key: cord-0878122-7h3qgmtx
authors: Kepp, K. P.; Bjork, J. P.; Baek, K. T.; Lallukka, T.
title: Estimates of excess mortality for the five Nordic countries during the Covid-19 pandemic 2020-2021
date: 2022-05-07
journal: nan
DOI: 10.1101/2022.05.07.22274789
sha: b3e9f164a17233a76f847df255ea3a5a5f6f5721
doc_id: 878122
cord_uid: 7h3qgmtx

Excess deaths during the covid-19 pandemic are of major scientific and political interest. Here we review excess all-cause death estimates from different methods for the five Nordic countries (Denmark, Finland, Iceland, Norway, and Sweden), which have been much studied during the covid-19 pandemic. In the comparison of the methods, we use simple sensitivity estimates and linear interpolations of the death data to discuss uncertainties and implications for reporting ratios and infection fatality rates. We show using back-calculation of expected deaths from Nordic all-cause deaths that a recent study in Lancet, which is a clear outlier in the overviewed estimates, most likely substantially overestimates excess deaths of Finland and Denmark, and probably Sweden. The other estimates are more consistent and suggest a range of total Nordic excess deaths of approximately half of that in the Lancet study, a more uniform ability to identify covid-19-related deaths, and more similar infection fatality rates for the Nordic countries.

Excess deaths (the difference between observed and expected deaths) during the covid-19 pandemic are of major scientific and political interest, as they provide objective estimates of the pandemic burden not confounded by different testing and registering of covid-deaths. [1] [2] [3] [4] All-cause excess deaths include deaths due to SARS-CoV-2 infection and other causes such as cancer 5 and are of interest from a total evaluation perspective. Here, we review several methods to estimate the final 2020+2021 all-cause deaths and uncertainties in these for the five Nordic countries (Denmark, Finland, Iceland, Norway, and Sweden).

We studied the Nordic countries due to i) special interest and insight by the authors, ii) they form a historically and culturally related entity with public health data of high quality, iii) they have been much studied during the pandemic, with claims of both failures (Sweden) and successes (e.g., Norway and Denmark) [6] [7] [8] , and iv) all five countries have their final annual all-cause deaths available for the full years 2020 and 2021 at the time of this analysis (the final data from Iceland became available April 27, 2022 ).

Our review is partly motivated by a recent paper in Lancet by Wang et al. 9 using a model for predicting global excess deaths, which concludes that excess deaths of Sweden, Denmark, and Finland are much larger 9 than previously estimated. 8, 10 The study also implies very large differences in the five countries' ability to identify covid-19 deaths, with ratios of excess deaths to official covid-19 deaths ranging from 3.2 and 5.0 for Denmark and Finland to -8.5 and 0.6 for Iceland and Norway. 9 While such registration criteria are never perfect, 11 these differences seem implausible given the relatively similar health systems and practices of the Nordic countries. Another surprising consequence of this model, when combined with infection estimates, is 6-7 times higher infection fatality rates (IFR) in Finland and Denmark than in Norway, and almost double that of Sweden. 12 Due to the topic's importance, these major differences warrant further scrutiny.

To understand the different model results better, we use the latest high-quality register data to examine the death estimates via linear interpolation. Specifically, we use annual all-cause Nordic death data to backcalculate the expected deaths required (but not reported) for stated excess deaths to be accurate. Second, we discuss the different model estimates in relation to the final 2020 and 2021 Nordic data and discuss limitations and realistic ranges via sensitivity tests.

Data used -We collected the final all-cause deaths for 2010-2021 from the relevant statistics authorities, divided into years in order to avoid seasonal effects (we note that Wang et al. 9 used both weekly and monthly data and did not have access to the final 2021 data in their estimates), Table S1 , as well as mean population data per year. The links to the sources of the data can be found in the Data availability statement.

Back-calculating expected deaths -Excess deaths are defined as observed real deaths subtracted by the expected deaths, equation (1):

Excess deaths = observed deaths -expected deaths (1) To test the validity of the model numbers we used reported excess deaths and the actual, final deaths for back-calculating the expected deaths implied via equation (2) : Expected deaths from model = observed deaths -excess deaths from model

We then compared these implied expected deaths with the actual death data to test the reasonability of assumed baselines of estimated deaths, and conversely, the stated excess deaths.

Challenges estimating excess mortality -Challenges when estimating excess deaths include: 1) the trends in population structure, notably aging and sizes of old age groups, should be accounted for; 2) depending on time period, seasonality and week/year overlap (ISO-week) if using weekly data vs. annual data; 3) different correlation times of death causes, with mortality in one time period correlating with the next period (mortality displacement) 13, 14 ; 4) unusual recent events could distort baseline estimates. If interested in individual causes of death, a range of additional assumptions emerge, beyond the scope of this study.

No method handles all issues perfectly. Linear interpolation on full-year data solves some of the issues as it averages out season but is sensitive to recent unusual events. Linear trends can handle population structure on short timescales but are sensitive to recent unusual events, as analyzed below. Yet this approach, as applied e.g. by Karlinsky and Kobak, 10 and Economist, 15 does not include any assumptions beyond linearity and thus serves an important purpose as sensitivity tests for understanding and comparing the data, which is essential 16 . Methods that use fixed functional (e.g., sinusoidal) forms to smooth out curves and e.g., reduce the impact of unusual influenza seasons or heat waves also exist, e.g., euromomo. 17, 18 Sensitivity analysis and comparisons -To understand ranges and uncertainties, we calculated 5-year and 10-year linear trends in all-cause deaths (2015-2019 and 2010-2019). The removal of single unusual years from provides an estimate of maximum baseline impact and was done for the recent years 2018 and 2019.

Changes of the population age have a large impact on expected deaths (and thus deduced excess deaths) 19 , with death rates being exponential in age, also for deaths due to covid-19, 20 and can be accounted for using mortality rates based on mean annual age-group-specific populations from the Nordic Council's aggregate data from the five statistical departments (see https://pxweb.nordicstatistics.org/). However, all estimates reviewed here only report total all-cause deaths, so comparison of age-specific deaths was not possible.

Excess death estimates for 2020 and 2021 were compiled from the method of Wang et al., 9 and from the method used by The Economist (via Sondre Solstad) in two different versions 15 ; one that includes the January and February 2020 death data in fitting the expected death trends, and one that does not.

We also studied the World Mortality Dataset (Ariel Karlinsky and Dmitry Kobak) 10 whose results may partly differ despite the similarities in the design of the models (See below). These models run weekly from December 30, 2019 to January 2, 2022, giving four days difference in total deaths relative to the yearly time series in Table S1 , and use linear trends to estimate expected deaths.

We also included in our overview the estimates by the World Health Organization (WHO) 2020 and 2021 excess deaths released May 5, 2022. 21 These models were produced by the Technical Advisory Group for COVID-19 Mortality Assessment and use a statistical model that, as WMD and Economist models, emphasizes the hard data for countries where these are available, which includes the Nordics, and predictions for those where they are not. 22 We did not include data for euromomo 17 in our review, because all-cause excess death numbers for the final years 2020 and 2021 are not yet available in a public form, but we intend to include these numbers in an updated overview as soon as they become available to the public in 2022.

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 9 , using Equation (2) (analysis for mortality rates in Figure S1 ).

Overview of death estimates - Table 1 shows an overview of the analyzed data for the five Nordic countries. While most methods are in some relative agreement, one of the methods reviewed, the new study by Wang et al. 9 in Lancet, produces very different results from other models studied, with potential major implications, perhaps best seen from the excess deaths per 100,000 people in Table 2 , with e.g., Sweden and Denmark (and almost Finland) having similar high deaths per capita, not seen with other methods.

To understand these differences in more detail, we used linear interpolations to estimate what the expected deaths would have been if they followed a trend in the actual annual death data and compared these to the final Nordic annual deaths for 2020 and 2021 to estimate what the excess death would correspondingly be via Equation (2) and subject these interpolations to sensitivity tests of time-period and unusual years. Figure 1 shows the actual all-cause annual deaths of the five Nordic countries for the years 2010-2021, updated as of April 27, 2022. We added a red line for each country indicating the average expected deaths of 2020 and 2021 required for the excess deaths estimated by Wang et al. 9 to be true, using Equation (2) . As seen from Figure 1 , the implied expected deaths (red lines) seem inconsistent with the actual data for the years prior to 2020 for Denmark, Finland, and Sweden. In all three cases, the expected all-cause deaths are substantially underestimated relative to both 5-year and 10-year trends of the data. For Denmark and Sweden, the implied expected deaths are lower than any observed deaths the previous 10 years despite a recent increasing trend. A similar result is seen for mortality rates that account for changing population size, Figure S1 (calculated as in Table S2 ). Thus, we conclude that the estimates are unlikely to be realistic.

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The copyright holder for this preprint this version posted May 7, 2022. ; https://doi.org/10.1101/2022.05.07.22274789 doi: medRxiv preprint Estimates of sensitivities -To understand the reviewed excess death estimates further, we supplemented them with some sensitivity tests. To do so, we used the annual Nordic all-cause death data to compute simple excess death estimates with 5-or 10-year linear trends as sensitivity estimates of the impact of time-period and tested the sensitivity to leaving out recent years with large potential impact ( Figure S1 ). These results in Table 1 should be seen as such tools for understanding uncertainties, not as full methods.

Two special years are notable: 1) Some countries had a particularly deadly 2017-18 influenza season 23 that is clearly measurable in the raw death data in Figure 1 of Denmark (Nordic influenza deaths typically cluster in January to March even if the season starts earlier). 2) Sweden had unusually low mortality in 2019, also clearly visible in Figure 1 . The interpolations without 2018 or 2019 show relatively little impact on Finland, Iceland, and Norway's deaths, but large effect for Denmark and Sweden, indicating that the excess deaths of the two latter countries are more difficult to estimate. Methods that do not account for these unusual years may suffer uncertainties as implied in Table 1 .

In principle, special periods of unusual low or high mortality could be smoothed out, but such removals could also produce errors due to mortality displacement (time correlations of deaths). 14, 24 If one discards 2019 completely, a maximum estimate of the impact of this, Sweden's excess mortality would be substantially lower. While Sweden experienced less mortality in 2019 and more in 2020, other Nordic countries had lower mortality in 2020, as noted previously, 8, 10, 25 but relatively more in 2021 (Figure 1 ). This could suggest mortality displacement 26 or e.g., immunity effects, although this needs to be explored further.

For Iceland, estimates also differ substantially percentwise partly due to the small numbers involved and to fluctuations, but the estimate by Wang et al. is still far from any other estimate in Table 1 . Figure 1 suggests that the implied baseline is rather high. In total, the excess deaths reported by Wang et al. for the five Nordic countries exceed by factors of 2.40 and 2.21 those deduced from the 5-year or 10-year trends, and this difference is not reduced by leaving out the most impactful special years.

Comparison of models -The total excess death estimates for 2020 and 2021 from the World Mortality dataset (WMD) 10 were compiled as in Table 1 . This method uses linear interpolations and thus carries the types of uncertainties analyzed above, in Table 1 . The WMD estimates agree well with the annual data trends as expected due to their similar methodology, with variations far from the estimates by Wang et al. In total, numbers by Wang et al. are 2.5-fold that of the WMD, an enormous difference considering that both models are supposedly fitted to hard available data for the Nordic countries ( Table 1) .

We also reviewed the estimates of two Economist models. Wang et al. provide a double-logarithmic plot of absolute excess deaths (their Figure S5 ) to suggest agreement between their data and the Economist, but such a plot is dominated by large countries, making discrepancies for individual countries less clear. Table 1 lists the Economist estimates both with and without the first two months of 2020 included when estimating baselines, which has a notable, relevant impact. Still, these estimates are far from Wang et al. For example, the Economist estimate for Denmark is more than four times below the 10,400 suggested by Wang et al.

On May 5, 2022 , the WHO updated their detailed estimates of the excess deaths of 2020 and 2021; 21 these data at the bottom of Tables 1/2 also show good agreement with the ranges of other methods, except having a remarkable, somewhat lower excess mortality for Norway. We find that this method also give total excess deaths for the five Nordic countries combined of approximately half that of Wang et al. Despite the variations in Table 1 , the numbers by Wang et al. 9 are outside the ranges for all five Nordic countries. For example, for Denmark, they reported 8,900−11,700, i.e., even their smallest number is much larger than other ranges in Table 1 . In this light, their narrow confidence intervals far from other ranges are concerning. Although Wang et al. did not separate years, their excess deaths also seem high vs. other estimates for earlier parts of the pandemic listing a few thousand excess deaths for Denmark and Finland. 27, 28 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The Nordic countries' capacity to identify covid-19 deaths -Wang et al. suggested that Nordic countries had enormous differences in their ability to identify deaths due to covid-19, with a ratio between excess and official deaths of 3.2 and 5.0 for Denmark and Finland, but only 0.6 for Norway and 1.2 for Sweden 9 . While we except differences, knowing the Nordic healthcare systems and pandemic responses, the many-fold under-registration seems highly implausible to us, as does the major heterogeneity in this capacity.

We calculated this ratio (until January 31, to account for a reasonable delay after incubation; Wang et al. counted only to Dec 31, 2021, thus underestimating reporting beyond the excess death estimates -we changed the period to enable direct comparison) as shown in Figure 2 (raw ratios are summarized in Table  S3 ). We find that the the Nordic countries' ability to identify covid-19 deaths (assuming most excess deaths are covid-19) is much more homogeneous with the other estimates than in the model by Wang et al. It is the only model that estimates that Sweden had more excess deaths than official covid-19 deaths, and in particular the apparent ability of Finland and Denmark to identify their covid-19 deaths is much more similar to other countries for the other studied estimates.

Impact of population structure -We want to clarify that total excess deaths as reviewed here cannot inform detailed country comparisons or policy implications without account of the distinct age structures of the countries, e.g., the mean population in 1-year age groups in 2020 in Figure S2 . The fraction of people >70 years varied from 9.9% in Iceland to 16.1% in Finland in 2020 when the pandemic started (Table S3 ). Figure  3 shows the death rates of the 5-year groups based on total deaths and the mean population of each age group (numbers in Table S4 , log-plot in Figure S4 for relative changes). By far most excess mortality is observed in the 70+ age groups, consistent with the exponential impact of age on (covid-19) mortality 20 . Different changes of the populations of the age groups from 2010-2019 ( Figure S3 ) are thus important for understanding expected deaths, rationalizing excess deaths, and performance comparisons or policy implications. Such analysis was not done in the reviewed studies and is beyond the scope of our review.

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The copyright holder for this preprint this version posted May 7, 2022. ; https://doi.org/10.1101/2022.05.07.22274789 doi: medRxiv preprint Figure S1 shows with a zoom on 70-89 age groups). (Logarithmic plot in Figure S4 ).

Implications for infection fatality rates -Death estimates also have consequences for IFR values (the fraction of total infections in the country that leads to death) to the extent they are mainly due to SARS-CoV-2 infection. To roughly estimate the consequence on IFR values for the different excess death estimates, we used a recent paper estimating global infection until November 14, 2021, before the omicron variant (Barber et al.) , 12 with infection estimates partly based on e.g., seroprevalence that seem reasonable compared to the historic Nordic seroprevalence estimates, with Sweden having approximately double the infection of the other Nordic countries up to November 2021 (22.4%, vs. 7.9-13.5% Table S5 ).

However, when deaths from the same model as Wang et al. (for the shorter period, and attempted corrected for non-covid-19 cases) were applied to these infection estimates, very surprising IFR values resulted, with e.g., average infections in Denmark and Finland being 6-7 times more deadly than in Norway and almost doubly as deadly as in Sweden (Table S5) . 12 Such differences are hard to explain by population or healthcare variations, pandemic management or vaccination strategies, and invite further scrutiny. Table 1 , under the simple assumption that the other estimates follow the same scaling and corrections for the time period of Barber et al., which of course is only indicative. Figure S5 shows these values as a rough indication of the IFR that would be implied by other estimates and models. The average IFR estimates for all other methods are 0.25 ± 0.16% for Denmark, 0.52 ± 0.09% for Finland, 0.00 ± 0.02% for Iceland, 0.31 ± 0.19% for Norway, and 0.40 ± 0.04% for Sweden, compared to the IFR values using the method of Wang et al. varying up to 1.2%. In other words, the various other methods studied here produce a range of IFR values that is much more similar and arguably much less controversial.

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In summary, combining Figure 2 and Figure S5 , we find it particularly anomalous that the same two countries, Finland and Denmark, that would be worse at identifying their covid-19 deaths by factors of at least 2-4 vs. e.g. Sweden, or 4-8 vs. Norway (Figure 2 ) would also at the same time coincidentally be the two countries where every SARS-CoV-2 infection had perhaps twice the lethality of infections in Sweden and 6-7 times higher fatality than infections in Norway (Figure S5) . The parsimonious explanation to these anomalies is that the excess death estimates by Wang et al. are not accurate, even beyond the implications of Figure 1 .

Since the remaining estimates all produce relatively similar results without these anomalies, we suggest that they are considered closer to the consensus for the true pandemic toll of the Nordic region.

We reviewed various estimates of the excess mortality during the pandemic 2020 and 2021 for the Nordic countries, which have been of much interest as both possible successes and failures, as an ideal study case due to their high-quality data and similarities. Our purpose was not to provide new advanced estimates, but to critically review existing methods and estimate uncertainties, limitations, implications, and plausible ranges in the numbers, especially due to recent debate on per capita deaths and registration differences, and our study should only be seen in this specific context.

As one of the methods (Wang et al. 9 ) produce very distinct results from all other studied estimates, additional analysis of this estimate was done. By back-calculating expected deaths we show that numbers by Wang et al. 9 seem inconsistent with actual data. Accordingly, excess deaths could be substantially overestimated relative to reasonable variations in the data for Finland and Denmark in particular, and to some extent for Sweden. We find that the main uncertainties in determining the excess deaths are the 2018 influenza, especially for Denmark and a bit less Finland, and the low Swedish 2019 mortality.

Our review of methods and sensitivity tests suggested that the overall excess deaths in the Nordic countries were perhaps 15,000-20,000. The WHO data that came out just on the last days of this paper's production (May 5, 2022) give results in the middle of this range (17, 716) . These numbers are approximately half that suggested by Wang et al. and imply that the Nordics had much more similar capability of identifying covid-19 deaths. The infection fatality rates were probably also much more homogeneous and consistent with expectations of pandemic management, e.g., the relevance of postponing infection until vaccines were available. The heterogenous results for Finland and Denmark, both many-fold lower ability to identify covid-19 deaths and the many-fold higher lethality of infections implied by the model of Wang et al. are probably due to the death estimates being substantially too high for these countries.

We note that the total excess numbers as reviewed here cannot directly inform performance estimates or policy implications even if they were accurate, as they miss context on population age changes over time.

Our review suggests that a method for estimating deaths when data are not yet available risks to fail substantially as hard data become available, which could have implications for other countries and global estimates. More generally, our study illustrates the need for data-focused quality control of complex models whose uncertainties and assumptions may be difficult to interpret. For policy implications and for wider public it is important to have a clear messaging, but high-quality data should not be subordinate to complex models. We warmly invite further studies that account in more detail for these topics and uncertainties. Denmark), James Wood and David Muscatello (School of Population Health, UNSW, Australia) Terese Jørgensen and Theis Lange (Copenhagen University), and Louise Emilsson (University of Oslo, Norway and Karolinska Institutet, Sweden) for stimulating discussions, and Dmitry Kobak (Tübingen University) and Ariel Karlinsky (Hebrew University), helpful discussion and confirmation of the WMD data.

Funding -This study did not receive any funding.

Data availability statement -All data required for the calculations in this work are available at the web pages of Statistics Denmark, Statistics Norway, Statistics Sweden, Statistics Finland, and Statistics Iceland as below: Economist estimates: https://www.economist.com/graphic-detail/coronavirus-excess-deaths-estimates WHO estimates: https://www.who.int/data/sets/global-excess-deaths-associated-with-covid-19-modelled-estimates Comparative Nordic data: mean population sizes, death rates: https://pxweb.nordicstatistics.org/pxweb/en/Nordic%20Statistics/Nordic%20Statistics__Demography__Po pulation%20change/ . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 7, 2022. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 7, 2022. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 7, 2022. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 7, 2022. ; https://doi.org/10.1101/2022.05.07.22274789 doi: medRxiv preprint Figure S5 . Infection fatality rates implied from Barber et al. 12 using similar methodology as Wang et al. 9 for deaths, and corresponding numbers for other methods obtained using the scale factors of Table 1 .

( * Economist model excluding Jan-Feb 2020 from trend calculation).

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The copyright holder for this preprint this version posted May 7, 2022. ; https://doi.org/10.1101/2022.05.07.22274789 doi: medRxiv preprint

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