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Better estimations of fatalities, infections numbers and infection fatality rates

Originally, the age-dependent IFRs calculated from the outbreak in Bergamo were used as-is for all countries to calculate the countries' potential fatalities and their overall IFR. However, the IFR values depend on several matters, for instance one being the “pressure” on the health system and disease preparations, which were not favourable to Bergamo during their outbreak.

It is also obvious that if Bergamo originally had a worse healthcare system it would have saved less lives and, hence, produced a larger number of fatalities. In other words, IFRs depend on the quality of the healthcare system. A country with a worse healthcare system will in general have higher IFRs that a country with a good one.

The purpose of this discussion is to come up with better estimations on the number of fatalities and infections for each country worldwide by calculating more realistic values for the IFRs for each.

Better adaptations of the age-dependent IFRs from Bergamo

Initially, the original, age-dependent IFR numbers from Bergamo were applied on all countries to calculate the countries’ generic IFRs, potential fatalities and the number of infections.

Bergamo was in the center of the pandemic outbreak in Europe. The infections came early and quickly, and the community was not prepared for what was about to happen. At the height of the outbreak, the situation was chaotic and the hospitals had to start triaging patients (see e.g. ) which means that fatality rates would most likely have become higher than if the Bergamo community had had the chance to ”flatten the curve” before the outbreak. There was a period of two weeks where the ICU usage peaked at close to 100% percent of the capacity ( ).

When applying the Bergamo rates to the rest of the world, we would like to have as precise numbers on IFRs as possible and whose are relevant for a typical, "generic" pandemic spread situation. The IFRs from Bergamo are obviously including the effect of the chaotic situation during their outbreak. However, most of the rest of the world have had a chance to implement various “curve flattening” and preparatory procedures before their outbreaks. The IFRs applied should reflect this. In other words, applying Bergamo IFRs unconditionally will create slightly too high values for most other countries that were affected later.

To accommodate for this, one would need to know how many lives would have been saved if Bergamo had gotten the option to “flatten the curve” and prepare better before the outbreak. I have not been able to find good figures on that, so assumptions are made:

We assume that the triaging in Bergamo, and the chaotic situation in general, affected the elderly most. This is so because younger patients will be prioritized.

If Bergamo province have had the chance of flattening the curve and prepare as the rest of the world, while still reaching the same level of infections in the end, we conservatively assume that:

For ages > 45, for 100 persons, lives_saved = 0.14 * (age - 45) , i.e. of those that died at age

would have been saved.

This adjustment of the Bergamo IFRs are applied to the calculations of the country-specific IFRs.

It might be that this adjustment is not enough to reflect the results of the chaotic situation in Bergamo back in the worst spring months. However, due to lack of proper research data on this, we do not want to overestimate the effect. 

If anyone has any good sources of excess deaths specifically due to the specific situation (i.e. no early curve-flattening and lack or preparations) that arose in Bergamo, please let me know.

Estimating a country’s healthcare system quality

For several calculations, an number representing the quality of a country's heathcare system is needed.

WHO has not since 2000 produced a rating of healthcare systems worldwide. ( ) Using figures that are 20 years does probably not reflect huge improvements in many countries since 2000.

There exists other lists, but when looking into the numbers, they show several shortcomings. Therefore, the following simplified solution has been selected: 

It is assumed that a country’s overall life expectancy at birth is quite proportional to the country’s healthcare system quality. Life expectancy has improved a lot in the last 20 years, especially in developing countries, which then probably reflect that these are “catching up” with the leading ones.

The quality indicator is calculated as the life expectancy at birth for the given country, divided by the life expectancy of Japan, which has the largest life expectancy for 2018.

How the healthcare system quality affects COVID-19 fatality rates

The IFRs are the "result" of fatalities due to infections, and a country's quality of its healthcare system affects the success in saving lives. The healthcare system quality indicator can be sufficient in general to give somewhat better figures on IFRs rather than assuming the Bergamo healthcare system quality for all countries.

In order to calculate this effect, we need to make a lot of assumptions. These are of course open for discussion. We will use some known figures from Norway, then estimate what these might be if the Norwegian healthcare system was “the worst one in the world”. That number will then show how the worst healthcare system relates to the Norwegian one. The number will then be used as part of the formula to calculate a healthcare system correction ratio to the IFRs for each countries.

As of 17 Sep 2020, the official figure is 267 COVID-19 deaths. Official figures include at least all hospital deaths.

We have in the next chapter discussed how many additional fatalities there might be, and referred to the report that assumed 50% underestimations in general in Lombardia. Since that report is based on the early Italian situation, we assume that in general underestimation is not that bad and set it to half of that. With an underestimation of 25%, 267 * 25% = 67 Norwegian deaths are not accounted for, totalling to 334 deaths in total.

At the time of writing, there have been 1077 holitalizations in total in Norway due to SARS-CoV-2. Of these 236 went all the way to ICU. ( )

It was not possible for me to easily find updated statistics on where the various deaths happened, but as of 28 April 2020, 195 persons had died according to official figures, with the following distribution ( ):

Upscaling these figures to current figures gives:

We assume that the 67 unaccounted deaths happened mostly at home (60% => 40 persons) and at elderly/health facilities (40% => 27 persons). This gives the final distribution:

In other words, of the 1107 hospitalization, 94 persons died. I do not have figues on how many of the 69 that died at hospital in April actually went into intensive care, so once again one needs to make assumptions:

If you are so sick that you are sent to hospital, you have a high chance of being sent to intensive care if your condition becomes serious. The condition might still get so serious that intensive care is not successful. Therefore, we assume that of the 94 hospital deaths, 80% (75 persons) happened at intensive care, and rest in “normal” hospital care (19 persons). This gives the final death distribution:

The task is now to estimate how many deaths Norway would have had with the same figures if it had a similar healthcare system as the Central African Republic (CAR), which had the lowest life expectancy in 2018. Once again, we need to make assumptions:

Intensive care deaths would most likely have been most of those submitted. Using 80% of 236, we get 156 deaths instead of 75.

If you were not so ill that you were not sent to intensive care, you still would probably have a fair chance of survival in the low quality system, so we assume that 25% of those hospitalized would die (instead of 2.3%), i.e. around 10 times as many. This gives  i.e. 841 * 25% = 210 deaths instead of 19.

The elderly and those at home would also have died, i.e. 193 and 47.

This sums up to 156+210+193+47 = 606 fatalities.

The ratio of fatalities for the worst healthcare system vs. Norway’s is then 606/334 = 1,814. I.e., the IFRs would almost double for Norway if the healthcare system was in a similar state as CAR’s, while still keeping other conditions unchanged. In other words, the IFRs of CAR needs to be multiplied by 1.814 to give more realistic IFRs for CAR vs. Norway.

It is reasonable to assume that due to the large number of uncertainties, assumptions and approximations, this ratio is very uncertain. It is fully reasonable to argue that the ratio is too low or too high. However, the point here is also to make sure that we do not risk overestimating the IFR too much, and that this ratio will give a much more realistic figure than no ratio at all.

The ratio to “upgrade” the IFRs is dynamically calculated and applied to all countries IFRs in the IFR_HSA column, giving a more realistic IFR that also considers the healthcare system quality of the country.

How the healthcare system’s quality affects the ability to correctly identify and report COVID-19 fatalities

It is evident that reporting of fatalities and infections depends on the country’s infrastructure with respect to several matters. For example, in Norway, the reported number of registered infections is at time of writing approx. 13000 while the health authorities estimate that around 80000 is or have been infected. The ratio of “real” infections vs. the number of registered infections is assumed to be 80000 / 13000 ~= 6.

Likewise, for the number of deaths, the report assumes that the “real” number of fatalities has been underestimated by 50% in general.

Both these figures are easily explainable. The task is to find a generic formula to better calculate the number of actual deaths and infections in a country due to underestimations.

We have stated that a country’s IFRs depend on the country’s quality of the healthcare system. It is reasonable to assume that the ability to report causes of death correctly correlate somewhat with that quality. 

We assume that the report from Italy is correct when it comes to underestimation of COVID-19 deaths at its time. However, the report is much based on the very specific and chaotic situation that arose early in Lombardia. It is reasonable to believe that curve flattering and other healthcare improvements since then have improved the percentage of correct identification of COVID-19-caused fatalities.

We therefore assume that a more correct number on underestimation up till now is 25% (instead of 50%) in countries with similar healthcare system quality as Italy.

In India, several sero-surveys have been performed on a randomly selected population. The surveys show a huge underestimation of infections (and deaths). The estimate will be based following report:

To estimate the percentage for the underestimation in India, we do the following:

The report covers a survey done in the latter part of May 2020 and early June 2020. At this time, the outbreak in India had gained quite some traction. In order to not overestimate the underestimation level, we use the reported fatalities at the end of the test periode. According to ECDC, India reported 6363 fatalities and 226713 infections on the 4th of June.

The Indian research paper shows that of the randomly tested group of adult persons, 0.73% had antibodies against COVID-19. This equates to a more likely infection number for India at 6403853 adults (approx 64% of the population). The report did not cover children. As children seem to get less infected (and also following the principle of not overestimating), we assume that the children infections were at the half of the rate of the adults, meaning that in total 8189351 persons were infected. The infection rate was then underestimated by a ratio of 8189351 / 226713 ~= 36 .

Using the currently assumed health system adjusted IFR for India, this gives an estimated, "more likely" fatality number of 20636. In other words, the fatalities in India are underestimated by a ratio of 20636 / 6363 ~= 3.243 , or by 224.3%.

As with the estimate on the underestinations in high quality healthcare systems, we assume that the estimations have improved in India also and similar countries since then. Hence, for the calculations we assume that the underestimation now is 60% of the May/June situation, giving an underestimation percentage of 60% * 224.3% = 134.59% . 

As of 26 Sep 2020 India had 93379 reported fatalities. This gives an estimate of 93379 * 2.3459 = 219059 real fatalities and 219059 / 0.252% (IFR_hsa) = 87 million infections in total.

This number is hard to get verified. There are some newer sero-surveys that indicate an even higher virus distribution, but these results are not published through scientific channels yet. There is also an interview with a professor in epidemiology from University of Michigan which looks legit and which estimates 30 million cases on 25 July and up to 100 million cases in the next six weeks (i.e. around mid September), which is somewhat in line with what is calculated. ( )

Until better figures become available, we assume that countries with the healthcare system quality as India has this underestimation. Based on this and the Italian estimate above, a generic formula is made which produces an underestimation percentage for any country of the world, and then the underestimation percentage is applied to the reported number of fatalities to produce a more realistic number.

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