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. 2021 May;36(5):545-558.
doi: 10.1007/s10654-021-00748-2. Epub 2021 May 17.

Using excess deaths and testing statistics to determine COVID-19 mortalities

Lucas Böttcher  1   2 , Maria R D'Orsogna  1   3 , Tom Chou  4   5
Affiliations

Using excess deaths and testing statistics to determine COVID-19 mortalities

Lucas Böttcher et al. Eur J Epidemiol. 2021 May.

Abstract

Factors such as varied definitions of mortality, uncertainty in disease prevalence, and biased sampling complicate the quantification of fatality during an epidemic. Regardless of the employed fatality measure, the infected population and the number of infection-caused deaths need to be consistently estimated for comparing mortality across regions. We combine historical and current mortality data, a statistical testing model, and an SIR epidemic model, to improve estimation of mortality. We find that the average excess death across the entire US from January 2020 until February 2021 is 9[Formula: see text] higher than the number of reported COVID-19 deaths. In some areas, such as New York City, the number of weekly deaths is about eight times higher than in previous years. Other countries such as Peru, Ecuador, Mexico, and Spain exhibit excess deaths significantly higher than their reported COVID-19 deaths. Conversely, we find statistically insignificant or even negative excess deaths for at least most of 2020 in places such as Germany, Denmark, and Norway.

Keywords: COVID-19; Excess deaths; Mortality; Test statistics.

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Figures

Fig. 1
Fig. 1
Examples of seasonal mortality and excess deaths. The evolution of weekly deaths in (a) NYC (over seven years) and (b) Germany (over six years) derived from data in Refs. [28, 29]. Grey solid lines and shaded regions represent the historical numbers of deaths and corresponding confidence intervals defined in Eq. (1). Blue solid lines indicate weekly deaths, and weekly deaths that lie outside the confidence intervals are indicated by solid red lines. The red shaded regions represent statistically significant mean cumulative excess deaths D¯e. The reported weekly confirmed deaths dc(0)(i) (dashed black curves), reported cumulative confirmed deaths Dc(k) (dashed dark red curves), weekly excess deaths d¯e(i) (solid grey curves), and cumulative excess deaths D¯e(k) (solid red curves) are plotted in units of per 100,000 in (c) and (d) for NYC and Germany, respectively. The excess deaths and the associated 95% confidence intervals given by the error bars are constructed from historical death data in (a-b) and defined in Eqs. (1) and (2). In NYC there is clearly a significant number of excess deaths that can be safely attributed to COVID-19, while in the first half of 2020 there had been no significant excess deaths in Germany. Excess death data from other jurisdictions are shown in the SI and typically show excess deaths greater than reported confirmed deaths [with Germany an exception as shown in (d)]
Fig. 2
Fig. 2
Biased and unbiased testing of a population. A hypothetical scenario of testing a total population of N=54 individuals within a jurisdiction (solid black boundary). Filled red circles represent the true number of infected individuals who tested positive and the black-filled red circles indicate individuals who have died from the infection. Open red circles denote uninfected individuals who were tested positive (false positives) while filled red circles with dark gray borders are infected individuals who were tested negative (false negatives). In the jurisdiction of interest, five have died of the infection while 16 are truly infected. The true fraction f of infected in the entire population is thus f=16/54 and the true IFR=5/16. However, under testing (green and blue) samples, a false positive is shown to arise. If the measured positive fraction f~b is derived from a biased sample (blue), the estimated apparent IFR can be quite different from the true one. For a less biased (more random) testing sample (green), a more accurate estimate of the total number of infected individuals is Nc+Nu=f~bN=(5/14)×54≈19 when the single false positive in this sample is included, and f~bN=(4/14)×54≈15 when the single false positive case is excluded, and allows us to more accurately infer the IFR. Note that CFR is defined according to the tested quantities Dc/Nc which are precisely 2/9 and 2/5 for the blue and green sample, respectively, if false positives are considered. When false negatives are known and factored out CFR=2/8 and 2/4, for the blue and green samples, respectively
Fig. 3
Fig. 3
Excess deaths versus confirmed deaths across different countries/states. The number of excess deaths D¯e as of March 30, 2021 [29, 31] (counted from January 2020 onwards) versus confirmed deaths Dc across different countries (a) and US states (b). The black solid lines in both panels have slope 1. In (a) the blue solid line is a guide-line with slope 3; in (b) the blue solid line is a least-squares fit of the data with slope 1.087 (95% CI: 1.052–1.121); blue shaded region). All data were updated on March 30, 2021 [22, 29, 31, 40]
Fig. 4
Fig. 4
Different mortality measures across different regions. (a) The expected apparent (dashed lines) and true (solid lines) IFR¯s in the US from December 29, 2019 up until February 6, 2021, estimated using excess mortality data. We set f~b=0.089,0.15 (black, red), FPR=0.05, FNR=0.2, and N=330 million. For the expected true IFR¯, we use f^ as defined in Eq. (6). Unbiased testing corresponds to setting b=0. For b>0 (positive testing bias), infected individuals are overrepresented in the sample population. Hence, the corrected IFR¯ is larger than the apparent IFR¯. If b is sufficiently small (negative testing bias), the expected true IFR¯ may be smaller than the expected apparent IFR¯. (b) The coefficient of variation of D¯e (dashed line) and IFR¯ (solid lines) with σI=0.02, σII=0.05, and σb=0.2 (see Table 3)
Fig. 5
Fig. 5
Mortality characteristics in different countries and states. (a) Running vales of relative excess deaths r¯, the CFR, the IFR¯=pD¯e/Nc with p=Nc/(Nc+Nu)=0.1 [35], the confirmed resolved mortality M, and the expected true resolved mortality M¯ (using γ=100) are plotted for various jurisdictions. (b) Different mortality measures may be higher or lower in different jurisdictions, providing ambiguous characterization of disease severeness. (c–g) The probability density functions (PDFs) of the mortality measures shown in (a) and (b). Note that there are only very incomplete recovery data available for certain countries (e.g., US and UK). For countries without recovery data, we could not determine M and M¯. The number of jurisdictions that we used in (a) and (c–g) are 136, 247, 127, 191, and 75 for the respective mortality measures (from left to right). All data from January 2020 onwards were included and last updated on March 30, 2021 [22, 29, 31, 40]
Fig. 6
Fig. 6
Different mortality measures across different regions. We show the values of M and CFR (a) and M¯ (using γ=100) and IFR¯=pD¯e/Nc with p=Nc/(Nc+Nu)=0.1 [35] (b) for different jurisdictions. The black solid lines have slope 1. If jurisdictions do not report the number of recovered individuals, Rc=0 and M=1 [light red circles in (a)]. In jurisdictions for which the data indicate D¯e<Dc, we set γ(D¯e-Dc)=0 in the denominator of M¯ which prevents it from becoming negative as long as D¯e≥0. All data were counted from January 2020 onwards and last updated on March 30, 2021 [22, 29, 31, 40]
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