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A big problem with the current COVID-19 epidemic is the difficulty of getting tested (due to mild symptoms and lack of testing kits). This makes it impossible for patients with little or no symptoms to know how likely it is to be infected and further spreading the disease.

There are estimations available but only take into account confirmed cases (and range between 10x-1000x of this number). How could one get estimations of the number of patients by using secondary features of the distribution that could be more robust? Age-adjusted death rate under intensive care could be one of several such parameters.

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Yiannis Dermitzakis
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  • From what you're asking, I think you are looking for $R_0$. The $R_0$, as you may know, is the number of new infections a single infected person will create in a population of people susceptible to the infection.. There are several papers which place the $R_0$ of the virus between 2 and 4 IIRC. – Demetri Pananos Mar 12 '20 at 06:53
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    Well, not exactly. I think it has to do with how to estimate the true number of infections (not infection rate) while having incomplete information. It was estimated that 80% of the infected do not show symptoms. I guess that was established by actually testing people with no symptoms and testing positive. This was done initially in Wuhan/China. So now we generally don't test non-symptomatic persons. But if we only test likely cases we "favor" the 20% of the symptomatic patients. Does this mean that the actual infected patients are just (positive tested patients)/20%? Or is there a better way? – Yiannis Dermitzakis Mar 12 '20 at 07:43

2 Answers2

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Death rate

Using death rate may work when people that die have most likely acquired the virus locally.

However, for the moment, many people die because they acquired the virus during a visit to another area, or because they got it from another person that acquired the virus abroad.

Thus this death-rate based number is not very accurate unless the virus has fully spread out (in which case it will be more likely to get infected from a local source).

For the cases of Wuhan, Italy and other epi-centers, which have more spread due to local infections rather than foreign infections, death rate might be a good probe (although you still have to deal with the delay).

In addition, while death rate might be more trustworthy than total cases of infection (just think about the Germans, with lots of supplies, are testing with a lot of thousands of people, while neighboring countries, with limited supplies, are trying to limit the use of testing as much as possible), it is still a biased number. It is not easy to determine/pinpoint the cause of death. Often a multitude of diseases are present. If a person with cancer or aids gets a pneumonia from nCoV-19, then what is the cause? The sampling of 'cause of death' is not very clear and becomes part of the analysis.

Statistics are only usefull for a comparison when they have a similar underlying basis.

  • Edit 1 (these numbers where not available before): I know about the case of the Netherlands, they compared the number of reported covid deaths and the number of total deaths. They found an increase in death rate with about 2000 people per week, but the number of reported covid-19 death cases is only about 1000 per week. So there might be a lot of people that are missed in the statistics about covid-19 (another explanation could be that those half those 2000 people are covid-19 and the other half are something else, but that is unlikely). A lot of people are not appearing in the statistics because they do not die in a hospital (but instead in their own house or in a care home).

    My view of these numbers is that the ubiquitous corona-case-dashboards and counters are flimsy and weak and are presenting dubious (biased) numbers. The underlying basis is doubtful when the numbers of different sources do not match.

    If you do want to use death rate numbers than the more rigid total death rate seems to be the better numbers (that means death due to all causes and not just the reports about covid-19). But these numbers are often not easily obtained/present (at least not publicly and stratified on a local scale) like the picture of the distribution of the cases in the Netherlands

    distribution netherlands source: Centraal Bureau voor Statistiek

    I have been trying to source this kind of stuff for multiple countries, but it is not easy. I imagine (hope) that this might be done behind the scenes on an international level. E.g. the euromomo project. But I do not know much about it and suspect that the data is mostly aggregrated at a national level (making it useless or at least not possible to make images like above) But I also imagine that governments are not spending time on getting these numbers accurate and instead waste their time on corona-apps.

  • Edit 2: I know of a research by the University of Oxford that has used exactly your approach of using the death rate in order to estimate the prevalence.

    The problem is that they introduce a parameter $\rho$, the proportion of the population at risk, which is a very uncertain parameter. This parameter $\rho$ is together with the time between the introduction of the index case(s) and the first reported death a relatively simple transformation between the current number of deaths and the total infected population. A similar calculation, but more simple without the Bayesian stuff around, is done in this blog post.

    Personally I am very skeptical about these calculations. There are some computations involved which make the appearance of a rigorous method. But effectively it is just scaling the current number of deaths with a factor in order to guestimate the current number of infected/immune people. The numbers involved in the determination of the scaling factor are very uncertain and biased. The posterior estimate of the number infected people is just as uncertain as the prior estimate of the factor $\rho$ and the time between first index case and first death (as well as other factors like estimates of growth rate and estimates of incubation time, and bias in reports about the number of deaths.... it is a big mess)

Travel data

The virus is mostly spreading out irregularly over a network. It spreads out differently at different scales, within the household, neighborhood, workplaces/schools, villages, agglomerations, countries, continents. You can sort of see the virus spread around with sudden jumps from large node/community to large node/community.

You can use occurrence of the virus in those nodes/communities as the variable (so you do not count individuals, since we do not know the presence in all individuals, but instead count the much better known presence of the virus in communities), and then use a model for the dynamics of the virus spreading between this different nodes in the network.

For instance. E.g. in region A you encounter x cases of disease among people that came from region B and y cases of disease among people that came from region C, while the travel to those regions is $r$ and $q$, then an estimate of the relative presence of the virus in regions B:C can be approximated by (x/r):(y/q).

I remember there was an early article on the spread of COVID-19 (I believe it was by Chinese scholars) that tried to estimate $R_0$ and included information about the frequency of travel between different regions.

Random tests

You can perform test on a sample from the population that does not show any symptoms and use the prevalence of the virus among this sample to make an estimate about the prevalence in the entire population.

If the prevalence is very small then this requires a very large sample which might be difficult. In that case one may perform the test among a sample where the suspicion of the prevalence is higher and gain some information about how many people have the virus in that group. Such a measure can be used to calibrate the estimates based on incomplete information (ie. along with other information, such as the rate at which people with the virus have the particular mild or severe symptoms, you get an idea about how much the current estimates are underestimating the true number of cases).

  • Edit 3 By now there have been a few of these type of screenings. For instance:

    When more of these results come in we are able to make a much more rigid estimate about the spatial distribution and prevalence of the disease.

Sextus Empiricus
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  • As a comment to death rate: there are reports all over the world saying that many deaths were not attributed to COVID-19, while they likely were caused by it. So the death rate is likely an underestimate of the actual death rate. Also, it depends on external factors like capacity and quality of healthcare. – Tim Mar 25 '20 at 09:42
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    @Tim very good point. I have added a 5th paragraph. Do you believe this covers it. (Besides underreporting I imagine that over-reporting could just as well occur) – Sextus Empiricus Mar 25 '20 at 10:30
  • @Tim the opposite is also happening. In Italy everyone who tested positive at the moment of death is added to the COVID-19 deaths count, even though the infection wasn't the cause of death. – DeltaIV Mar 25 '20 at 11:07
  • About random testing, the case of Vo' Euganeo in Italy where everyone was tested is interesting: https://www.theguardian.com/commentisfree/2020/mar/20/eradicated-coronavirus-mass-testing-covid-19-italy-vo it’s not random, but it does offer a view of the percentage of asymptotic infections – DeltaIV Mar 25 '20 at 11:18
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    @YiannisDermitzakis I noticed you accepted the answer. I have now made two edits to it. One is a reference to research from Oxford University that took your approach, and another is a renewed view of the death rate reports based on more data from national statistics agencies (which indicates that the reports on covid-19 can be, have been, wrong at least in the order of a factor 2). – Sextus Empiricus Apr 20 '20 at 08:11
  • Regarding your edit 1, even the comparison of deaths this year with average of previous years underestimates the deaths directly caused by COVID-10. The lockdowns have almost certainly reduced mortality due to other transmissable diseases such as seasonal flu. In other words, if we had a lockdown but no COVID-19, deaths would be lower this year than in previous years. – mkt Apr 20 '20 at 08:25
  • @mkt-ReinstateMonica you mean because of such things like less road accidents etc? That might be possible but it is not so certain, while a lockdown can be a cause for reduced death, it is also a cause for increased death (this could be verified because there are also more detailed tables about cause of death). Indirectly this could be verified with the regions that do not *yet* have many cases with covid-19. The regions that have a decrease in death rate are only limited. Based on that I believe that the lockdown does not have a strong influence on the death rate due to other causes. – Sextus Empiricus Apr 20 '20 at 08:40
  • The increase of death rate in the regions with the most cases is about a factor 4 (these are also smaller regions, the cities with larger population and less elederly tend more towards a factor 2). That is a large factor. So I imagine that this increase dominates the potential (small) decrease in the baseline due to the lockdown (even when covid-19 would be absent). – Sextus Empiricus Apr 20 '20 at 08:42
  • @SextusEmpiricus I specifically meant other illnesses; the drop because of road accidents is generally easy to correct for because it is categorised separately. And I don't mean to argue that is a large effect, merely that it is a bias, and the size of the effect is likely to be higher in places where the disease is still early in its trajectory. The argument mainly relates to cities, where such transmission is likely to be higher. – mkt Apr 20 '20 at 08:48
  • We should also not overestimate the effect of the lockdown. While we are locked up inside our homes we still need to go shopping to get food and elderly still need care from nurses. The virus keeps spreading even with a lock down, because a lock down does not mean that *all* life stops. The lock down is effective in reducing the rapid spreading over large distances, and reduces events that cause superspreading, But disease still goes on. So those other illnesses may still reach the elderly while they are together in care homes or hospitals. – Sextus Empiricus Apr 20 '20 at 08:50
  • In addition, those other diseases are only partially infectious diseases (there is also a baseline of heart attacks, cancers, etc. something which may actually go up now due to increases pressure on the health systems). Normally there is a lot of increase in deaths during the winter (summer around 50k deaths/week in summer and 60k deaths/week in winter, in Europe), but this is already less around spring. The increase due to covid is around a factor 3 (locally). Maybe there is some decrease in the baseline due to the lock down, but it will not be more than a factor 1 and most likely a lot less. – Sextus Empiricus Apr 20 '20 at 08:53
  • The strongest indication is that we do not see a lot decrease in death rate in regions without covid-19 but with the same lock down measures. – Sextus Empiricus Apr 20 '20 at 08:56
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It seems that there is a blog post that also deals with this question.

If you have deaths in your region, you can use that to guess the number of true current cases. We know approximately how long it takes for that person to go from catching the virus to dying on average (17.3 days). That means the person who died on 2/29 in Washington State probably got infected around 2/12. Then, you know the mortality rate. For this scenario, I’m using 1% (we’ll discuss later the details). That means that, around 2/12, there were already around ~100 cases in the area (of which only one ended up in death 17.3 days later). Now, use the average doubling time for the coronavirus (time it takes to double cases, on average). It’s 6.2. That means that, in the 17 days it took this person to die, the cases had to multiply by ~8 (=2^(17/6)). That means that, if you are not diagnosing all cases, one death today means 800 true cases today.

Here is another dashboard with a similar estimation methodology:

Estimating The Infected Population From Deaths

Yiannis Dermitzakis
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    Trying to guess the infected population I've seen something similar done https://www.ft.com/content/5ff6469a-6dd8-11ea-89df-41bea055720b (if that financial times article is blocked you can go to the original article draft dropbox [pdf](https://www.dropbox.com/s/oxmu2rwsnhi9j9c/Draft-COVID-19-Model%20%2813%29.pdf?dl=0)) there's a lot of computation involved, but in the end it is just a lot of guessing obscured by mathematics. There is very little we can say about the infected population. Or at least with *just* this data about the number of deaths, it won't be a data driven guess that we make. – Sextus Empiricus Mar 25 '20 at 08:48
  • Worth reading before looking at the blogs: https://www.buzzfeednews.com/article/ryanhatesthis/im-not-an-epidemiologist-but-the-rise-of-the-corona – Tim Mar 25 '20 at 09:40
  • @Tim While this is a worthwhile read, remember that the blog post linked at the beginning of this answer (the famous "Coronavirus: Why You Must Act Now " post by Tomas Pueyo) was endorsed by many leading experts. – Itamar Mushkin Mar 25 '20 at 10:35
  • @ItamarKushkin *"endorsed by many leading experts"* What do you mean by that? It can't be wrong? There is a lot of number-magic around. This appeal to ethos sounds a bit awkward to me. It is not really to the point/argument. Imagine a magician can make a body disappear and experts believing it. – Sextus Empiricus Mar 25 '20 at 13:19