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The 2020 Novel Coronavirus Outbreak

The Reported Mortality Rate of Coronavirus Is Not Important

Why the reported “mortality rate” of the Wuhan coronavirus (2019-nCoV) is misleading and distracts us from the severity of the outbreak in China and Asia.

Andy Chen
Andy Chen
Feb 3 · 15 min read

Update (Feb 10): Some researchers have estimated the case-fatality rate. In my new post, I summarize their research and explain why it’s worse than it looks.

At the start of 2020, murmurs of a mysterious SARS-like coronavirus started to spread in the city of Wuhan, in Hubei, China. Soon enough, the world knew what was going on. This new type of virus, which was given various names such as Wuhan coronavirus, novel coronavirus and 2019-nCoV, brought back memories of the 2003 SARS outbreak which infected around 8000 people and killed 800 worldwide.

These viruses were similar in the way it crippled people. Like SARS — Severe Acute Respiratory Syndrome — the novel coronavirus gave people fevers, coughs, and other non-specific symptoms. Many patients ended up in the hospital, struggling to breathe as the doctors hooked them up to mechanical ventilators, hoping they would eventually fight the virus away on their own.

This outbreak caused a stir in the international community. The public did not know the severity of the outbreak, and wanted to know what was being done to protect them, if the situation got worse. Was it time to panic?

In their attempt to understand the severity of the outbreak, people started reporting the mortality rate of the novel coronavirus.

The Public Reaction To Coronavirus

CNN International: 9.5M followers (2020)

Science News: 3.1M followers (2020)

In general:

Correction: Mortality Rate Is Not Case-Fatality Rate

People are confusing the case-fatality rate and the mortality rate, which are not the same thing.

The case-fatality rate basically splits cases into deaths and recoveries.

The mortality rate doesn’t do this. It is usually calculated for the purposes of seeing what the leading causes of death are, in the general population.

Some people specify precisely what they mean, but the vast majority of people around this time are mistaking the mortality rate for the case-fatality rate.

How They Calculated The Case-Fatality Rate for Novel Coronavirus

The media probably sourced data from the National Health Commission and divided the cumulative death count by the cumulative number of confirmed cases for 29 Jan 2020 (any date around this time produces similar numbers).

This produces a figure in the ballpark of 2.2%. I assume that this is the methodology that the media have used, because others have used it in demonstrations. Either that, or they have been mindlessly parroting other sources.

What They Leave Hidden In The Footnotes

(1) It Does Not Properly Account For People Who Are Still Alive And Infected

“While an epidemic is still evolving, only some of the individuals affected by the disease will have died or recovered. Only at the end of an epidemic can an absolute value be calculated, taking into account total deaths, total recoveries and people lost to follow-up. Calculating case fatality as the number of deaths reported divided by the number of cases reported irrespective of the time elapsed since they became ill gives an underestimate of the true case fatality ratio.” — from a World Health Organisation document dated May 7, 2003, titled “Update 49 — SARS case fatality ratio, incubation period”.

For now, we assume that the reported figures are true (hint: it’s not).

If the reported figures are true, then the calculated case-fatality rate is an underestimate, because the outcome of people who have already died is certain (death), but the outcome of people who are still alive is unknown (death or recovery). These people who are presently alive but don’t eventually recover will not be counted as deaths, if the case-fatality is calculated during the outbreak. And this is not a trivial number.

We can take the cumulative confirmed cases at the time (29 Jan) and subtract deaths and recoveries to get the number of people alive at the moment, and then look at the current number of severe cases. This gives us 1370 severe cases out of 7417 patients still alive, so about 18% of cases were classified as severe at the time.

The key question: how many of these severe cases will not result in recovery?

In a study conducted at a Wuhan hospital on the coronavirus, it was noted that:

“Patients with severe illness developed ARDS and required ICU admission and oxygen therapy.”

Terminology:

  • ARDS — Acute Respiratory Distress Syndrome — occurs when there is severe inflammation and fluid build up in the lungs. This is a very serious condition that requires emergency care.
  • ICU — Intensive Care Unit — is a department of the hospital which specializes in treating the most life-threatened patients.

We look at the 13 patients who were admitted to the ICU in this study. 5 out of 13 died (38%).

The figures for SARS was similar. A past study reported that 13 out of 38 (34%) critically ill SARS patients at a Toronto hospital died within 4 weeks.

We had 18% of cases at the time classified as severe. If we are optimistic and say that the true proportion of deaths among severe cases is 15%, then we are still miscounting by 0.18*0.15=2.7%. In other words, 2.2% of all cases have already died, and another 2.7% may die soon.

Of course, I’m not claiming that this is the correct figure. I picked an optimistic assumption to show what the case-fatality could be at best, but it is likely to be worse. The central point — by taking deaths over cases as a case-fatality rate, and ignoring the people who are currently ill, the case-fatality rate is being severely miscalculated.

(2) No One Knows The True Figures

All estimates assume that the reported figures are accurate, but they are not. The reported figures are very likely going to be less than the true figures: see my previous post. Even Chinese state media confirmed that there was a shortage of testing kits, and this should have been known by commentators, given the speed of the outbreak.

“In Wuhan of Hubei Province, the epicenter of the outbreak, over 12,000 new test kits have been issued to test institutions and designated hospitals, which has enabled the city to test nearly 2,000 suspected case samples in a single day, compared with only 200 samples at the early stage of the epidemic, said the municipal health commission Tuesday.” — from Xinhua article.

Given that hospitals need to prioritize patients, it would be reasonable to assume that they would test the severe cases first. If this is the case, then the confirmed figures would disproportionately includes severe cases, thus inflating the reported case-fatality.

Edit (Feb 4, 2020): Another scenario worth considering is one where the symptoms for most people are very mild and they recover quickly. If these people dismiss their illness for the common cold and hence, do not report their illness, this would increase the number of true coronavirus cases and reduce the case-fatality rate.

On the other hand, we also have to consider the possibility of deaths being under-reported. It is possible many severely ill people could not travel to the hospital or did not want to wait in a crowded hospital, but then died in their home without being included in the official death count. In this case, the true case-fatality rate could be higher than the reported rate.

Unlike confirmed cases, where the reported numbers are almost certainly less than the true numbers, we now have uncertainty in both directions. We can’t narrow down the true case-fatality rate — it could be higher or lower than is currently reported.

There are too many sources of uncertainty to get an accurate case-fatality rate.

Is Case-Fatality The Main Issue? General Issues with the Case-Fatality Rate

(1) Case Fatality, On Its Own, Does Not Indicate Outbreak Severity

Many people are taking case-fatality to be an indicator of outbreak severity. This is only part of the story, and possibly even less.

This plot shows the spread and case-fatality of viruses which have historically been deadly to human society. Notice that not many viruses have a case-fatality near 100%.

Why don’t the deadly “outbreak viruses” have a near 100% case-fatality rate?

If a virus has high case-fatality, then we’d think that it would be deadly to any individual who becomes infected. But if it’s only infects one person, then it is not deadly to society.

An outbreak which is “deadly to society” (kills a lot of people) can be thought of as the result of a good ability to spread and a non-trivial case-fatality rate. So we have the common cold which spreads easily, but the case-fatality rate is very, very low, so it is not a severe outbreak. On the other hand, there is no such thing as an “outbreak” of ruptured aortic aneurysms, because while they are deadly and kill 80% of people before they reach hospital, they are not contagious at all. It is the viruses which balance these two — easy transmission and fatality — that end up being the most devastating to human society.

If you are interested, you can simulate interactions between infectiousness and fatality with an agent-based model (browser-based Netlogo).

Balance between the two properties is significant. Theoretically, increased fatality rates can lead to less overall deaths, which is extremely counter-intuitive. A virus can cause mild and asymptomatic cases which are not severe enough to kill or even keep people at home. This allows the virus to be exposed to the wider public, by letting the infected people carry on with their normal lives. But if the virus is immediately lethal to all infected people and their symptoms stopped them from going out, it would actually prevent the virus from spreading freely. A mixture of lethality and non-lethality creates the worst sort of virus, as it would allow the virus to kill some people, and use other less-affected people to spread the virus.

Unfortunately, this seems to be what is happening with the novel coronavirus — and it is what makes this specific virus so devastating. The virus is lethal enough to send people to hospital and cause death. But it is not always lethal, and unlike SARS, this virus spreads while the infected person is asymptomatic and unaware. This happened in Germany — a woman from China inadvertently infected a German businessman while being asymptomatic, and this man went on to infect three others.

This makes the issue of containment far more difficult. It also doesn’t help that it has multiple routes of transmission: airborne particles, and the newly discovered fecal-oral route, which would be devastating to areas with poor sanitation.

It is not good to view case-fatality as the indicator of outbreak severity. In the current situation, even if it is 2.2%, it is spreading far too easily and at this rate, it will be devastating to society.

Update (Feb 4, 2020): The incident in Germany was incorrectly reported — the woman was not completely asymptomatic. The researchers did not actually contact the woman, and relied on reports that the woman did not appear to have symptoms. Other sources indicated that she felt tired, had muscle pain and took paracetamol.

This is not proof that asymptomatic transmissions are impossible, and my point is still relevant. Tiredness and muscle pain can have many causes, and it was likely that the woman did not expect to have novel coronavirus, which led her to not self-quarantine.

(2) Case-Fatality Is Not Equal To The Probability of Dying

Why do all coins have a 50% probability of landing heads or tails? It is because we assume that all coins are symmetric, equivalent and interchangeable.

Unlike coins, humans are not all equivalent. They differ in age, genetics and lifestyle.

People are not equally susceptible to the same disease.

If we want to know the probability of death if we catch the coronavirus, we do not need to focus on and estimate precise case-fatality rates.

For example, if we look at data from the SARS outbreak in 2003 (SARS causes similar symptoms), we can clearly see how the probability of death increases with age, and many of these figures are not near the 10% overall case-fatality rate.

“…the case fatality ratio is estimated to be less than 1% in persons aged 24 years or younger, 6% in persons aged 25 to 44 years, 15% in persons aged 45 to 64 years, and greater than 50% in persons aged 65 years and older.” — From a World Health Organisation document dated May 7, 2003, titled “Update 49 — SARS case fatality ratio, incubation period”.

We can also estimate our probability of surviving based off where we live, because case-fatality is highly dependent on access to healthcare services — this should be obvious. For example, Cholera is an infection that causes severe diarrhea and leads to severe dehydration and electrolyte imbalance. The case-fatality rate can range from 30–50%, but with access to an oral rehydration solution (containing water and electrolytes), the rate can drop to under 1%.

Thus, if you are young and healthy, and you live in an area which is not population-dense and has sufficient healthcare services, you should be fine as long as the outbreak does not get too severe in your area. But you still shouldn’t be reckless and expose the vulnerable to the risk of infection.

What To Be Concerned About

Low Case-Fatality Rates Are Only Possible Because Of Modern Healthcare Services — What If We Lose These?

We know that case-fatality depends on access to healthcare services. This would be especially true for coronaviruses. But what would happen if the outbreak became too widespread, causing hospitals to run out of capacity and leaving people without access to healthcare services?

To see how we would fare without access to modern healthcare services, we look to the past. Spanish flu had no treatment at the time of outbreak in 1918, and it ended up causing at least 50 million deaths in the world with a case-fatality rate exceeding 2.5%. If SARS and MERS only achieved 10% and 34% with modern healthcare, then we could imagine it being far worse without it. Since the novel coronavirus produces similar symptoms and requires similar treatment, we may have a catastrophic situation if the outbreak strains healthcare resources, and thus, prevents additional patients from being admitted to hospitals.

The Availability of Resources — Where Is The Breaking Point?

Most of the figures we have now apply to Wuhan and Hubei. Hubei, the province of Wuhan, is economically in the top half of China’s provinces. Their healthcare system is decent, with 2.17 physicians and 5.46 hospital beds per 1000 people (from the 2015 China Health Statistics Year book). These numbers have probably grown since then. Wuhan, a city of 11 million, is one of 15 “new tier-1” cities, and according to a local government report in 2014, Wuhan had 6.51 hospital beds and 3.08 doctors per 1,000 people. Was this enough?

They built two new hospitals to add 2,500 additional beds.

They sent thousands of medical staff from across the country to Wuhan.

Wuhan, a relatively well-resourced Chinese city, still required additional resources to cope with the outbreak.

Do Other Countries Have Enough Resources?

Here, we focus on the Asian countries which are currently experiencing the brunt of the outbreak.

To see whether other countries would be able to deal with an uncontained outbreak of novel coronavirus, we look at three pieces of information:

  1. Current level of containment (as of Feb 2, 2020): origin (purple), confirmed domestic transmissions (red), recent arrival (pink), no reports (grey).
  2. Number of visitors from China (data from 2018): thick edge indicates more inbound travelers.
  3. Hospital beds per 10,000 people (data from Global Health Observatory, from various years in the decade of 2010): larger circle indicates more hospital beds per person. Also on the node label.

These variables are supposed to indicate vulnerability to uncontained spread, probability of more cases ariving, and vulnerability to running out of resources. I do not take into account actions already taken, such as border control measures, and I assume that the density of hospital beds in a country correlates with the number of ICUs, mechanical ventilators and other resources needed to deal with novel coronavirus. This assumption may not be true, but hopefully it is close enough.

The graph shows that human-to-human transmissions have already been reported in the areas which receive the most inbound travellers from Mainland China — Taiwan, South Korea, Japan, Thailand and Vietnam. Of these areas, Thailand (21 beds per 10,000 people) and Vietnam (26 beds per 10,000 people) seem vulnerable and may need to impose some stronger containment measures. Many other countries such as India, Cambodia and the Philippines will need to be monitored and aided if there is evidence of an uncontained outbreak.

Importantly, all of these countries need to be aided in their detection capabilities. Any delay in detection gives an opportunity for the virus to start spreading, and once this happens, the problem grows by orders of magnitude.

Looking further at the data, Timor-Leste reports 59 hospital beds per 10,000 people which seems relatively high. According to GHO data (physicians per 1000 people), they also report 0.7 physicians per 1000 people, while China has 1.8. The other countries which have less than 1 physician per 1000 people are Vietnam, Myanmar, Thailand, India, Nepal, Bangladesh, Indonesia, Afghanistan and Cambodia. While not all of these countries are likely to have uncontained outbreaks, we must be prepared to send aid, if the worst-case scenario does happen.

What Should We Do?

China is a better-resourced country and has the capability to deploy state resources to achieve goals very efficiently. Despite this, it is still struggling to contain the virus.

We should not downplay fears with “statistics” and “data”, like was done with the “2.2% mortality rate”. Statistics is not about the final reported numbers, rather, it is about identifying properties of the generating process, and in this case, whether it is capable of generating extreme values. Fear isn’t necessarily bad — it is often better to overreact and avert a crisis, than to underreact and let the problem grow exponentially.

And on a individual level, we should exercise appropriate caution wherever we are, until the outbreak is over. It is not a problem if people are more distant to each other during this time. Be a good citizen and don’t expose others to risk — use masks, carry tissues, and wash your hands.

One day, someone might look back and say that there was no need for panic because we all turned out fine. But maybe, just maybe, it is this fear that is leading us to take the necessary actions to protect ourselves.

Do We Have An Answer? Thailand — 19 infected, 8 recovered.


March 8 Review

This is a good opportunity to review.

There are some contradicting reports. We need serological testing to see if some people had been infected and recovered on their own without detection. It is looking extremely possible that the number of cases was significantly higher than reported, so the fatality rate is lower.

However, this does not mean fatalities is going to be low. The other part about too many cases overwhelming the hospitals turned out to be extremely relevant. This is now playing out in Italy.

And with regards to the lag time problem, I thought that it would become less important after the initial outbreak in Wuhan, but it seems like people made the same mistake with the data in South Korea.

I didn’t expect people to calculate case-fatality rates by country, but if they want to, then it is important to consider this only after the initial stages of the outbreak.



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Andy Chen

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Andy Chen

Math, stats, data. Influenced by the complex systems perspective. I prefer to take the critical view.

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