Coronavirus: Global Lockdown Underway Without Reliable Data
March 20th, 2020Via: Stat News:
The data collected so far on how many people are infected and how the epidemic is evolving are utterly unreliable. Given the limited testing to date, some deaths and probably the vast majority of infections due to SARS-CoV-2 are being missed. We don’t know if we are failing to capture infections by a factor of three or 300. Three months after the outbreak emerged, most countries, including the U.S., lack the ability to test a large number of people and no countries have reliable data on the prevalence of the virus in a representative random sample of the general population.
This evidence fiasco creates tremendous uncertainty about the risk of dying from Covid-19. Reported case fatality rates, like the official 3.4% rate from the World Health Organization, cause horror — and are meaningless. Patients who have been tested for SARS-CoV-2 are disproportionately those with severe symptoms and bad outcomes. As most health systems have limited testing capacity, selection bias may even worsen in the near future.
The one situation where an entire, closed population was tested was the Diamond Princess cruise ship and its quarantine passengers. The case fatality rate there was 1.0%, but this was a largely elderly population, in which the death rate from Covid-19 is much higher.
Projecting the Diamond Princess mortality rate onto the age structure of the U.S. population, the death rate among people infected with Covid-19 would be 0.125%. But since this estimate is based on extremely thin data — there were just seven deaths among the 700 infected passengers and crew — the real death rate could stretch from five times lower (0.025%) to five times higher (0.625%). It is also possible that some of the passengers who were infected might die later, and that tourists may have different frequencies of chronic diseases — a risk factor for worse outcomes with SARS-CoV-2 infection — than the general population. Adding these extra sources of uncertainty, reasonable estimates for the case fatality ratio in the general U.S. population vary from 0.05% to 1%.
That huge range markedly affects how severe the pandemic is and what should be done. A population-wide case fatality rate of 0.05% is lower than seasonal influenza. If that is the true rate, locking down the world with potentially tremendous social and financial consequences may be totally irrational. It’s like an elephant being attacked by a house cat. Frustrated and trying to avoid the cat, the elephant accidentally jumps off a cliff and dies.
Research Credit: SU
Nevermind for a while the Korean tests. In the UK they tested 72,818 persons as of March 21.
https://www.gov.uk/guidance/coronavirus-covid-19-information-for-the-public
Only 5,018 came out as positive, which suggests that tests were done on the population at large, not mainly on highly suspicious cases as elsewhere.
In effect, this allows to know how much the virus is present in the general population, and also how murderous it is. One could think that still, highly suspicious cases are overrepresented in this sample. But it does NOT seem to be the case.
Crunching the data with an infection fatality ratio inferred from the tests, the % of infected people who volunteer for testing is the same as that of volunteers in the whole population. For other infection fatality ratios, the correlation quickly disappears.
So here it is.
Infection fatality ratio = 0,05 %
Number of infected people in the UK : 4.7 million
As the UK health system has not collapsed yet, this does not account for surplus deaths from unavailable care, which may increase the infection fatality ratio by up to 6 times apparently.
Starting February 27, number of tests per day :
7690
8986
10483
11750
13525
13911
16659
18083
20338
21460
23513
24960
26261
27476
29764
32771
37746
40279
44105
50442
56221
61352
66976
72818
Positive results :
15
20
23
35
40
51
85
115
163
206
273
319
373
456
590
798
1140
1372
1543
1950
2626
3269
3983
5018
Deaths per day, starting March 5 :
1
1
0
1
2
1
2
2
1
10
14
20
16
33
40
33
I assumed the communicable period started 1 day before symptoms onset, which was followed by death 14 days later.
one must read :
infection fatality ratio = 0.05 %
Please note that the number of infected people in the UK is not a forecast. It’s the number of infection as of today.
By the way from the same data I was able to calculate that in the mean, each infected person contaminated about 6.5 others in the UK between the 6th and the 21st of March. It is not yet clear what is the variability in contagion.
Possibly I overestimated the length between the onset of symptoms and death, since people over 70 seem to die earlier : https://www.ncbi.nlm.nih.gov/pubmed/31994742/
Erratum : the above sets of number are mislabelled. The two first sets are not values per day, but accumulated values.
With a more sophisticated approach I recalculated the number of new contamination per infected person at 3.7.
Infection fatality ratio could be closer to 0.04 % if the time before death is shorter with old people.
I’m trying to find the real ratio of severe cases.
Wrong again. Now I see a 2.1 value for the number of new contamination per infected person.
Here’s the method :
I have mean value on five days for new contaminations (estimation), centered on the 26th of February. Let’s call it NC1. In approx. 4 days these people will become contagious, and this will last ten days.
So on the 11th of March (NC15), it’s the last day that NC1 people are contagious. It’s also the first day of contagion for the NC11 batch.
NC15 = NC1*R/10 + NC2*R/10 + … + NC11*R/10
with R the mean number of new contaminations per infected person, assuming these contaminations are uniformly dispersed during the contagious period.
R = 2,50
I have 6 days when I can calculate R, the mean value is 2,31.
/
I come back to an IFR of 0.05 % as old people have a slightly longer incubation period.
I now believe the risk of developping a severe or critical form is > 0.4 %, although this is based on a mix of UK and French data. It’s a young result as well.
@soothing, thanks.
You’re welcome.
I find that an IFR of 0.07 % for instance fits well to a 17-days delay between the beginning of the contagious period and death. I have not enough data for longer delays.
IFR is more stable and maintains correlation at 0.04 %, with a delay of 14 days.
By the way, for the length of the contagious period, I use this study : https://www.ncbi.nlm.nih.gov/pubmed/32146694
Instead of a uniform distribution of new contaminations along the contagious period, I gave weights to each day, according to this study : https://www.medrxiv.org/content/10.1101/2020.03.15.20036707v2
I also corrected a mistake in the equation (there was a day too many).
Results from the earliest days to the latest :
2,59
2,09
1,78
1,73
1,54
1,56
1,94
1,78
1,57
It has to come below 1 for the virus to be stopped.
Reminder : this is from UK data.
I think I applied circular reasoning : I inferred the IFR from the part of positive cases in tests, then I figured out that the % of infected people who were tested was the same as the that of the whole population.
This means that in fact, positive cases may be overrepresented in the data. This invalidates all my maths. The good news is that the IFR may actually be lower than 0,04 %.
Unless a good part of COVID-19 deaths are not reported, as they are attributed to other causes. This seems to be happening in Italy. In France, COVID-19 cases are sometimes recorded as simple flu cases, but since the flu season is over, it shows in the statistics. Consider this was a very hot winter in Europe as well.
I attempted an estimation of the maximum number of unrecorded deaths in France base on available evidence and informed opinion (75 %), and applied it to the British data.
The IFR stabilizes for a 17 to 18 days period between infection and death, at 0,07 %.
And sorry about that, but comment 14 is overly optimistic. It is the other way around. The fewer cases for a given number of deaths, the higher the risk.
Which means the 0.07 % IFR value is possibly way off the mark, even though UK tests after the 26th of February were supposed to be at random, conducted “at 11 hospitals and 100 general medical offices on people who have flu-like symptoms including a cough, plus shortness of breath and a fever”, which at that early phase did not have much more risks of being infected.
https://www.reuters.com/article/us-china-health-britain-idUSKCN20K1G1
https://www.bbc.com/news/uk-51641243
“Up to now, people have only been tested if they displayed symptoms having recently returned from one of the countries where there has been an outbreak, including China, South Korea and northern Italy.
Public Health England said it was now working with some hospitals and GP surgeries to conduct tests on some other patients.
In eight hospitals, patients in intensive care with severe respiratory infections will be tested for the virus.
In 100 GP surgeries, those coming in with milder flu-like symptoms – dry coughs, fever, shortness of breath – will be tested.”
Not quite at random then. Although the first death was announced only on the 5th of March, so critical care beds may not have been occupied by COVID-19 patients so much until then.
Mixing French and US data on visits to doctors for the flu and flu symptoms prevalence in the general population, and applying it to British test results, I find a rather large discrepancy (1.4 to 5.4 times) compared to raw test results.
I now have an IFR value that stabilizes when using a 17-day delay between infection and death. It ranges from 0.05 to 0.34 %. This last value accounts for possible miscategorized deaths.
Once again these infection fatality ratios end up being multiplied when the health system overloads.
Using Chinese data discriminated by age, internal consistency seems to fare better at 0.05 than 0.34 %.
The city of Vò experienced the first Italian covid-19 death, on the 23rd of February. The town was quarantined and the whole population of 3,300 was tested twice, once around the 6th of March, and another time about 9 days later.
The first round 89 persons were found positive, the second one 6. This way they managed to completely stop the epidemic there.
50 to 70 % of cases were asymptomatic or quasi-symptomatic. There were obviously more than 96 infections in Vò, because the delay between the death that happened there and the trials was longer than the median contagious period, for instance. Testing for antibodies would be the next logical step.
At a fatality rate of 1%, for a sample of 96, this means a maximum boundary of 2.62 % for the whole population (at 99 % confidence). Check it with your local statistician. Multiply by maybe 6-10 for maximum number of severe cases.
Re-interpolating Chinese data, I find that actually both IFR values are internally consistent, but then only if for the worst one there is no difference in the way British and French administrations report deaths, and if for the best one the French governement does not report 75 % of the COVID-19 deaths.
I have made a major revision to my argument. Trying to determine the representativity of UK test samples, I figured out that the 100 General Practitioners that administered the tests after the 26th of February must have not come met so many people with flu symptoms. In fact, the 20,000 or so flu-sick peope who went to the doctor every day at that point had to dispatch between about 7,000 such practitioners. This way I find an IFR of about 0.3 or 0.5 %.
Maybe 4 times that in case of complete collapse of the health system. The elderly are particularly at risk, as even with access to respirators they can be 10 times as impacted.
The great unknown in the maths then is the part of people with flu symptoms who don’t go to the doctor.
The great unknown in the maths then is the part of people with flu symptoms who don’t go to the doctor.
That’s where the orders of magnitude lower fatality rate comes in.
https://dnyuz.com/2020/03/26/stanford-medical-professors-covid-19-death-toll-estimates-may-be-orders-of-magnitude-too-high/
Well here’s the answer I believe : https://www.clinicaladvisor.com/home/web-exclusives/most-flu-cases-asymptomatic/
and now it’s 0.02 or 0.03 %
up to 0.15 % in case of health system failure, I should add.
If all the deaths are concentrated in a short time window, funeral ceremonies can be seriously shortened.
Also there’s the co-morbodity issue that I barely scratched, and good be a big component of it all considering who is most at risk from COVID-19.
What made me put it aside for a while is the death rate in the north of Italy for influenza / pneumonia type of illness, unknown of since 1969. Also it started at the very end of winter. And in France as I said, there’s been a resurgence of deaths from the same causes even as the season had already ended, meaning the peak was behind.
ONS data on England and Wales is based on death certificates that mention “deaths involving Covid-19”.
https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/bulletins/deathsregisteredweeklyinenglandandwalesprovisional/previousReleases
As it covers deaths outside of hospitals as well, one ends up having to multiply NHS numbers by 1.3.
In effect this implies an infection fatality ratio for SARS-CoV-2 of 0.03 % at usual hospital capacity. Bound to go up to maybe 0.15 % in case of total collapse of the health system. For people over 75 years old, the death rate in that case would be closer to 1 % (assuming the whole population gets infected).
I didn’t mention that the people in Vò are quite old.
http://demo.istat.it/bilmens2018gen/index.html
Deaths are 3 times more frequent than births there, compared to 1.2 times for Italy.
This means the proportion of asymptomatic or quasi-asymptomatic cases may be quite higher than 75 %.
In turn this implies a lower fatality rate and a more advanced propagation than I previously thought.
Death figures seem to be falling worldwide, even where lockdown measures were less strict (the Netherlands, Sweden).
https://www.worldometers.info/coronavirus/coronavirus-death-toll/
Could this be the impact of spring ?
https://www.medrxiv.org/content/10.1101/2020.03.16.20037168v1.full.pdf
Or is just about everyone in the northern hemisphere infected by now ?
I noticed another mistake in my math, but it is pretty informative. Using reductio ad absurdum, I was able to confirm that the UK tests were indeed quite representative. This brings the IFR to 0.06 % when using ONS data to truthify the NHS releases. The mortality rate quickly shot up in mid-March to stabilize at 0.17 % or so, suggesting this is the death rate when hospitals are packed.
The implication is that about 15 million persons were infected in the UK by early April. The propagation may soon stop though, as the reproduction number R is already below 1. I note that it started to fall way before the first repressive measures, suggesting an impact of ‘natural’ social distancing and/or the weather.
Here’s my formula :
R = NC13/(NC1*0,03 + NC2*0,03 + NC3*0,04 + NC4*0,05 + NC5*0,06 + NC6*0,10 + NC7*0,12 + NC8*0,23 + NC9*0,23 + NC10*0,12)
See comments 7 and 13 for explanations. I changed the time from infection to beginning of contagious period to 2 days.
And by the way the questions I asked in comment 31 are answered. It was just a ‘weekend effect’ in the recording of the data. Deaths tolls resumed their rise, as they did last week.
0.37 % fatality rate based on random sample testing for antibodies in a German town of about 12,000 people : https://www.spectator.co.uk/article/covid-antibody-test-in-german-town-shows-15-per-cent-infection-rate-0-4pc-death-rate
Possibly a sample of 500, not 1,000 : https://www.land.nrw/sites/default/files/asset/document/zwischenergebnis_covid19_case_study_gangelt_0.pdf
So it could really be between 0.29 and 0.50 % with 99 % confidence. Since the German health system is supposed to be well equiped, could this be the effect of inappropriate protocols ?
Here’s a quite detailed version of my reasoning on the fatality ratio and the proportion of asymptomatic cases.
Starting on February 27th, the British started “random” testing mainly through 100 general practitioners.
Since the length of medical consultations in the UK averages 9 minutes and 22 seconds, we may think that during an 8-hour day of work, these doctors saw about 50 people each.
We need to take a look at the data on people with flu symptoms. There’s a reporting service in the UK that relies on 360 general practitioners, of which there are about 7,000 in total. This allows to estimate that about 111,000 people went to see the doctor for a flu during week 9, ending on the 1st of March. Assuming it was about the same the following week (I guess you can find the data now, I didn’t bother to check), and allowing for a day of rest, this means 18,500 visits per day, of which 264 would have seen the GPs who were given the tests.
Let’s make it 300, considering the doctors worked overtime for the occasion.
The rest of the math is more precise.
On the 6th of March (a typical day in early March), 2,255 tests were given, 48 of which returned positive.
What’s very useful is that we know from a study linked to at comment 26 that for each British individual visiting the doctor for the flu, 19 of those who have it (and have the symptoms as well) do not.
Let’s call A the proportion of asymptomatic COVID-19 cases.
Since the contagious period has a median value of about 10 days, with 2 to 3 days before the onset of symptoms (median value again), I consider that 30 % of non-asymptomatic individuals in the contagious period are presymptomatic.
((48-A*48)*0.7/300)*18500*19*(1/(1-A)) = 48*0.7*18500*19*(A-A^2)/(A-A^2)/300
= 48*0.7*18500*19/300 = 39,368 people in Britain with COVID-19 in about the middle of the contagious period. http://oaps.umac.mo/bitstream/10692.1/47/1/OAPS_2014_FSS_001.pdf
The median length between symptoms onset and death is 14 days, so we need to look at COVID-19 deaths 11 days after March 6th to find the fatality ratio. Sixteen deaths occurred on the 17th, the average value on 3 days being 23. So the infection fatality ratio for people infected in early March was 0.06 %.
The case of Gangelt, discussed at comment 34, is about a town that was heavily impacted, in one of the European countries with the eldest population. Considering severe cases may be 4 times as frequent as deaths when health systems are not overloaded, it is not that inconsistent.
Anyway, it is now possible to infer the asymptomatic ratio.
From the 13th to the 23rd of March, 412 people died from COVID-19 in the UK. This translates into roughly 687,000 people in the contagious period on March 6th. This is about one hundredth of the population, so of the 2255 persons in the sample, about 23 should have been found positive if they were representative of the population at large.
110000*19 = 2,109,000
About 3 % of the British had symptoms of the flu at the time, so there is one person in these 23 that we should count as such.
The 25 in surplus should represent the other individuals with flu symptoms.
22/48 = 46 % of asymptomatic and presymptomatic cases, implying about 22.8 % of strictly asymptomatic cases.
It is consistent with this study : https://www.medrxiv.org/content/10.1101/2020.03.03.20028423v3
At first it seems inconsistent with the results from Vò, which indicated a minima of 50 % asymptomatic infections.
Check out this study though : https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3565270
Asymptomatic cases produce more asymptomatic cases than symptomatic cases do. Possibly in the range of 50 % (implying that when symptomatic cases are quarantined, you end up with a high ratio of asymptomatic cases).
I forgot to adjust NHS deaths counts from ONS data. So the fatality rate reaches 0.09 %, and asymptomatic cases 40 %, but this last estimate can vary widely for a small change in the initial proportion of positive cases.
And there’s yet another major error. I assumed that the asymptomatic ratio was the same in the sample and among all infected people. I managed to build equations with 3 variables : these two asymptomatic ratios and the fatality rate, and I get results on the order of 0,05 % to 0,07 % for asymptomatic ratios of 50 to 20 % respectively. In the second case it would mean sick people have less risks to be infected than others, which is not necessarily an unrealistic option considering competition for receptors and ressources among pathogens.