The number of death cases caused by COVID-19 is not an appropriate indicator for assessing the consequences of the SARS-CoV‑2 pandemic and the effectiveness of measures taken to manage it. For one thing, the attribution of cause of death (death due to COVID-19, death with COVID-19, or unrelated death) and the quality of completed death certificates differ considerably between countries [1]. For another, the number of deaths caused by COVID-19 also depends on how frequently COVID-19 was tested for—testing capacity was often inadequate, especially during the early phase of the pandemic.

Excess mortality during the pandemic is an alternative for which the aforementioned definitional problems do not matter. However, it is not possible to distinguish between direct and indirect effects of COVID-19 when calculating excess mortality. Indirect effects include, for example, delayed cancer treatments or changes in healthcare utilization. In principle, one would need to find out what the mortality rate would have been in the pandemic period if the pandemic had not occurred. Since this is not possible from an epistemological point of view, calculation of excess mortality compares the number of deaths observed during the pandemic with the number of deaths that would have been expected based on mortality rates in pre-pandemic years.

Published excess mortalities often differ even for the same country. For example, the total number of excess deaths estimated for five northern European countries (Denmark, Finland, Norway, Sweden, Iceland) for 2020 and 2021 varied between 14,738 and 37,708 in five different studies [2]. For 2020, both an under-mortality of 2% and an over-mortality of 6% were published for Germany [3, 4]. The reason for such discrepancies is that estimating excess mortality requires a number of subjective methodological choices. The aim of this paper is to raise awareness of these methodological issues.

The following example is presented to briefly illustrate how excess mortality is calculated in principle. Table 1 shows the individual steps for calculating the standardized mortality ratio (SMR) for the population of the city of Frankfurt am Main in Germany. Table 2 contains the data necessary for the calculation, which include the number of deaths and the population for the years 2018–2020 separately for five age groups. Here, the number of persons in the population is equated with the number of person-years. First, the mortality rate per 1000 person-years is calculated for each age group in the two pre-pandemic years—for example, 3244 deaths in 32,655 person-years among people aged 80+ years in 2018 yields a mortality rate of 99.34 per 1000 person-years. Then, for each age group, the mean mortality rate is calculated from the 2018 and 2019 mortality rates. Finally, for each age group, we calculate how many deaths one would expect to occur in 2020 if the mortality rate in that year were exactly equal to the mean of the two pre-pandemic years. With 35,348 person-years among people aged 80+ years in 2020, one would expect 3385 deaths using the mean mortality rate of the two previous years of 95.763 per 1000 person-years. For the four other age groups, the number of expected deaths is calculated in an analogous manner. For all age groups combined, 6034.7 deaths would be expected to occur in 2020 if the age-specific mortality rates in 2020 had been the means in the two pre-pandemic years. Finally, the SMR is calculated as the ratio of the number of observed deaths and the number of expected deaths for 2020, i.e., SMR = 5982/6034.7 = 0.991. An SMR value greater than 1 indicates excess mortality, while an SMR value less than 1 indicates under-mortality. Thus, with an SMR of 0.991, there is minimal under-mortality. This simple calculation involves several choices that are responsible for the fact that published excess mortality figures often differ widely, even for the same country [5,6,7]. Six reasons for the wide range in reported excess mortalities are described below.

Table 1 Calculation of the expected number of deaths for 2020 using the data of Table 2
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Table 2 Age-specific deaths cases and age-specific population of the city of Frankfurt am Main for the years 2018–2020
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Lack of age standardization

As populations age, the number of deaths increases even if age-specific mortality rates remain the same. For example, in Germany, the number of people over 80 was 4.8 million in 2016 and 5.8 million in 2020 [3]. Without age standardization Germany would erroneously be found to have an SMR > 1, even if age-specific mortality rates remained constant. Levitt et al. stated that age standardization was not performed in three out of four published studies of excess mortality calculated for the whole world, and thus these three studies have a serious methodological flaw [6].

Choice of reference period

The number of expected deaths is calculated from mortality rates in the pre-pandemic years. However, there is a wide range of possible choices for the reference period. For example, in Germany, the number of deaths was 939,520 in 2019 and 954,874 in 2018. If 2019 is chosen as the reference year, the number of deaths expected in 2020 will be lower than if 2018 or 2018 and 2019 together are chosen as reference years. However, the choice of the reference period is quite arbitrary. Levitt et al. calculated excess mortality for 33 countries for 66 reference periods each [7]. The excess mortalities for one and the same country vary considerably depending on the selected reference period. For Germany, the minimum from the 66 excess mortalities is −4.4% and the maximum is 4.5% (United States: 14.3 and 18.7%, respectively; Sweden: −12.5 and 4.2%, respectively).

Choice of index period

The choice of the index period has a large impact on the estimated excess mortality. For example, the index period may be limited to a single wave of the COVID-19 pandemic, or it may include several years. Imagine that a multimorbid patient would have died in February 2021 without COVID-19 disease, but as a result of COVID-19 disease, the patient died as early as November 2020. If excess mortality is calculated for 2020 only, this death case will increase excess mortality. However, if 2020 and 2021 are chosen as the index period, this death does not increase excess mortality because the patient would have died during this 2‑year period with and without COVID-19 disease. A large proportion of deaths caused by COVID-19 involved vulnerable individuals with only a short life expectancy remaining. When a short index period of several months is chosen, such deaths increase excess mortality. However, this excess mortality decreases when the index period is extended. Levitt et al. calculated excess mortality for 33 countries, varying the length of the index period [7]. As expected, lengthening the index period resulted in a decrease in excess mortality.

Extrapolation of mortality rates

Once the reference period is established, there are several ways to calculate the mortality rate expected for the index period. In the example presented, the mean of the age-specific mortality rates from the reference period was used. Often, the years of the reference period show a trend in mortality rates over time. In most Western European countries, mortality rates decreased steadily from 2009 to 2019 [7]. Therefore, the expected mortality rate could alternatively be determined by extrapolating this trend. The extrapolation of a falling mortality rate leads to lower figures for the expected mortality rate and thus to a higher excess mortality rate [5]. However, extrapolating a trend in mortality for several years may result in generating an unrealistically low number of expected deaths. By using a spline function, which describes nonlinear curves by the piece-wise use of polynomials, the World Health Organization (WHO) had calculated numbers of expected deaths for Germany for 2020–2022 that were significantly lower than the number of deaths during 2015–2019. The high number of excess deaths calculated using this method was later revised downward by the WHO from 195,000 to 122,000 [8]. There is no standard for extrapolating mortality rates from reference years. An argument against extrapolating mortality trends is that they may not persist, as observed in the United States in recent pre-pandemic years [9].

Factoring out other irregularly occurring risk factors

Studies of excess mortality also differ in whether additional deaths from other irregularly occurring risk factors, such as heat waves and seasonal influenza, were factored out [6]. For example, heat-related deaths during the index period led to more observed deaths and thus higher excess mortality, whereas heat-related deaths during the reference period led to more expected deaths and thus lower excess mortality is calculated. There is currently no standard for whether or not to exclude heat-related or influenza-related deaths.

Data quality, number of age categories

Preliminary data on deaths provided by offices for national statistics are often updated after initial publication. Therefore, excess mortality results may differ when data provided at different times are used [5]. Furthermore, studies on excess mortality often differ in the choice of age categories. Kowall et al. gave an example to show that the SMR estimated for Germany in 2020 was higher when 5‑year age groups were used instead of 20-year age groups [5].

Figure 1 shows the combined excess deaths for 2020 and 2021 from four studies published in eLife, The Economist, The Lancet, and by the WHO, as well as from two further analyses by Levitt et al; Levitt 1 was age-adjusted, Levitt 2 was not age-adjusted [6]. For Germany, the estimated numbers of excess deaths ranged from 54,740 to 203,000, and for 33 selected (mainly OECD) countries combined, these numbers ranged from 1,609,862 to 2,780,726. The estimated number of excess deaths was lowest in the only age-standardized analyses—this was Levitt 1. The studies also differed in the choice of reference period, whether or not to exclude heat waves, and the modeling of the reference period [6]. These examples show how much methodological differences affect the estimated excess mortality.

Fig. 1
figure 1

Excess deaths estimates during 2020–2021 for Germany and for 33 selected countries The numbers shown in the figure are reported in [6]. These are results from four studies published in eLife, The Economist (Econ), The Lancet, and by the World Health Organization (WHO), as well as from two further analyses by Levitt et al.; Levitt 1 was age-adjusted, Levitt 2 was not age-adjusted

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Conclusion

Excess mortality is important as an indicator of the health consequences of the COVID-19 pandemic and for evaluating the measures taken. Unlike cause-of-death statistics evaluations, the calculation of excess mortality using standardized mortality ratios does not depend on the attribution of causes of death and the quality of the death certificates. However, the wide range of methodological choices described here means that comparability of excess mortalities estimated for different regions or countries cannot be taken for granted. We suggest that future studies should not only present the result for a single set of analytical choices, but also for sets with different analytical choices, so that the dependence of the results on the choices becomes explicit.