Coronavirus - Modelling Aspects Only

[johnhemming]

I think 5 million as the real number, is more realistic than 1 million. I

There was an opinion poll that concluded that about 20% of people think they have had it.


Part of post deleted to keep thread to modelling aspects, rather than personal experience. Edited by Zico - 5.29pm on 4th April, 2020

[alphab1]

#297721Unread postby zico » April 4th, 2020, 9:17 am
Updated figures for today are
41,903 positive cases and 4,313 deaths.
Daily figures are 3,735 new cases and 708 deaths.

The important figure is the new cases, which is down 17% on the previous few days total.
It's a daily increase of 9.8% (I used 10% in my model, so no need to update it).

This is welcome news, and hopefully tomorrow will bring another large percentage fall in new cases.


New cases do not represent new infections but new detections. They may include patients infected (say) 14 days ago and since then. There are possibly many more infected persons in the country not yet detected. I think comparing this figure 3735 for today's NEW cases with 4450 for yesterday (https://www.worldometers.info/coronavirus/country/uk/) does not tell us anything about the true spread of the infection.

On the other hand, if we could compare the number of new (net) number of hospital admissions with that of the previous day, and plot the chart we can have a real understanding of whether the effect of the virus is growing or subsiding. I have been unable to locate a source like worldometer giving this number along with the number of deaths.

Regards.

[dealtn]

#297721Unread postby zico » April 4th, 2020, 9:17 am
Updated figures for today are
41,903 positive cases and 4,313 deaths.
Daily figures are 3,735 new cases and 708 deaths.

The important figure is the new cases, which is down 17% on the previous few days total.
It's a daily increase of 9.8% (I used 10% in my model, so no need to update it).

This is welcome news, and hopefully tomorrow will bring another large percentage fall in new cases.


New cases do not represent new infections but new detections. They may include patients infected (say) 14 days ago and since then. There are possibly many more infected persons in the country not yet detected. I think comparing this figure 3735 for today's NEW cases with 4450 for yesterday (https://www.worldometers.info/coronavirus/country/uk/) does not tell us anything about the true spread of the infection.

On the other hand, if we could compare the number of new (net) number of hospital admissions with that of the previous day, and plot the chart we can have a real understanding of whether the effect of the virus is growing or subsiding. I have been unable to locate a source like worldometer giving this number along with the number of deaths.

Regards.

Well I think if there is nothing special about the methodology of detecting infections changing between the two days then you can infer "something" from it. If there are differences in sampling then you would need to be very careful to draw anything meaningful for sure, which the scientists might (the layman probably not).

Either way a single day's data, well the rate in change between two consecutive days, isn't enough statistically speaking to infer much, but should that become a trend it will be. Daily rates have fallen already and not meant a reversal, so at best it's those "green shoots" again.

[fca2019]

I modelled some forecast figures in excel and things do look bad in the uk. John H's point is interesting that 20% think they have had it. I don't think this is that puzzling. We kept flights open from high risk areas, allowed cheltenham with 250k punters to go ahead, and the kaiser chiefs outdoor concert, packed tube and public transport, BJ bragging about shaking everyone's hands, up until very recently. So inevitably uk is being hit hard. Hope green shoots happen soon but I doubt it will be next week.

[zico]

#297721Unread postby zico » April 4th, 2020, 9:17 am
Updated figures for today are
41,903 positive cases and 4,313 deaths.
Daily figures are 3,735 new cases and 708 deaths.

The important figure is the new cases, which is down 17% on the previous few days total.
It's a daily increase of 9.8% (I used 10% in my model, so no need to update it).

This is welcome news, and hopefully tomorrow will bring another large percentage fall in new cases.


New cases do not represent new infections but new detections. They may include patients infected (say) 14 days ago and since then. There are possibly many more infected persons in the country not yet detected. I think comparing this figure 3735 for today's NEW cases with 4450 for yesterday (https://www.worldometers.info/coronavirus/country/uk/) does not tell us anything about the true spread of the infection.

On the other hand, if we could compare the number of new (net) number of hospital admissions with that of the previous day, and plot the chart we can have a real understanding of whether the effect of the virus is growing or subsiding. I have been unable to locate a source like worldometer giving this number along with the number of deaths.

Regards.

Thanks for a useful line of thinking.
Yes, you're right that these are "new detections" not "new infections" and also the number of them is constrained by the lack of available testing resources. I'm assuming that "new cases" are actually "2nd stage cases" where people are being hospitalised. This seems a reasonable assumption because over 40% of tests are now positive, which indicates that in the general public, only people whose condition worsens are being tested before hospital treatment. The negative tests will almost certainly be on NHS workers, to check they are OK to return to work.

Your point could also help to explain why my model apparently has such a high "death rate" defined as the ratio of "detections" to "deaths". If the reported "detection" figures are only a percentage (say 20%) of infections, then my 54% "death rate" is consistent with a true death rate of around 11% (compared to 12% European stats reports for hospitalised patients). My model assumes a 10-day lagged relationship between "reported infections" and "reported deaths", so from a modelling point of view, it doesn't really matter what the reported infections figure covers as long as it has a consistent relationship to actual infections.

(If my model is correct, than even with sharply decreasing new "daily infections" the daily deaths figure will still increase for several days yet.)

[zico]

I modelled some forecast figures in excel and things do look bad in the uk. John H's point is interesting that 20% think they have had it.

Can you summarise how you have forecasted?
It's clear from today's briefing that London has been first and fastest to see the effects of the virus, so I wouldn't be surprised if the %infected is much higher in London & South-East than elsewhere in the country.

I've just thought of a way to estimate the proportion who have had the virus - what do you think of the following logic?

European stats show 30% of people getting the virus need hospitalisation.
Let's assume everyone hospitalised in the UK is getting the test, that's 42,000.
Add on 20% for people in care homes not hospitalised - another 8,400 gives 51,400 which is 30% of all cases with symptoms.
That gives 170,000 with symptoms.
Virus takes 5 days to show symptoms, another 7 days to develop to serious 2nd stage.
So the 170,000 were infected 12 days ago.
Virus spread doubles every 3 days, so multiply 170,000 x 2 x 2 x 2 x 2 = 1,360,000 who have the virus as of today - and will get mild or severe symptoms.

Of course the big unknown is % of people who've had it with no symptoms.
Let's assume that's 50% of all cases (I've seen that figure somewhere!), so 1,360,000 / 50% = 2.72 million people in the UK.

Comments and critiques welcome.

Edited 1 time because I thought of a possible way of estimating total numbers who've had the virus.

[Sorcery]

I modelled some forecast figures in excel and things do look bad in the uk. John H's point is interesting that 20% think they have had it.

Can you summarise how you have forecasted?
It's clear from today's briefing that London has been first and fastest to see the effects of the virus, so I wouldn't be surprised if the %infected is much higher in London & South-East than elsewhere in the country.

I've just thought of a way to estimate the proportion who have had the virus - what do you think of the following logic?

European stats show 30% of people getting the virus need hospitalisation.
Let's assume everyone hospitalised in the UK is getting the test, that's 42,000.
Add on 20% for people in care homes not hospitalised - another 8,400 gives 51,400 which is 30% of all cases with symptoms.
That gives 170,000 with symptoms.
Virus takes 5 days to show symptoms, another 7 days to develop to serious 2nd stage.
So the 170,000 were infected 12 days ago.
Virus spread doubles every 3 days, so multiply 170,000 x 2 x 2 x 2 x 2 = 1,360,000 who have the virus as of today - and will get mild or severe symptoms.

Of course the big unknown is % of people who've had it with no symptoms.
Let's assume that's 50% of all cases (I've seen that figure somewhere!), so 1,360,000 / 50% = 2.72 million people in the UK.

Comments and critiques welcome.

Edited 1 time because I thought of a possible way of estimating total numbers who've had the virus.

You may appreciate these studies from Nic Lewis :
https://judithcurry.com/2020/03/25/covi ... infection/
https://judithcurry.com/2020/04/01/impe ... to-add-up/

I especially liked his disussion about the case of the Diamond Princess cruise ship, a closed system where the virus ran wild for weeks and a case where everyone was tested on disembarkation. A huge petri dish.

[UncleEbenezer]

I especially liked his disussion about the case of the Diamond Princess cruise ship, a closed system where the virus ran wild for weeks and a case where everyone was tested on disembarkation. A huge petri dish.

A sample dominated by certain demographics unrepresentative of the population at large: noone poor or young goes on a cruise! And inexplicably keen to be cooped up for long periods in a confined space: prison for the rich?

I played with some models, but stopped when we started to hear from credible and better-informed sources, including Prof. Ferguson (who suggested infections might be in the 2 million ballpark when the official figure was a little over 20k) and David Spiegelhalter. Now I'm just waiting for the antibody test, from which we can get a much better idea if it's administered in a way that can gather data.

As for total infections, the more the better. If we're in the millions then we're on the way to population-level immunity and a no-longer-novel virus.

[AJC5001]

A sample dominated by certain demographics unrepresentative of the population at large: noone poor or young goes on a cruise!

What about the crew?

Adrian

[Sorcery]

I especially liked his disussion about the case of the Diamond Princess cruise ship, a closed system where the virus ran wild for weeks and a case where everyone was tested on disembarkation. A huge petri dish.

A sample dominated by certain demographics unrepresentative of the population at large: noone poor or young goes on a cruise! And inexplicably keen to be cooped up for long periods in a confined space: prison for the rich?

I played with some models, but stopped when we started to hear from credible and better-informed sources, including Prof. Ferguson (who suggested infections might be in the 2 million ballpark when the official figure was a little over 20k) and David Spiegelhalter. Now I'm just waiting for the antibody test, from which we can get a much better idea if it's administered in a way that can gather data.

As for total infections, the more the better. If we're in the millions then we're on the way to population-level immunity and a no-longer-novel virus.

If you had followed the links you would have found that he or the study was challenging corrected for age distribution. Just the simple stats that I worked out from the Diamond Princess were 19% infection rate (though it's possible had they been in quarantine for longer, then this might have risen) , 51% asymptomatic, 0.2% death of people in board (despite the old age bias) seem to be guestimates that are being realised.

[Itsallaguess]

With Italy and Spain being ahead of the UK on the infection-curves, we might be able to take some comfort from their own trajectories in terms of where and when we might start to turn corners in both the 'Daily new Cases' and 'Daily new Deaths' figures.

Looking at the charts below, we can see that both Italy and Spain saw a peak of 'Daily new Cases' (left hand charts) 11 days after their first day of full lock-down. That also tallies very closely with the 10-day peak in 'Daily new Cases' seen in the UK, followed by a trended decline from those 11-day/10-day points in all three countries, with it still being early days yet with regards to a potential UK trend, of course..

On the charts to the right of the 'Daily new Cases', we can also see the 'Daily new Deaths' graphs, and again we can see similarities between both the Italy and Spain charts. Italy have seen a peak of 'Daily new Deaths' 17-days after their first full day of lock-down, and we can see that Spain (currently..) show a peak of 'Daily new Deaths' 18-days later. Clearly it's early days for Spain in this regard, but the Italy trend from their 17-day peak of 'Daily new Deaths' is now quite a strong one..

When we look at the UK charts at the bottom of the screen-shot below, we can see that the projected 17-day/18-day peak of 'Daily new deaths' for the UK may well come around April 10th/11th.

Source for charts - https://www.worldometers.info/coronavirus/#countries



Cheers,

Itsallaguess

[bionichamster]

Death rate is the key to this, and the available data are very confusing.

The European Centre for Disease Prevention and Control ECDPC), Stockholm, 2020 gives a death rate for hospitalised cases of 12% which should be a whole lot more accurate than what comes out of my simple model.
However, the UK stats show 5,000 confirmed cases by 20th March and 1,000 deaths 7 days later (27th March) which gives a death rate of at least 20%.
Applying the ECDPC death rate to the highest daily new cases figure (4,300) would give daily deaths of 630, but UK daily deaths are already higher than that, and we only reached the 4,300 figure 4 days ago, so these figures shouldn't yet be translating into new deaths.
One possible explanation is that UK new cases are actually more severe hospitalisation cases than were previously seen in Europe.
It's puzzling.

https://www.ecdc.europa.eu/sites/defaul ... VID-19.pdf

Extract

Among all cases:Hospitalisation occurred in 30% (13 122of 43438) ofcasesreported from 17countries (median country-specific estimate,interquartile range(IQR):24%,11-41%)Severe illness(requiring ICU and/or respiratory support) accounted for 2 179 of 49 282 (4%) cases from 16 countries(median, IQR:3%, 2-8%).Among hospitalised cases:Severe illness was reported in 15% (1 894of 12 961) of hospitalised cases from 15countries (median, IQR: 16%, 10-24%).Death o

The big problem seems to be that every country is testing at different rates, and those rates are changing significantly as some countries (e.g. UK) are still ramping up testing from relatively low levels compared to others; and that 'ramping up' is at different rates (between countries) too. The rate at which testing increases is likely to be different to the increase in infected individuals too (i.e. not exponential). Basing a model on positive cases declared each in those circumstances is to say the least problematic! The uk death to cases ratio looks bad but is almost certainly exaggerated by a lower testing rate hiding many of the mild cases, as testing is likely significantly biased towards the more serious and hospitalised cases.
Even in high testing countries there is likely a bias towards testing hospitalised and more serious cases.

BH

[zico]

Iag, Many thanks for the graphs. I've adjusted my model now to use a 7-day lag and it gives much more sensible looking results, with a peak of around 1,000 deaths around 9th April. However, plugging in Italy's new cases profile for their days after their 20th March peak shows UK daily deaths will still be 80% of peak level for the 10 days after the UK peak, whereas Italy figures show a quicker drop after their peak day. Hopefully I'm wrong, and we follow the Italy and Spain trajectories for a faster decline in the daily death rates curve.

I expect that for all countries, when hospital workloads are at their peak, there will be an increase in % of care home deaths, as people in care homes will be much less likely to be considered for hospital treatment. (There is guidance to this effect already in several areas of the UK) These cases may not show up in the statistics until later on, so the current tabulations may underestimate these cases.

[zico]

Latest daily figures are grim - 5,903 new cases (32% higher than the previous peak). 621 deaths is lower than previous 2 days, but it's the new case increase that will affect future deaths.
Peak deaths now likely to be pushed back a couple of days, and be a higher figure.

[dealtn]

Latest daily figures are grim ...

I guess the issue we have now is consistency across daily numbers. If the methodology of testing is changing, such that more tests are happening, and amongst different groups, that introduces "noise" into the data that isn't obvious from a simple graph, say.

I don't have any data but say there are 20% more tests occurring than a few days ago, and a lot of those extra tests are of NHS staff who have been exposed to the virus through their patients, but not developed any symptoms themselves so continuing to work, then we might be "seeing" an uptick in asymptotic new cases, but still consistent with the virus being contained. These "new cases" might be "old cases". Detecting them is still helpful of course in preventing the spread, but with the downside of inconsistency in the data.

Still too early to tell.

[zico]

Latest daily figures are grim ...

I guess the issue we have now is consistency across daily numbers. If the methodology of testing is changing, such that more tests are happening, and amongst different groups, that introduces "noise" into the data that isn't obvious from a simple graph, say.

I don't have any data but say there are 20% more tests occurring than a few days ago, and a lot of those extra tests are of NHS staff who have been exposed to the virus through their patients, but not developed any symptoms themselves so continuing to work, then we might be "seeing" an uptick in asymptotic new cases, but still consistent with the virus being contained. These "new cases" might be "old cases". Detecting them is still helpful of course in preventing the spread, but with the downside of inconsistency in the data.

Still too early to tell.

I hope you're right.
Number of tests in last 3 days has been 10,590 then 9,406 then 12,334 (this being the most recent).
Percentage of positive tests has been 42%, 40%, 48% for the last 3 days (48% being the most recent).
Given the relationship between new cases and deaths, it's very clear that only a percentage of deaths from Covid-19 are being identified as "new cases" with the remaining cases presumably being determined from post-mortems.

From a statistical viewpoint, the 32% increase in new cases is extraordinary and very unexpected, given that the previous 4 days had seen an apparent stabilisation around a peak daily figure of around 4,300. A sudden big leap like this simply doesn't make statistical sense.
One possible explanation is that the daily testing figure has increased - a lot - to 12,334 (compared to 10,590 and 9,406 in the 2 previous days).
To try to adjust for the effects of increased numbers of tests, I've assumed the percentage of positive tests remained unchanged but only 10,590 had been tested today, the number of positive tests would have been 5,068 which is still bad news, but not as bad as today's stark headline figure of 5,903.

It seems counterintuitive, but as the government increases the number of daily tests (which is a good thing) the number of new positive cases will also go up (which looks like a bad thing, but actually it won't be, because there will be more new cases detected, not actually more new cases in reality). Hope this makes sense, happy to explain further if it doesn't.


Edited - formatting change to make the figures slightly clearer, and added possible explanation for today's huge jump in "new case" figure.

[johnhemming]

Latest daily figures are grim - 5,903 new cases (32% higher than the previous peak). 621 deaths is lower than previous 2 days, but it's the new case increase that will affect future deaths.
Peak deaths now likely to be pushed back a couple of days, and be a higher figure.

The new case rate is mainly affected by the number of tests.

[zico]

The new case rate is mainly affected by the number of tests.

Yes, the big increase in tests has (I think) made some difference.
My edited post (now above your post) and your post crossed in the ether just now, and I've addressed (I think) your point.

[Itsallaguess]

It seems counter-intuitive, but as the government increases the number of daily tests (which is a good thing) the number of new positive cases will also go up (which looks like a bad thing, but actually it won't be, because there will be more new cases detected, not actually more new cases in reality).

Hope this makes sense, happy to explain further if it doesn't.

Yep - that makes sense, and whilst a change in UK testing right now is going to play havoc with any attempts to 'overlay' infection-rates from other countries (see my earlier Italy and Spain charts, for instance), we can only hope that all we're really doing here with the latest UK 'Daily new Cases' figure is still measuring a 'dropping trend' (that would hopefully have continued dropping using the previous testing regime, and hence still aligning with our hoped-for inter-country alignment..), but simply capturing 'higher numbers' of that dropping trend as we do so..

Time will tell, of course...

Cheers,

Itsallaguess

[dspp]

It seems counter-intuitive, but as the government increases the number of daily tests (which is a good thing) the number of new positive cases will also go up (which looks like a bad thing, but actually it won't be, because there will be more new cases detected, not actually more new cases in reality).

Hope this makes sense, happy to explain further if it doesn't.

Yep - that makes sense, and whilst a change in UK testing right now is going to play havoc with any attempts to 'overlay' infection-rates from other countries (see my earlier Italy and Spain charts, for instance), we can only hope that all we're really doing here with the latest UK 'Daily new Cases' figure is still measuring a 'dropping trend' (that would hopefully have continued dropping using the previous testing regime, and hence still aligning with our hoped-for inter-country alignment..), but simply capturing 'higher numbers' of that dropping trend as we do so..

Time will tell, of course...

Cheers,

Itsallaguess

The cheapest way to observe if this is the case is to carry out relatively small numbers of randomised testing in the population. But you have to have excess test capacity to do this, over and above that reqd for hosp (with-cause) testing..