Novel Coronavirus (2019-nCoV) fatality rate: WHO and media vs logic and mathematics

On January 29th, 2020 Dr. Michael Ryan, Executive Director of World Health Organization (WHO) on a press conference said that Novel Coronavirus (2019-nCoV) fatality rate is 2%.

During the following days many (if not all) big media corporation published articles with the following statements:

“The mortality rate for the new coronavirus is about 2.1%, currently far lower than the 9.6% of SARS.” BBC

“With a fatality rate of around 2%, which experts agree appears to be the current level for the virus” CNN

“Health experts say they are encouraged by the steady rise in the number of recoveries. They take it as evidence that the treatments meted out have been effective and that the virus does not appear to be as deadly as SARS. SARS had a mortality rate of 9.6 percent, and about 2 percent of those reported to have been infected with the new coronavirus have died.” The New York Times

“The Wuhan coronavirus seems to have a low fatality rate, and most patients make full recoveries.” Business Insider

“The number of confirmed cases and deaths indicate that it is around 2 percent, significantly lower than SARS’ 10 percent.” The Harvard Gazette

What is wrong with all this statements? I believe that they are false and misleading.

How this 2% figure has been calculated?

It’s so called ‘case fatality rate’ (CFR) = total number of deaths known by today divided divided by total number of known cases confirmed by today.

CFR=10% for SARS 2003 epidemic means that 10% of confirmed cases died.
What does CFR=2% means for Novel Coronavirus epidemic? Almost nothing.

SARS 2003 epidemic already ended years ago, all patients either died or recovered. So, we can use this formula and the result tells us how many of confirmed cases died (a proportion).

But Novel Coronavirus patients (confirmed cases) are still being (most of them) sick in hospitals, many of them in ICUs. The virus doesn’t kill a person immediately. There is a lag between infection confirmation and death. It means, that, for example, by today (Feb 4, 2020) only those patients died, that have been registered as ‘confirmed cases’ a few days, probably a week, or even more than a week ago.

Median time (based on first 41 cases) between symptoms onset and admission into ICU – 10.5 days. And it’s not death yet. They got Coronavirus confirmation probably somewhere between symptoms onset and death. So, there is a lag between case confirmation and death.

Image: The Lancet – Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China

What does it mean for a fast growing epidemic (exponentially, e.g. +20-50% confirmed cases daily, like Coronavirus epidemic is growing). It means that current death/cases value is useless and real fatality rate probably is much greater than 2%. Most of about 17500 cases (by February 2) are new cases (7 days before there were only about 2800 cases). So, it’s more likely (if we assume that average lag between case confirmation and death is 7 days) that we have 362 deaths among 2800 cases = 13% case fatality rate. It might be less than 13% if the lag is shorter, but it might be greater than 13% if the lag is longer. In reality the lag is not just one figure, it’s a distribution (for some people it’s shorter, for other people it’s longer). This method is also biased, we don’t have all required data to use this method, but it shows what is wrong with CFR = deaths/cases.

Let see what happened in 2003:

“The death rate from severe acute respiratory syndrome has more than doubled, to 5.6 percent, since the epidemic was first detected in mid-March, causing deep concern among health officials.

Although the overall death rate, according to World Health Organization statistics, has hovered around 4 percent in the last three weeks, it has varied widely among the 26 countries, plus Hong Kong, with cases of the disease, known as SARS.

When W.H.O., which is the lead agency investigating SARS, first reported daily statistics, the death rate was about 2 percent. It was 2.4 percent on March 17 and 1.8 percent on March 18. The known number of cases then was fewer than 220.

But as the number of cases has increased — to 3,861 yesterday — the death rate has also steadily risen, leaving health officials worried. Lacking a precise explanation for the rise, health officials have generated a number of theories. In outbreaks of other new infections, the death rate has usually fallen with time.

”It’s worrying, and we hope it is not an indication of a continuing trend,” said Dr. Klaus Stöhr, scientific director of the W.H.O.’s SARS investigation.” The New York Times

Well, scientific director of the WHO was worrying in April 2003 because of CFR=5.6% instead of initial 1.8%. This is what happened by the middle of the summer. CFR raised up to almost 10%.

Does it mean virus mutated or something other changed in ‘real world’? It’s possible, but not necessary at all. Real fatality rate (among confirmed cases) is average (in reality it’s different for different groups of people depends on age, sex and other factors) probability to die for a ‘confirmed case’ person. The real fatality rate during the entire epidemic could be the same, but CFR calculated as deaths/cases will be changing. Just because CFR is based on wrong math that doesn’t take into account the lag between time of case confirmation and death.

So, why journalist are telling us “Coronavirus CFR=2% is less than SARS 10%”? Why they are comparing final CFR for SARS epidemic with current CFR for Coronavirus? Why they forgot about CFR=1.8% for SARS on early stage of SARS 2003 epidemic? Current CFR for a growing epidemic is not a rough estimation, it’s just a value based on wrong math.

Methods for Estimating the Case Fatality Ratio for a Novel, Emerging Infectious Disease (American Journal of Epidemiology Copyright © 2005 by the Johns Hopkins Bloomberg School of Public Health).

Assessing the severity of the novel influenza A/H1N1 pandemic (BMJ 2009)

I created a few models to show that CFR value is not correlated with real fatality rate:

Image: Andrzej Leszkiewicz

So, it’s possible that, while real fatality rate is about 30%, CFR=2-3%.

One more model:

Image: Andrzej Leszkiewicz

In this mode real fatality rate is 99%! But CFR on early stage of the growing epidemic is slowly growing starting from almost 0%. By the end of epidemic CFR is correct and we see that 99% of ‘confirmed cases’ died.

This is just an extreme and scary model, not a model of real epidemic, but it shows us that CFR based on current total number of deaths and confirmed cases is biased and misleading and can’t be used to estimate number of deaths and to compare an epidemic with other epidemics. It doesn’t give us ‘an early estimation’. It gives us just some figure that is not correlated with real fatality rate.

The following graph shows us reported SARS 2003 number of deaths (blue line) and calculated number of deaths (purple line) based on formula: cases confirmed 12 days ago * fatality rate 9.5%:

Image: Andrzej Leszkiewicz

Calculated number of deaths is really close to real data. And, while real fatality rate is 9.5%, CFR calculated as deaths/cases is growing from about 1.8% to 9.6% and CFR calculated as deaths/(deaths+recovered) is growing from 7.7% to 14.8% and then decreasing to 9.6%. Both formulas returns misleading results while an epidemic is growing. And both formulas are correct when an epidemic ended (ending):

Image: Andrzej Leszkiewicz

When an epidemic is growing faster CFR is even less reliable, because we get more and more new cases just in a few days, while older cases are still being alive and probably not even developed severe condition yet.

And Novel Coronavirus epidemic is growing fast (by number of confirmed cases). Much faster than SARS epidemic in 2003:

Image: Andrzej Leszkiewicz

The above charts are screenshots from my Interactive analytical report with a lot of charts and information regarding Novel Coronavirus (not optimized for mobile devices). Report includes dashboard with coronavirus outbreak statistics an interactive models where you can change ‘lag between case confirmation and death’ and ‘real fatality rate’ and you’ll see how it affects CFR value.

I believe that for a fast growing epidemic CFR is not just bad estimation of real case fatality rate, but can’t be used at all. If real ‘case fatality rate’ can be over 10% while calculated is just 3% then it makes no sense to use such math.

The most recent data: 20,626 confirmed cases worldwide, including 426 fatalities.

Does it mean 2% fatality rate? No. 7 days ago there were only about 4500 confirmed cases. About 15500 cases have been confirmed during the week. This people for now probably didn’t even develop severe condition yet. But many of them will be dying… I hope someone will find a drug that stops the virus and they will cure everyone who is still being sick. But don’t get fooled by current CFR=2% figure. It means fatality rate among confirmed by today cases already can’t be lower. But it doesn’t mean that 98% of confirmed by today cases will survive. Final fatality rate can be 2% or even less (if there will be more new cases, but no so many deaths), but it can be much greater as well. We can’t use current CFR = deaths/cases figure to compare this epidemic with past ended epidemics like SARS.

By the way, 2,788 people in severe and critical condition has been reported by today. And same issue as with CFR appears with % of severe/critical cases. Divide current number of severe/critical cases by number of confirmed cases and you’ll  get about 13.5%. But it doesn’t mean that 13.5% of ‘confirmed cases’ eventually require intensive care. Probably much more than 13.5%. Same issue – it’s take time for a virus to do severe/critical harm to an infected person. UPD (2/7/2020):  “So the second week is what determines whether the illness becomes critical. The third week determines whether critical illness leads to death. ” [sourceAnd real % of severe/critical cases is very important. It determines how many hospital beds, doctors, medical personnel and equipment we will need to support lives. Lack of the resources will increase real fatality rate.

UPD (2/7/2020): WHO did it again. They voiced that “of 17K patients (4 days ago) 15% – severe cases, 82% – mild cases, 3% – critical cases.” Same math. Number of severe cases divided by total number of cases = 15%. Wrong math. It’s just 4 days since they confirmed 17K patients. There is no clinical outcome for most of them yet. There was no enough time.
UPD (2/12/2020): 17.3K- Feb 2, a 6 days before – 4.4K cases => 12.9K (75%) cases were less than a week old sice confirmation. Quotes: ‘going from mild to severe symptoms takes about a week.’ ‘some patients who enter the 2nd week will suddenly get worse’

And, while the media will be spreading the misinformation again, I’m sure they will publish numbers, but they won’t show people the context. This is the context:
Journalist: “how critical are mechanical respirators and what data you have on organ failures?” WHO: “from 17K patients – 15% severe cases, 85% – mild cases”
Journalist: “this is not what I asked about”
WHO: “we don’t have any other details”

Make your own conclusions…

The best way to calculate real fatality rate among confirmed cases is to take into account only cases that already ended by either death or recovery. But epidemic is growing fast, there was no enough time for people to die/recover and we don’t even know how many patients of first 100 patients recovered by today…

This article claims that by Jan 22, 2020 13 (32%) patients were admitted to an ICU and 6 patients died and 7 (17%) were still being in hospital with unknown outcome (of first 41 cases)

This article claims that by Jan 25, 2020 23 (23%) patients have been admitted into intensive care unit and 11 (11%) patients of 99 died while 57 (58%) remained in hospital with unknown outcome (of 99 patients).

Probably 41 and 99 cases is not relevant sample. I don’t want to claim that real fatality rate is 5%, 10%, or 15%, or 20%. I wish it be 0%. But I claim that CFR value calculated as deaths/cases in current situation (fast growing epidemic) gives us totally useless and unreliable figure on early stage of fast growing epidemic. And we need to know real fatality rate. What WHO and media did by publishing 2% is probably good to delay panic for a bit. But if real fatality is much bigger and this epidemic will turn into a pandemic then this delay will be short and no one will ever believe in what WHO and media share with us. Lie is a wrong method to delay panic. It creates rumors. Rumors create panic. One more negative side of this misinformation is that people (including doctors and authorities) will not be ready to meet real threat. I already see that some epidemiologists believe in this biased figure shared by WHO and by media. And I’m afraid even members of some governments will believe in 2% figure, because WHO all media wouldn’t lie (?). It’s so easy to believe in authority. It’s a bit more complicated to do own math. It will lead to underestimation of the threat, insufficient plans will be written and insufficient measures will be taken while there is a real threat of a deadly pandemic.

I have to notice that I’m talking only about mathematical point of view and only about ‘case fatality rate‘ – fatality among ‘confirmed cases’. For sure it’s possible that official statistic doesn’t show us real situation. It’s also possible that there are people that got sick and recovered  with no symptoms. This article is not about mortality rate,  it’s not about how many people in China or globally are gonna die. It’s about published by WHO and media ‘case fatality rate’ which is based only on confirmed cases and won’t change because of unreported mild cases. It’s a mistake to say ‘Coronavirus fatality rate will be lower than current estimation because of mild cases’ and compare it with SARS CFR at the same time. Because SARS CFR=10% is based on deaths/ confirmed cases calculation as well and doesn’t take into account mild cases.This article is not a about reliability of data provided by China (number of cases and deaths). This article is not about ‘true fatality rate’ (based on all cases, including asymptomatic and not tested). This article is about fatality rate among confirmed cases and about wrong math and mathematical fallacies that gives us wrong and misleading figures even when based on valid number of confirmed cases and deaths.

UPD 2/9/2020: But, if you really want to talk about real fatality rate (among all infected people incl. asymptomatic, mild cases) you can’t use lack of data to justify wrong math. Having (unreal, but let’s assume we have it) right now all data on mild cases, but using the same approach and similar formula (number of deaths divided by number of all infected people) will be compromised by the same mathematical fallacy. Number of mild cases should be fast growing as well on this stage of the epidemic. So, the result will be wrong (underestimation) as well.

Don’t mix this terms:

Case fatality rate (CFR) – a measure of the severity of a disease and is defined as the proportion of cases of a specified disease or condition which are fatal (e.g. CFR = 10% of people with disease confirmed died)

Mortality rate – a measure of the severity of a disease and is defined as the number of deaths in a particular population, scaled to the size of that population (e.g. mortality rate = 100 deaths per 100,000 population)

I’m not an epidemiologist and not a scientist. I’m Excel VBA and Power BI  developer and consultant, data analyst. And this article is just my opinion (with a couple links to more reliable sources). But when I see an interested for me subject I strat to study and I’m trying to understand. I’ve noticed the problem (while I was making the report mentioned earlier in the article) and I believe that I has to share this information with people. If you don’t agree with the article, then proof that I’m wrong using math and reliable scientific sources. As for me, WHO press conference and media like BBC and CNN are not reliable sources. The American Journal of Epidemiology is a reliable source, isn’t it?

I know, that the main argument against the above will be very simple – the appeal to authority. For one person WHO, BBC and CNN is the authority. No comments. For other person Johns Hopkins is the authority. Well, the appeal to authority is not the best argument if it’s not a reference to science based document published by ‘the authority’. Like this one:

Methods for Estimating the Case Fatality Ratio for a Novel, Emerging Infectious Disease (The American Journal of Epidemiology Copyright © 2005 by the Johns Hopkins Bloomberg School of Public Health).

I feel a bit strange. I’m (almost) alone against ‘the authority’. Main subjects of the latest WHO press conference was misinformation. And I believe that it’s WHO started a campaign of misinformation when they voiced this 2% figure without letting journalists know what it means and what doesn’t. Lately this figure has been shared by media corporations. I understand that most people don’t read scientific articles in The American Journal of Epidemiology, I understand that probably there are great epidemiologists who know how to save lives, but don’t understand mathematics and I understand that many journalist just don’t care about the truth. They are writing ‘fatality rate is low’ now, tomorrow they will be writing ‘fatality rate is increasing! is virus mutating?’. And it will be a great click-bait to get more readers. But I hope there are journalists that are willing to share truth first of all. I want to see a piece of truth and science, questions and discussion in the media instead of the appeal to authority and parroting.

The author accepts no responsibility or liability for any losses incurred in connection with any decision made or action or inaction in reliance upon this the article.

Andrzej Leszkiewicz,
Krakow, Poland
Twitter: https://twitter.com/avatorl
E-mail: a@avatorl.org

P.S. My web site is almost empty. I write my thoughts in social media, not here. The web site is only for big articles on important subjects. So far I have written here only about child militarization in Russia and later the article has been published by InformNapalm.

Take a few minutes and read. The latest update, not included into the article – they already had (by the end of 2019) more than one million of children wearing military uniform and taking military training in schools on daily basis.

Copyright: Andrzej Leszkiewicz.

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