with a spreadsheet shed any old sh.t all over the place".

We need some research on whether a substantial fraction of the articles published in January were already about covid-19 but we didn't realize it at the time. However it's probably the case that there are a significantly higher number of research articles published in the past month compared to the same period in previous years, despite the lockdown. Or maybe because of it.

shpalman wrote: ↑

Wed Apr 15, 2020 5:16 pm

I've seen yet another couple of preprints trying to model if the virus arrived in Italy some time before the official first cases, or trying to figure out how many cases are really circulating in the population.

This is probably a sign that there are actually a huge number of preprints being shared around a susceptible population on ResearchGate and medRxiv and we're only seeing a relatively small proportion of those on social media; it's clear a lot more testing is required but fairly early on the authorities couldn't keep up with "review and trace co-authors" and had to go to "let any moron with a spreadsheet shed any old sh.t all over the place".

We need some research on whether a substantial fraction of the articles published in January were already about covid-19 but we didn't realize it at the time. However it's probably the case that there are a significantly higher number of research articles published in the past month compared to the same period in previous years, despite the lockdown. Or maybe because of it.

Preprints aren't really publications though, they're by definition unreviewed* pre-publication drafts. I'm not sure what the authorities could do to keep crap out - if they start reviewing things they're not preprints anymore.

*I know they often have a comment section, but the contents of the MS doesn't need to have been checked by anyone independent.

Twitter conversation about the herd immunity and "four weeks behind Italy" b.llsh.t https://twitter.com/Kit_Yates_Maths/sta ... 77632?s=09

Some models from Singapore https://ddi.sutd.edu.sg/

A laughably sh.t paper, ostensibly from Manchester University but mostly written by two management consultants, has been getting attention for suggesting that half of the UK population is currently infected. (It was 26%, or 29%, they aren't quite sure, on the day it was accepted by the journal, but in the meantime if the model is right it would now be between 54% and 84%.) I blogged about it, but it had already appeared on the radar of several other people. It would deserve no more than a "commendable effort, but you do need to do a lot more reading" as a first-year undergraduate statistics project.

shpalman wrote: ↑

Sun Apr 26, 2020 12:50 pm

Twitter conversation about the herd immunity and "four weeks behind Italy" b.llsh.t https://twitter.com/Kit_Yates_Maths/sta ... 77632?s=09

“Nice” to see someone referencing the pillocks from plandemic.

Perhaps herd immunity achievable with just 20% infected. Paper is here (though it's "yet to be peer-reviewed").

Brightonian wrote: ↑

Fri Jul 17, 2020 9:24 am

Perhaps herd immunity achievable with just 20% infected. Paper is here (though it's "yet to be peer-reviewed").

More from Sunetra Gupta who was suggesting in March that perhaps 50% of the population had already been infected at that point. Proved wrong by serology studies showing that even by late May only 17% of people in London, and 5% of the overall population, had been infected.

There are interesting ways to play with herd immunity.

For example, if bus drivers and NHS workers have had it and are immune that's a huge chunk of potential super-spreaders out of the equation, while uninfected couples working from home would be super-under-spreaders. It's no coincidence London had the worst first wave, because London has many more potential super-spreading possibilities.

It's not unreasonable to assume the first wave was biased towards health workers, gregarious people and others who need to have loads of daily contacts with people. While the last wave will be biased towards the section of the population who have low social contact. The basic maths equation might give 67% for herd immunity, but a better model would adjust for different population segments, taking it down to say 50%.

I bet these effects have far bigger impact on herd immunity than stuff about immunity from cold coronoviruses. But this segmentation will only kick in at, say, 30% and doesn't really matter while we are still at 10%.

lpm wrote: ↑

Fri Jul 17, 2020 10:50 am

There are interesting ways to play with herd immunity.

For example, if bus drivers and NHS workers have had it and are immune that's a huge chunk of potential super-spreaders out of the equation, while uninfected couples working from home would be super-under-spreaders. It's no coincidence London had the worst first wave, because London has many more potential super-spreading possibilities.

It's not unreasonable to assume the first wave was biased towards health workers, gregarious people and others who need to have loads of daily contacts with people. While the last wave will be biased towards the section of the population who have low social contact. The basic maths equation might give 67% for herd immunity, but a better model would adjust for different population segments, taking it down to say 50%.

I bet these effects have far bigger impact on herd immunity than stuff about immunity from cold coronoviruses. But this segmentation will only kick in at, say, 30% and doesn't really matter while we are still at 10%.

I dont think so. People with fewer social contacts would still spread the disease, but more slowly. The only way you are going to bring down the rate of herd immunity is if a significant proportion of the population has no contact at all while someone is contagious.

It's easy to prove with maths?

A virus has R=4. Using the 1-1/R thing implies herd immunity at 75%.

But half the population has blue eyes, half brown. The disease is more infectious for blues. They have R=6, browns have R=2, giving the population average of R=4.

First wave burns through 20% of the population. But not evenly - 30% of blue eyes get it, 10% of brown eyes. Of the 80% of the population still at risk, 35% are blue and 45% brown.

The average R falls from 3 to 2.875, if my calculator worked correctly. Now 1-1/R is 65% instead of 75%.

In the second and third waves, the virus keeps burning through the blue eye population, until there's enough herd immunity for them - while brown eyes will make up the majority of the never infected by the time the virus burns out.

In the real world, nurses will have been both catchers and givers of the virus, so them getting immunity over time has a far bigger impact on herd immunity than an average person getting immune. When it comes to handing out limited numbers of vaccine, you'd start with super-spreaders if you wanted to slow the spread, rather than isolated elderly people.

lpm wrote: ↑

Fri Jul 17, 2020 1:41 pm

It's easy to prove with maths?

A virus has R=4. Using the 1-1/R thing implies herd immunity at 75%.

But half the population has blue eyes, half brown. The disease is more infectious for blues. They have R=6, browns have R=2, giving the population average of R=4.

First wave burns through 20% of the population. But not evenly - 30% of blue eyes get it, 10% of brown eyes. Of the 80% of the population still at risk, 35% are blue and 45% brown.

The average R falls from 3 to 2.875, if my calculator worked correctly. Now 1-1/R is 65% instead of 75%.

In the second and third waves, the virus keeps burning through the blue eye population, until there's enough herd immunity for them - while brown eyes will make up the majority of the never infected by the time the virus burns out.

In the real world, nurses will have been both catchers and givers of the virus, so them getting immunity over time has a far bigger impact on herd immunity than an average person getting immune. When it comes to handing out limited numbers of vaccine, you'd start with super-spreaders if you wanted to slow the spread, rather than isolated elderly people.

Yeah, but half of people aren't superspreaders, they wouldn't be super if that was the case, they'd be normal. If only a few percent are super, R isn't going to change very much if you give them special treatment, so the herd immunity threshold won't change much either.

The maths still works if you do a range, from orgy enthusiasts at R=100 to lighthouse keepers at R=0. The population made immune by the first wave is never going to be a random sample.

lpm wrote: ↑

Fri Jul 17, 2020 3:59 pm

The maths still works if you do a range, from orgy enthusiasts at R=100 to lighthouse keepers at R=0. The population made immune by the first wave is never going to be a random sample.

I don't think your maths is wrong. Just the example you chose over eggs the effect somewhat. For example, if was going to be in charge of distributing a vaccine that will take a year to roll out, those who are riskier in terms of spreading would be close to the top of the list, using pretty much the same reasoning as you. But while every little helps, outside of a vaccine to see a large drop in R, I reckon you need to lower the contact that everyone has with everyone else.

If the EU or US get a vaccine, and they decide to give the idiots in Britain 100,000 doses, where do you use them?

As you say, I think the maths would show to use them on NHS super-spreaders, not vulnerable elderly, because you save more lives of the vulnerable elderly by knocking back R. You address the fiercest bit of the exponential, so that one dose prevents a dozen other infections in a chain.

But I'm not sure what the equations actually look like.

lpm wrote: ↑

Fri Jul 17, 2020 6:51 pm

But I'm not sure what the equations actually look like.

In the UK, the equation will look something like vaccine = risk + number of contacts. If that doesn't make much sense to you, don't worry - Boris Johnson will explain all the details to you in a news briefing.

Behind the scenes, special advisor Dominic Cummings will employ a donor's brother's company some of the country's finest minds to run the numbers, and the lowest-bidding private sector partner to handle distribution. The numbers indicate that the 100,000 vaccines should go to the 90,000 wealthiest people/incorporated entities in the country, a strategy lead by the science of trickle-down immunity.

Of the 80,000 self-administered home vaccination kits sent out under G4S's able stewardship, at least 70,000 will arrive at the intended recipient (at a best guess - the data isn't recorded), many of which were registered addresses in dodgy off-shore tax havens.