key: cord-331354-ungzlp6b
authors: Mimkes, J.; Janssen, R.
title: Test-adjusted results of mortality for Covid-19 in Germany, USA, UK
date: 2020-11-04
journal: nan
DOI: 10.1101/2020.11.03.20225268
sha: 
doc_id: 331354
cord_uid: ungzlp6b

In a disease, where all infected persons show symptoms, it is reasonable to calculate mortality by case to fatality rate CFR. Deaths follow infections by a certain time lag. However, in the Covid-19 pandemic many infectious patients show no or hardly any symptoms. The reported infections and deaths do not run parallel, but diverge with the volume of tests. Our investigations for Germany, USA and UK indicate that deaths do not follow the number of infections, but the positive rate of tests, multiplied by a constant factor F and shifted by about two weeks. These test adjusted results of mortality allow for the estimation of the number of deaths of Covid-19 about two weeks ahead, even in a sharply rising state of the pandemic. This gives medical authorities two weeks of time to plan for resources.

Mortality is the most important indicator of a pandemic and scientists all over the world are estimating mortality from Covid-19. A good introduction has been given in a scientific brief by the World Health Organization WHO [1] . In a pandemic, two time series are generally reported: the time series of daily infections (I k), and the time series for daily deaths (D k), as provided by the Johns-Hopkins-University (JHU) in USA and the Robert-Koch-Institute (RKI) in Germany. A wide range of values has been reported in the literature for the CFR, varying with time and location [2] [3] [4] . In this paper we concentrate on mortality in Germany, USA, and UK.

The series of daily registered new infections (I k) and the series of daily deaths (D k) are given in figs. 1 and 2. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 4, 2020. ; https://doi.org/10.1101/2020.11.03.20225268 doi: medRxiv preprint 

Normally, in mortality calculations the series of daily deaths (D k + L) follows the series of daily infections (I k) by a time lag (L) and is smaller by the case fatality ratio CFR, D k + L = CFR * I k.

(1)

In fig. 2 the maximum of deaths (300) follows the maximum of infected (6000) in fig. 1 about two weeks (L = 13) later, and is smaller by the factor CFR = 300 / 6000 = 0.05. This leads to D k + 13 = 0.05 * I k (2) Eq. (2) has been plotted in fig. 3 . Data and calculation of CFR mortality in fig. 3 agree for the first Covid-19 wave from March to June, as would be expected. But from July on the calculations of daily deaths drifts away to higher numbers, whereas the actual death data stay close to zero between July and September, indicating only rising numbers in October. As the deaths in fig. 3 do not follow is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 4, 2020. ; https://doi.org/10.1101/2020.11.03.20225268 doi: medRxiv preprint the infections, the CFR is not any more constant, but is time variant, CFR k. A similar observation has been made in many countries, as shown for USA and UK, below. In a recent paper the authors [5, 6] proposed to explain the disagreement between calculations (eq. 1) and mortal data in fig. 3 by considering a change in test volume. Indeed, the test volume in fig. 4 in Germany has been increased from July until September by a factor of 3.

For a more detailed analysis, we divide the infection numbers I k by the test volume T k. Then we scale the result by a mortality factor F = 2500 to obtain an optimal approximation to the deaths series of the pandemic in fig. 5 . 

and we obtain a test depending mortality CFR k = 2500 / T k.

. CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 4, 2020. ; https://doi.org/10.1101/2020.11.03.20225268 doi: medRxiv preprint A test adjusted approach to mortality In order to explain the test depending mortality CFR k in eq. 3 and fig. 5 , we propose a test adjusted approach to mortality: In diseases where many infectious patients show no or hardly any symptoms, we do not know the total number of infections. But we can determine the daily number of infections I k, T by the positive rate P k of daily infections of a certain daily test volume T k, I k, T = P k * T k.

In eq. 3 we may now replace the ratio I k / T k by the positive rate of tests P k of eq. 4,

In eq. 5 and fig. 5 the number of daily deaths D k + L follows the daily positive rate P k, and not the daily number of infections I k as in eq. 1. The daily numbers of infections and deaths are now represented in eq. 4 and eq. 5 by the daily positive rate P k and the daily test volume T k. The daily test volume T k and the daily positive rate of infections P k are given by the Robert-Koch-Institute, in figs. 4 and 6. The time lag L between infection and death is about 13 days in Germany.

The relationship between the number of daily deaths and the number of daily infected in eq. (1) is invalid, if the daily test volume is not constant. High numbers of infected do not necessarily mean high number of deaths.

This statement does not diminish the danger of Covid-19, but puts it on a scientific basis. Accordingly, the daily positive rate of tests should be published in addition to the presently dominating infection numbers, which are used for other purposes like tracking.

The daily positive ratio of tests leads to a realistic estimation of the number of deaths two weeks in advance in eqs. 3 or 5 and in fig. 5 .

This gives medical authorities two weeks of time to plan ahead for the numbers of severely ill patients, which are closely related the number of deaths. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 4, 2020. ; https://doi.org/10.1101/2020.11.03.20225268 doi: medRxiv preprint JHU data for USA For USA, the Johns-Hopkins-University (JHU) provides the series of daily registered new infections (I k) and the series of daily deaths (D k) in figs. 7 and 8. The daily test series is shown in fig. 9 . is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 4, 2020. ; https://doi.org/10.1101/2020.11.03.20225268 doi: medRxiv preprint The mortality factor F calculates the number of deaths of a country at a certain positive rate of testing (P k), accordingly, the mortality factor will depend on the population of a country if the modalities of testing are comparable.

Since the population in USA (320 million) is larger than the population in Germany (83 million) by a factor of about 4, we would estimate F USA = 4 * F Ger = 10,000. This estimation is of the same order as the result above, and supports the test adjusted approach to mortality of Covid-19 in Germany and other countries. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 4, 2020. ; https://doi.org/10.1101/2020.11.03.20225268 doi: medRxiv preprint

In UK, the test adjusted infection data (I k / T k) also lead to a realistic prediction of the death series of the Covid-19 pandemic ( fig. 11) . The time lag is about 14 days and the mortality factor F UK about 2,700, deviating slightly from those in USA and Germany, if related to the population. Fig. 11 . Daily deaths data by JHU (bars) in UK and calculation of D k + 14 according to eq. 1 (dashed line) and eq. 5 (solid line). Test data since 31.03.20 [8] .

In a pandemic with symptomatic and asymptomatic courses of the disease like in Covid-19, the pure number of infections is not significant for the danger of the pandemic. The indicator for the number of deaths is the positive rate (P k) of tests. It is a scale for the number of deaths, and in addition, it is known about two weeks earlier.

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