Making Sense of Coronavirus Stats

The whole situation surrounding the corona virus strikes me as a spectacular clusterfuck of global proportions.

I wouldn't put much confidence on any of those numbers. There's a whole bunch of factors that could skew an estimate of the mortality rate in either direction.

Off the top of my head, here's a few:

-The hospitals in Wuhan are completely overloaded, so:

    -the true mortality rate is going to be higher due to lack of intensive care for people who would otherwise pull through, creating a gap between the mortality rate in wuhan and elsewhere.

    -only the worst cases are going to be dealt with in hospitals, skewing the reported mortality rate towards the higher end.

    -Wuhan is taking extreme containment measures. For instance, [people are probably being welded into their rooms](https://www.the-sun.com/news/378365/coronavirus-patients-welded-into-homes-in-china-as-death-toll-spirals-to-813/) God knows what happens to them and how their infections turn out.

-The spread of the virus is rapid and exponential, so mortality can only be lower bounded by taking total dead/total cases

-It's faster to die than to recover, so you get the opposite effect from looking at deaths/(deaths + recovered)

-China seems to have a different method for reporting causes of deaths, leading to underestimation of the mortality rate.

-China has really bad air pollution, and there's weak evidence that smokers might be more suceptible to this disease. Men also smoke far more than women in china and it's being reported that men are disproportionately affected by the disease.

-CPP is probably not being very transparent or outright lying about the situation.

 -for instance as I understand it WHO officials have still not been allowed into Wuhan.

 -this is probably also happening internally such that even CPP officials can't really get a good grasp of the situation if they wanted to.

 -there are rumors of crematoriums operating 24/7 indicating that the real death rate is far higher than the reported death rate.

-Some paper also indicated (very)weak evidence of discrepancies in susceptibility between Asians and other races and at the moment I'm unaware of any confirmed deaths that aren't east asian. Apparently 2 4 Iranians died from the virus.

-I've also heard rumours of widespread online censorship, evidenced by trending misspellings of #coronavirus but without the proper spelling trending on twitter and moderator and administrator actions on reddit. Further obfuscating the underlying situation.

-There are rumours of possible reinfection and even that the second time round might be worse along with heavy censorship/firing of the people starting these rumours in china.

-Many countries are only screening people who have had direct contact with people coming in from china, and there's evidence of many asymptomatic/weakly symptomatic carriers. Thus, external death rates will also be difficult to estimate, as many unusual pneumonia deaths will not be attributed to the virus and the total number infected will not be known either.

-There's also evidence that the incubation period might be in some cases even higher than 14 days. This skews estimates based on total infected vs total dead.

-The tests we are using are new and have false positive and negative rates, further skewing the numbers.

All these factors either add uncertainty or skew the numbers in one direction or the other in a way that is both region and context dependent. When you put all of it together you get mortality rate estimates ranging anywhere from 0.1% up to +15%, and who knows about the long term effects of the disease.

Mortality rate estimation, at this stage, is very hard. The relevant problems:

• Severe cases are more likely to be detected than minor cases (but we don't know how much more likely)
• Nearly all of the quantitative data comes from China, which is underreporting both cases and deaths in an unknown ratio
• Cases which end in death resolve faster than cases which end in recovery

On top of which:

• No one knows the morbidity rate at all
• There are unconfirmed rumors that recovery may not confer lasting immunity (this is a priori unlikely but would make the situation much worse)
• The prior is a sample from a distribution which contained SARS, MERS, and an large but unknown number of variations of common cold
• The timeline for a cure could be anywhere from a month (chloroquine or remdesivir works) to never

The practical upshot of all of which is, the confidence intervals are all wide enough to drive a truck through.

I think this is one situation where we should value the lesswrong maxim of being aware when your level of knowledge is very limited. Hold onto your uncertainty.

As a long term investor I am very aware that statistics out of China are particularly unreliable. Even the hierarchy in China seems to have trouble getting a true picture. I saw an interview with one of the doctors in Wuhan where he related the extreme difficulties of getting people to report the bad news about what was happening up the management tree. Perhaps reflecting this, President Xi sent his man, Shanghai Mayor Ying Yong, to Wuhan, to get a first hand view.

https://fortune.com/2020/02/14/china-coronavirus-wuhan-hubei-province-ying-yong-tesla/

Even on the official statistics it appears Covid-19 is an order of magnitude more contagious than influenza and has a fatality rate also an order of magnitude worse. The fact that over 10% of the passengers on the Diamond Princess contacted the virus in a few weeks testifies to the contagiousness of the disease. There are troubling hints from China that deaths are far higher than admitted. The admitted deaths from covid-19 in Wuhan are no more than 10% of normal deaths in the city, yet, cremation houses are said to be having trouble keeping up, and are bringing in supplies and staff from outside to manage the workload.

from the CDC. (the definition of "mortality rate")

A mortality rate is a measure of the frequency of occurrence of death in a defined population during a specified interval.

i.e not based on number of cases v. death, it's population v. death.

Death rates are not the only thing we should be worried about. SARS lead to long-term problems for survivors:

Forty percent [of studied SARS survivors] reported some degree of chronic fatigue and 27 percent met diagnostic criteria for chronic fatigue syndrome; people with fatigue symptoms were also more likely than those without them to have psychiatric disorders. For comparison, far less than one percent of Americans met chronic fatigue syndrome criteria, according to the U.S. Centers for Disease Control and Prevention, although many more than that have symptoms.

It's important to know to what extend similar problems might appear with this coronavirus.

I think the numbers from China are basically completely meaningless other than signaling 'higher than they want you to know'.

As much as I hate to say it, the cruise ship that currently represents ~50% of the PCR-confirmed out of China cases is going to be a gold mine of information, as you KNOW where and when they were infected and can track their outcomes. Will be biased towards the elderly a bit.

Let's take the out-of-China data as reported at the moment I am writing this as provisionally true due to efforts at contact tracing which are robust in large chunks of the world. I suspect there are a lot of low-symptom clusters that are being missed, as evidenced that you can have South Korea suddenly up and find 50 people and Iran suddenly up and report 2 deaths out of nowhere. But it's a baseline for now. 1095 confirmed, and 11 dead, for a naive ratio of ~1%. But in the case studies I have seen, most deaths seem to be happening after ~3 weeks of illness, ~80% of cases in well-documented clusters resemble flu and nothing worse for a week or so, and 20% go longer with worse disease and risk mortality. So if we go back 2 weeks we get to 227 confirmations and a naive ratio of 5%, and 3 weeks we get to 110 and a naive ratio of 10%. A lot of the people who are seriously ill and dying now were not caught in that early time though, so combined with the likely missing of low-symptom clusters I think the estimates of mortality rates of 1% to 3% seem quite reasonable. There will be higher morbidity, and I have seen case studies of SARS survivors that they often have chronic issues for the rest of their lives.

Age structure of the population will make different nations differently susceptible to death as well, from what I am seeing death rates may not be rising above 1% until people are in their forties or fifties and reach 15% for those in their eighties.

Anyways, I think the outside-of-China numbers are still low. Many nations are not applying molecular tests to those who do not have travel history to hot spots and will thus necessarily miss local transmission if the initial traveler was not caught. We just saw Iran suddenly report two deaths with no foreign contacts testing positive for the virus and shut down a city of 1.5 million people. If we assume a death rate of 1% and a disease course of 2 weeks, with the sheer infectivity of this disease I suspect there are several hundred infected in Iran alone.

I think for approach 2 you want the ratio of deaths:(deaths+recoveries) rather than just deaths:recoveries. This means that the 2 approaches actually give the same result.

This method may lead to an overestimate as deaths occur earlier in the illness than declarations of recovery. If deaths occur at a constant rate between diagnosis and recovery then it would be more like half this value (depending on how the infection rate is changing). Looking at it like this gives 5.8 - 11.5% mortality.

An alternative method would look at average time from diagnosis to death and look back to how many diagnoses there were that many days ago. For Sars/Mers this looks like 10-18 days which would give death rates for Covid-19 of 4.4% - 12.4% which is pleasingly similar to the above method but might not actually mean anything!

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There's some but not a lot of interest in this topic on LW; I have a mailing list with primarily rationalist types on the topic; PM me email address to be added

This report was the first report from official sources that made sense to me. Experts are estimating that a large portion of people infected with the virus only show mild symptoms, or are even asymptomatic. Those people are unlikely to get tested in hospitals. If we factor them in, this dilutes the CFR and, according to current estimates, it will likely more than cancel out the delay for confirmed deaths compared to confirmed infections.

Now that you have a definition for mortality rate - time for an update in your post?

I presume more people will be reading so clarification would be valuable.