Corona Virus Case Fatality Rate

I spend too much time browsing the internet these days so I’ve been tracking the coronavirus fairly closely since the middle of January when it was announced to the world and Johns Hopkins went live with their web-site which was conveniently all ready to go on day zero.

I am a firm believer in conspiracies.  Scrupulous men and unscrupulous men conspire to achieve their ends and always have done.  And the unscrupulous men, by definition, are not restrained by an ethical code in their choice of methods.  I also try to avoid wasting too much time worrying about exactly which conspiracy theories are correct and which are not.  Some undoubtedly are, many aren’t, it’s often hard to tell which is which and at the end of the day it doesn’t really matter.  Truth and good and right remain constant and unchanging, and that some men commit evil acts does not change the actions I should take to help realize a better world.

So the coronavirus may well have been the result of a conspiracy, or it may not.  It has undoubtedly been the subject of a great deal of propaganda.  It may be that it is entirely a psy-op, or it may be that psy-ops have been launched around it, or it may be that all the stories, rumors, theories and interpretations which erupted all over the internet were the result of an entirely spontaneous human reaction to uncertainty.

If it is a psy-op, then I initially reacted exactly as presumably intended, with panic.  I saw the statistics emanating from Wuhan and immediately focused on the case fatality rate; now there’s a phrase which has entered the vernacular faster than any other in living memory.  Having some facility with math, I jumped to the conclusion that the reported CFR must be much lower than the actual CFR because of the time lag, and my earliest estimates were frankly pretty terrifying.  I foresaw quarantines and school closures.  I wrote to my daughter’s university pointing out that they had 1,000 Chinese students, approximately 20 of whom, by my estimate, had returned from Wuhan following the Christmas break each with a 0.17% chance of being infected.  I demanded to know what they were doing to prevent an epidemic.  Then stories about asymptomatic and aerosol spread surfaced.  New and deadlier mutations were proposed as the cause of apparently higher CFRs in Iran and Italy.  In Hong Kong the virus was spreading through pipes.  Dr Li Wenliang died, was resurrected, and died again, managing to one up Jesus in the process.  I bought two 50lb bags of rice, a gas mask and a pulse oximeter; my wife assured me we already had plenty of toilet paper.

Nevertheless as time passed it became fairly clear that, notwithstanding the chaotic hospital scenes and undoubtedly significant number of tragic deaths, the CFR was lower than I had feared, and most of the deaths were amongst the already sick and elderly.  The majority of “sensible” sources now point to the 72,314 patient study from China indicating an overall case fatality rate of 2.3%, where most of the fatalities were ≥60 years of age, and/or had pre-existing, co-morbidities.  We are now confidently assured by our governments and the WHO that the CFR is somewhere between 1% and 3% provided sufficient hospital beds (15%) and ventilators (5%) are available.  And, in order to make sure that adequate resources are available, we must “flatten the curve” by closing our borders, closing our schools, closing our bars, cancelling sports, avoiding large gatherings, working from home, and bumping elbows should we somehow still manage to meet another human being.  At the same time we are told that these special measures should last a few weeks, perhaps two or three months at most before the peak has passed and we can return to normal.

The problem is that these two assertions cannot both be true.  The virus will continue to circulate until such time as somewhere between 60% and 80% of the population have become immune.  So 250 million people must suffer the illness here in the US before the outbreak will be over, and perhaps 150 million or so (this number is a finger-in-the-air estimate) before we can start to relax the special measures.  The US has 924,000 hospital beds and, as of 2010, approximately 160,000 mechanical ventilation devices, of which approximately 60,000 are full featured whatever that means.  If we assume that each patient requires a bed and/or ventilator for seven days and that half of these resources can be devoted to COVID-19 patients, then our hospitals can cope with 1.6 million new infections per week of which 80,000 will require access to a ventilator.  If we are able to throttle the number of new cases, it will take something like two years before we can start to relax the restrictions on behavior.  The US has significantly more mechanical ventilators per capita than other countries, so most nations will face an even longer timeline.

I do not believe these numbers.  Bubbling along all the while, just below the surface of the dominant narrative, has been the suggestion that the CFR was overstated owing to the number of uncounted cases.  Articles and blogs frequently make a passing reference to the undercounting of cases contributing to a significant overstatement of CFR in previous epidemics before going on to completely ignore this fact and later assert a fatality rate based on calculations from unadjusted data.  I believe that the number of uncounted cases is much larger than has been suggested elsewhere, and that the fatality rate, hospitalization rate and ventilation rate (for lack of a better term) are therefore all concomitantly lower.

Consider the following seven points.

Firstly the CFR from the Chinese study itself is calculated from 44,672 cases, 74% of which were from Hubei province during peak chaos, a period when the Chinses admitted they could not possibly test all or even most cases and it seems probable that a patient in serious condition was far, perhaps overwhelmingly, more likely to receive testing than a patient with mild or no symptoms at all.

Secondly, for the same reason that this study is heavily biased towards Hubei province during the period where hospitals were overwhelmed, this 2.3% case fatality rate is reflective of patients who, in many cases, did not receive adequate medical care.

Thirdly we now have significant data from several other countries to examine, and it makes for interesting reading.  Specifically we see large variations in the real time ratio of fatalities to confirmed cases.  Italy for example lists 2,978 deaths out of 35,713 cases today for a ratio of over 8.3%.  South Korea on the other hand lists 91 deaths out of 8565 cases for a ratio of 1.1%.  While some pundits are suggesting that the virus has mutated and Italy is being ravaged by a far more deadly strain, a quick look at the number of tests performed shows that as of March 9th Italy had conducted only 60,761 tests to find its claimed 9,172 cases on that date, while South Korea had conducted 210,144 tests to find only 7,478 cases.   Common sense would suggest that the reason for Italy’s apparently high CFR had a great deal more to do with the lack of testing, and therefore discovery of milder cases, than with a newly emergent killer strain of the virus.  Even South Korea has tested only 0.4% of its population, and almost certainly missed a great many cases especially as we know many people are completely asymptomatic.  The numbers from Iran also make for a very interesting analysis.  On March 9th, Iran was claiming to have 7,161 cases and a little over 400 deaths.  However this article from the Atlantic, published on that same day,  makes a very credible case that hundreds of thousands, perhaps even millions were already infected on this date.  Even if we accept that Iran might also have been understating the number of deaths as some sources have asserted, it would seem that the true CFR is likely to be significantly below 1%.  And then there is Germany with 12,327 cases and just 28 deaths for a ratio of 0.2%.  I have been unable to discover exactly how many tests Germany has been conducting, but I’m betting it’s a lot and the result is, quelle surprise, a very low CFR.

Fourthly my own personal experience tells me that we are missing large numbers of cases.  We’ve all read the stories of people who couldn’t get tested despite clear risk factors, classic symptoms, and the examining physician begging the CDC for a test.  I believe those days are now behind us, but I personally know at least four people who currently have symptoms (fever, malaise, persistent cough) which are a match for a mild case of the virus.  None of them has been tested.  Only one of them actually called his doctor and he was told not to worry and that he didn’t need a test.  I’m not suggesting that any of these people necessarily have the virus, but if we are not testing people who have these symptoms, let alone the people without any symptoms, then we are absolutely going to massively undercount the number of cases.

Fifthly there has been much discussion of R0, most of it focused on the relationship between this number and the difficulty of containing the epidemic, or showing how it results in a near-exponential curve of cases in the early stages of an outbreak, and perhaps a little on its impact on herd immunity which will only kick in and start to eliminate the disease once the proportion of immune people reaches 1 – 1/R.   Most studies have concluded that R0 is somewhere between 2 and 3, with outliers arguing for a higher value including this one which put the estimate possibly as high as 6.6.  However all these studies are based on a best fit analysis of the curve of recorded cases, and I am arguing that this is precisely the data which is most unreliable.  Given that this illness appears to last for quite some time and people are infectious during the average five day incubation period in addition to the symptomatic period, an R0 of 2.5 would appear to imply that the average infected person would manage to transmit the virus to someone else perhaps once every six or seven days, but we now have countless examples of the infection spreading much faster than this.  Four people attend a meeting in Singapore for a couple of hours with a fifth infected person, and all of them are infected by the time they leave.  One of them then goes on a ski holiday and infects everyone staying in his chalet.   A man sits on a long distance coach and infects nine other people sitting up to 14 feet away from him.  Trump meets with a Brazilian delegation, one of whom tests positive for the virus.  A few days later fifteen members of this delegation test positive.  “Super-spreaders” you cry, but super-spreaders are supposed to be rare, and while it is true that a random sample of anecdotes from the press is about as far from proper scientific method as you can get, these stories seem typical and some of them, by their nature, are not the result of selection bias.  We know that other viruses which can be spread by aerosol often have very high R0 values indeed.  Measles is one example where R0 is believed to be between 12 and 18.  If this virus had a much higher R0 than the frequently cited 2.5 then the consequences would be a much shorter doubling time for the epidemic (which appears to be the case in Europe), a much higher number of cases, and a much greater proportion of the population catching the virus over a much shorter period of time, than in a normal flu season.  This in turn could lead to hospitals becoming overwhelmed and a rapid surge in fatalities while the fatality rate itself remained low.

Sixthly China appears to be indicating that it believes the epidemic in Wuhan has peaked and they are demobilizing their emergency hospitals and starting to relax their controls.  Since we know that the epidemic will only subside once at least 60% of the population have been infected and Wuhan has a population of over 10 million people, then that suggests that the Chinese believe that several million people in Wuhan have had the virus.  A CFR of just 1% would imply tens of thousands of deaths, and even the Chinese would struggle to hide that many bodies.  I shall watch with interest to see if the number of cases in Wuhan starts to surge again as the quarantine is relaxed; if it does not then we can be pretty sure the CFR is far below 1%.

And finally the Diamond Princess cruise ship.  This is a particularly interesting dataset because, uniquely, all passengers were tested.  Out of 3711 passengers, 712 tested positive and there were seven fatalities for a CFR of just under 1%.  This study was written before all the cases were discovered, and shows that the average age of the passengers and crew was 58, and more than 1,200 passengers were over 70 years old.  Over 330 passengers under the age of seventy were infected, and the difference in apparent infection rates between age groups suggests to me that more passengers in this age group might well have been exposed to the virus and successfully fought it and completely recovered prior to testing.  Not a single person under the age of seventy, out of the more than 330 infected, died.

The net is that there is significant reason to believe that the virus has a CFR well below 1%.  I suspect it will fall in the range of 0.1% – 0.5% and quite probably at the low end of that range, provided patients have access to good medical care.   However it is extremely infective and spreads astonishingly fast.  It will therefore infect a great many more people in a much shorter period of time than the regular flu and consequently has the ability to overwhelm our hospitals by virtue of the number of cases rather than the virulence of each case.

If my conclusions turn out to be correct, the good news is that the pandemic will be gone before you know it.  We’ll all get it within a couple of months, 99.8% of us will live through it, and it will be over by May or June.

I hope and pray that I am right.

Oh – and if I did decide I wanted to waste my time thinking about conspiracy theories, I would start by wondering whether the astonishing testing debacle here in the USA was truly the result of an almost incomprehensible degree of incompetence and bureaucratic bungling, or whether not even our government could commit such a series of blunders except by somebody’s design.

UPDATE:  Also see this study from the UK’s top medical journal:

“Italy has had 12 462 confirmed cases according to the Istituto Superiore di Sanità as of March 11, and 827 deaths. Only China has recorded more deaths due to this COVID-19 outbreak. The mean age of those who died in Italy was 81 years and more than two-thirds of these patients had diabetes, cardiovascular diseases, or cancer, or were former smokers. It is therefore true that these patients had underlying health conditions, but it is also worth noting that they had acute respiratory distress syndrome (ARDS) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pneumonia, needed respiratory support, and would not have died otherwise. Of the patients who died, 42·2% were aged 80–89 years, 32·4% were aged 70–79 years, 8·4% were aged 60–69 years, and 2·8% were aged 50–59 years (those aged >90 years made up 14·1%). The male to female ratio is 80% to 20% with an older median age for women (83·4 years for women vs 79·9 years for men).”

UPDATE 2:  This is a study on the case fatality of swine ‘flu in 2009.

“There is very substantial heterogeneity in published estimates of case fatality risk for H1N1pdm09, ranging from <1 to >10,000 per 100,000 infections (Figure 3). Large differences were associated with the choice of case definition (denominator). Because influenza virus infections are typically mild and self-limiting, and a substantial proportion of infections are subclinical and do not require medical attention, it is challenging to enumerate all symptomatic cases or infections.^{2, 45} In 2009, some of the earliest available information on fatality risk was provided by estimates based primarily on confirmed cases. However, because most H1N1pdm09 infections were not laboratory-confirmed, the estimates based on confirmed cases were up to 500 times higher than those based on symptomatic cases or infections (Figure 3). The consequent uncertainty about the case fatality risk — and hence about the severity of H1N1pdm09 — was problematic for risk assessment and risk communication during the period when many decisions about control and mitigation measures were being made”

In other words, the confirmed case fatality rate for swine ‘flu bore no relation to the actual fatality rate.  And it is very likely the same thing is true for coronavirus.

UPDATE 3:   Singapore has zero deaths from 385 cases.  The exact number of tests are also not tracked on worldometer, but this article notes that less than 1% of their tests are coming back positive so we know that they have tested at least 38,500 people (more than half as many tests as Italy) to find just 385 cases. Here’s what the article says about the testing process: “On testing, the threshold for getting a test is pretty low. For the first week, we tested only people from Wuhan or Hubei province, then we tested anyone who had been in China within the last 14 days.  By the end of January, all of our public hospitals could do tests. Then we moved to enhanced screening – we tested anyone coming to a hospital with a respiratory illness, anyone who had been in contact with a COVID-19 patient.  Now, it’s even become more liberal. If you’re a hospital staff member with a mild cold, we’ll give you a test.”   This recent study suggests that 86% of infected people are completely asymptomatic.  If this is correct then even Singapore is missing a large number of cases, and so has considerably more than 385 infected people and they still have zero deaths.

UPDATE 4:  With apologies to Mr. Lightwood who, forty years ago, made a sterling effort to hammer at least a minimal understanding of the German language into my skull, I don’t speak a word of German.  However I am told that this site indicates that the Germans have been doing more testing than most countries (over 100,000 tests more than a week ago) which is further confirmation of my hypothesis.