The Role of Age Distribution, Time Lag Between Reporting and Death and Healthcare System Capacity in Case Fatality Estimates of COVID-19

Background: European countries report large differences in coronavirus disease (COVID-19) case fatality risk (CFR). CFR estimates depend on demographic characteristics of the cases, time lags between reporting of infections and deaths and infrastructural characteristics, such as healthcare and surveillance capacities. Methods: We used publicly available data from ocial reports of the national health authorities of Germany, Italy, France, and Spain on COVID-19. These include age-specic numbers of cases and deaths for different dates, which we used to compute age-standardized CFR ratios using a standard European population for standardization. Moreover, we investigated the impact of different potential time lags on the estimation of the CFR using data published by the European Centre for Disease Prevention and Control (ECDC). Finally, we described the association between case fatality and the intensive care bed capacity. Results: We found that age-standardized CFR estimates increased from the beginning of March to mid-May 2020 in all included European countries. In Germany, CFRs are lower than in other countries. However, the differences are much larger when comparing the crude risks rather than the age-adjusted risks. Thus, the different age distribution of the cases account for a major proportion of the reported differences. Case fatality estimates using time lags of 1-10 days converged in all countries over time, however, there is no optimal time lag to assess the CFR during the pandemic. Time lags that provided the most constant estimates and approach best the observed CFR after the pandemic ranged from 5-10 days in different countries and at different time points during the pandemic. For the association between intensive care bed capacity and fatality we found that days with a high need for intensive care beds were positively correlated with daily hospitalization fatality in France, Italy, and Spain, but not in Germany. Conclusions: Our results highlight that cross-country comparisons of crude CFR estimates can be misleading and should be avoided. However, to adjust for potential sources of bias more disaggregated data and information on surveillance and health care capacities are needed. Filling these gaps and harmonizing data across European countries will facilitate further analysis.


Background
Different case fatalities of COVID-19 have been reported in affected countries. Until May 14th, 2020, over 4.3 million con rmed cases and close to 300,000 associated deaths have been identi ed globally (1). The crude case fatality risk (CFR) estimate, namely the cumulative number of deaths divided by the cumulative number of cases, is known to be biased (2). The main sources of bias are given in Table 1. A distinction must be made between factors that in uence the actual lethality (as denoted by * ), such as healthcare capacity and those that bias the estimates of the CFR, such as an underassessment of cases. Higher CFR given an older population with a higher load of comorbidities (3)(4)(5)(6)(7)(8)(9)(10)(11) Surveillance and testing Surveillance system and different testing capacities Overestimation of CFR given a poor surveillance system and poor testing capacity, as fewer currently infected persons in relation to deaths are counted (2,(12)(13)(14)(15)(16)(17)(18)(19) Methods and capacities to record deaths Underestimation of CFR given low capacities and poor quality methods to record deaths due to the disease resulting in a smaller numerator of deaths / current reported infected; (20) Overestimation of CFR, if all deaths are counted regardless of whether the patient died of the target disease or another cause given the same number of infected/diseased (20) Time lag Deaths occur time-delayed after infection Underestimation of CFR given a time lag of several days between case registration and death resulting in a smaller nominator of current deaths / current infected (11,21) Healthcare system * Healthcare system capacity measured as number of intensive care beds per 100.000 inhabitants Higher CFR given a low healthcare capacity and an additional excessive demand for intensive care beds during the pandemic resulting in more deaths and therefore a higher numerator of deaths / current infected (4,17,(22)(23)(24)(25)(26) Different demographic characteristics of infected cases regarding age, comorbidities, or underlying risk factors, as well as different underlying population structures of the respective countries, might explain different CFRs. There is increasing evidence that old-age and comorbidities -such as hypertension, diabetes, cardiovascular disease, or chronic lung disease -are major risk factors for severe COVID-19 infection outcomes (6,27,28). The higher susceptibility to disease as well as the higher prevalence of comorbidities in the elderly has an impact on the morbidity as well as mortality of this subpopulation resulting in higher CFRs in countries with an older population compared to countries with a younger age structure, which is apparent in the COVID-19 pandemic (3-10).
Different surveillance systems and different testing capacities across countries lead to huge variations in the number of tests performed (12,13,16,17,29).
Underassessment of reported infections therefore differs among countries (14,15). Furthermore, surveillance and testing capacities in uence the probability of detecting infections early and thus to enact countermeasures. Capacities and methods to record deaths as having been caused by COVID-19 also differ between countries (20). While in some countries, post-mortem screening of all deaths has been installed, other countries are only performing this when there is clinical suspicion (30).
There exists a time lag between reporting of an infection and eventual death of said individual. The distribution of the time lag may differ between countries.
This delay is not re ected in crude CFR estimates (21). A more robust estimate would be given by dividing cumulative deaths by cumulative recoveries. This, however, is not a reliable estimate as well due to a low number of recoveries during the early stages of the pandemic, when a high relative increase of infection numbers and an incomplete reporting of recoveries are witnessed (31). Therefore, some authors propose to investigate the cumulative deaths in relation to lags of various days of the cumulative infection numbers (21,31). However, as a result of the high transmission rates of the virus in the early stages of the epidemic, the estimates depend strongly on the appropriate lag, and both under-and overestimation of the true CFR can occur (32). Gianicolo et al. (11) calculate age-standardized CFRs with a time lag of 7 days ranging from 0.8% in South Korea to 2.4% in Italy. In contrast, they report crude CFRs of 2.2% for South Korea and 12.6% for Italy.
Furthermore, CFRs are in uenced by the healthcare system capacity of the affected countries. Previous studies have shown, that healthcare capacities differ substantially among countries, and even among regions within countries (4,17,(22)(23)(24)(25)(26). A healthcare system overwhelmed by the pandemic may result in higher CFRs.
All factors mentioned above may explain differences in CFRs in affected countries to a certain degree at different time points during the COVID-19 pandemic.
It is unclear, how much of the difference in during-epidemic CFR estimates is explained by each of these factors. The aims of this paper are as follows: (i) to quantify the difference in during-epidemic case fatality due to COVID-19 between the countries Germany, Italy, France, and Spain attributed to differences in the age structures among the reported cases, (ii) to investigate the time lag between case reporting and death and its effect on CFR estimation, and (iii) to discuss the association between CFR and the healthcare system capacity. The selected countries are interesting for our study, as they are the four most populous countries in the European Union (EU), covering more than half of the total population of the EU (33). Moreover, these countries show different levels in COVID-19 CFRs and have born a large part of the COVID-19 disease burden over the study period.

Data And Methods
To investigate the age effect, we obtained the cumulative numbers of cases and deaths of Germany (34), Italy (35)(36)(37)(38), France (39,40), and Spain (41) (43). For our investigation of the impact of the healthcare system capacity, we used estimates for the available critical care beds from the OECD (44) and of needed critical care beds for COVID-19 patients on a daily basis from the Institute for Health Metrics and Evaluation (IHME) (45)(46)(47)(48).
We use the following notation: n ijk and d ijk denote the total cumulative number of cases and deaths, respectively, for age group i, country j, and up to day k. δ. jk denotes the number of deaths at day k, i.e. d . jk = ∑ k κ = 1 δ jκ . Figure 1 illustrates the development of the crude CFR estimates of the four selected countries in percent between March 4th (i.e., calendar week 10) and May 14th (i.e., calendar week 20), 2020 as obtained by CFR jk = d . jk /n . jk . These crude estimates do not take into account the factors listed in Table 1. All curves increased over the study period. We observed signi cant differences between the curves. Our study aims to explain these differences to some extent.
The rst aim was to identify the role of the cases' age structure in the overall CFRs and to derive age-speci c and age-standardized CFR estimates of Germany, Italy, France, and Spain. Based on the age-speci c cases n ijk of the four European countries, we calculated the age-speci c CFR, CFR ijk = d ijk /n ijk , the total crude CFR estimate, CFR jk = d . jk /n . jk and the age-standardized CFR estimate as C FR jk = ∑ i w i × d ijk /n ijk using the European Standard Population as a reference. To illustrate the relative effect of the different age distributions of cases in the countries considered, we calculated the ratio of the relative differences between the crude and age-adjusted CFR estimates, using Germany as the reference country, as it is the country with the lowest crude CFRs.
For the second aim, namely, to investigate the effect of different lags on the CFR estimate, the unknown distribution of the time lag Δ between reporting of a case and death was considered. Verity et al. (49) estimated the average time from infection to death at about 14 days. Thus, the average time from reporting a case to death is several days shorter. The effect of Δ on the CFR estimate was evaluated by calculatingCFR k , Δ = d . jk /n . jk − Δ for the pandemic for k = 0 over the study period with Δ = 0, …, 10. We graphically determined the values Δ , which appear to converge to the nal CFR of the epidemic over time, in particular during the peak of the epidemic. We then present the gures for Germany, Italy, Spain and France. measure for the daily hospitalization fatality, we suggest the number of COVID-19 related fatalities of a particular day divided by the number of hospital admissions due to COVID-19 of the last 14 days: A period of the preceding two weeks was used to (a) remove the weekly periodicity and (b) because of a reported median hospitalization length of stay of 8 days (50, 51). As a measure of the utilization of healthcare capacities, the number of intensive care beds needed for COVID-19 patients was chosen. The analysis only included days where at least 5% of the total number of intensive care beds of a country were needed for COVID-19 patients because with lower numbers no overload of the intensive care bed capacity could be expected (44).
We then related the daily hospitalization fatality to the number of intensive care beds needed (45)(46)(47)(48). The total number of intensive care beds available is included in Fig. 4 as a threshold, above which demand exceeded capacity.

Results
Aim 1. During-epidemic crude and age-standardized CFR estimates, alongside CFR ratios of Germany, Italy, France and Spain Table 2 provides weekly estimates of crude and age-standardized CFRs, estimated as explained in the section Data and Methods. Moreover, the standardized CFRs are normalized to Germany's age-standardized CFR as the baseline, to investigate how much higher the CFRs were in Italy, France and Spain compared to Germany after accounting for the age structure of the cases. Trends in all countries examined are similar, with higher age-speci c risks in older age groups. At the end of our study period, age-speci c case fatalities for persons above the age of 79 were over one fth in all study countries, whereas age-speci c fatality for those under 60 years of age was consistently below 5% in all countries (see Tables 3-6 in the Appendix). Until mid-May, the proportion of cases exceeding 60 years of age (among those with known age) was above 50% in Italy, Spain and France, compared to approximately one third in Germany, yet the trend in Germany was positive. For Germany, the age-standardized CFR estimates show a smaller increase than the crude CFRs over time, caused by the changing age distribution of the cases towards a higher proportion of older cases. Trends in all countries examined are similar, with higher age-speci c risks in older age groups. At the end of our study period, age-speci c case fatalities for persons above the age of 79 were over one fth in all study countries, whereas age-speci c fatality for those under 60 years of age was consistently below 5% in all countries (see Tables 3-6 in the Appendix). Until mid-May, the proportion of cases exceeding 60 years of age (among those with known age) was above 50% in Italy, Spain and France, compared to approximately one third in Germany, yet the trend in Germany was positive. For Germany, the age-standardized CFR estimates show a smaller increase than the crude CFRs over time, caused by the changing age distribution of the cases towards a higher proportion of older cases.     Figure 3 shows the crude estimates for the CFR during the study period using lags of 0 to 10 days. yielded to an underestimation of the CFR at peak times of the pandemic. This underestimation was stronger in Germany, and therefore the comparison of the estimates with those from the other three countries showed larger differences at this period compared to mid-April. For example, the estimated crude CFRs in Germany and Spain on March 21st were 0.24% and 5%, respectively. On April 16th, these were 2.7% and 10.4% and on May 14th the numbers were 4.5% and 11.9%. The corresponding CFR ratios decreased from 20.8 to 3.9 to 2.6.
Aim 3. Describe the association between case fatality and the intensive care bed capacity We de ne the daily hospitalization fatality as the deaths on a particular day relative to the total number of hospitalized cases admitted during the previous two weeks. In Italy, e.g., 195 persons died on May 14th, 2020, and 10,341 cases were hospitalized in the previous two weeks, which leads to a daily hospitalization fatality of 1.89%. Figure 4 illustrates the daily fatality of hospitalized cases in association with the needed intensive care bed capacities. The total available intensive care bed capacities, taken from OECD (44), are indicated by vertical lines. Italy, and Spain. For Germany, the number of intensive care beds occupied by COVID-19 patients has so far consistently been below the available capacity.

Discussion
There are large differences in the reported CFRs between countries. We discussed factors that may explain shares of these differences. We present evidence that a large proportion of the differences of CFRs between the four countries included here can be attributed to different age distributions of cases. Moreover, we have shown, that crude CFR estimates are strongly biased at peak phases of the pandemic due to lags between case reporting and death. This bias becomes smaller when daily case numbers decrease. It is unclear, how different CFRs among the European countries are indeed an indicator of differences in healthcare capacity. In the countries considered here, we could show an association between the number of intensive care beds needed for COVID-19 patients and daily hospitalization fatality.
Our analysis only considered the impact of the three factors demographics, delay in deaths after infection, and healthcare system capacity on CFR estimates of COVID-19. There are certainly other factors, which play into country-speci c differences as well. Among those may be environmental factors, such as air pollution or climatic circumstances (52). Moreover, there are differences in the overall mortality among countries (53), which should be taken into account for a holistic international comparison of COVID-19 and general cause-speci c mortality.
Generally, differences in CFR estimates which remain after adjusting for population structure, time lags, and health care capacity are most likely an indicator of different extents of underreporting of COVID-19 cases across countries caused by limited surveillance capacities of the countries' health systems.
Compared to crude CFRs in the countries assessed, our ndings of less diverse hospitalization fatality suggest that varying underreporting of cases may be responsible for a substantial part of the difference in estimated age-standardized CFRs. Underassessment of COVID-19 cases can be assumed for most countries, with varying extent (54). E.g., a recent seroprevalence studies assessing underassessment of reported cases from Geneva, Switzerland estimates that only one of 11.6 cases were actually reported in April and May in Geneva (55).
For persons not belonging to population groups at high risk of severe COVID-19 clinical courses, the disease in some cases appears with only minor symptoms or no symptoms at all (56). Thus, many mild cases may not appear in the statistics and therefore bias the data towards the more severe cases (2,19), overestimating the overall fatality risk. For example, the number of undocumented cases was estimated to be 86% of all infections in China at the end of underassessment is a study conducted on the cruise ship Diamond Princess (58). All passengers were tested, and 696 Passengers were tested positive.
According to recent data, thirteen individuals have died due to COVID-19, yielding a crude fatality risk of 1.83% (59), resulting from the passengers' high mean age. The age-standardized CFR in this population is 0.65%. Although the study population was small yielding an imprecise estimate, it may roughly indicate the proportion of unobserved cases among other populations, assuming the fatality in the ship's population was comparable to that of the countries considered in this paper.
Besides underassessment due to underdetection of asymptomatic or mildly symptomatic cases, the diagnostic accuracy of tests plays a role. The WHO recommends RT-PCR to detect the virus in pharyngeal swabs (18 would also result in underreporting of COVID-19 and therefore in an overestimation of case fatality. The extent of underassessment of cases can also be assumed to vary during country infection dynamics. Underreporting may appear more severely in the early and later stages of the epidemic (2), as the disease in the earlier stages can be mistaken as another respiratory syndrome due to similar symptoms (60).
In the peak stages of the epidemic, there might be an overload of the reporting system due to the high number of cases and limited capacities of laboratories (18), which might lead to a general underestimation of cases and therefore an overestimation of the fatality risks.
As an important limitation of our work, we found that public data on the age structure of infected and deceased were missing in public reports on COVID-19 in many European countries. Even for the included countries, this data was partly only available at speci c time points, for roughly aggregated age groups, or only for a selection of all reported cases or deaths. For other countries, age-speci c data are not openly available at all. Another limitation of this work is that we were not able to gain information on the distribution of comorbidities relevant to COVID-19 over age groups of infected and deceased in the European countries assessed, thus limiting our understanding of differences in CFR estimates due to differences in comorbidities. For the analysis of the association between fatality and the healthcare load measured by intensive care beds needed, we could not incorporate the age structure or severity of hospitalized cases into our computations, because these data were not available. Additionally, we did not have access to daily numbers of intensive care beds available for COVID-19 patients, which is why we chose to retain the absolute values of intensive care beds needed.
For publicly available data to have public health consequences, better reporting of data on healthcare capacities on a daily or at least weekly scale is needed in Europe. More detailed data on the demographics of the cases and deaths would help our understanding of the demographic impact on the CFRs. There are very few countries providing this information in a su ciently detailed form (such as Spain and Italy do) and many countries do not offer age-strati ed data at all or do not provide their data by sex. This biases our understanding of the severity of the disease, as genders show signi cant differences in susceptibility to severe disease and general mortality (53,61). Even health authorities offering data on the age structure of the cases and deaths do not separate the age groups in the same manner (see, e.g., Tables 3-6). Important databases give only the crude case and death numbers, without further disaggregation, which might lead to misinterpretation of the true mortality differences among the countries. Moreover, this data should be merged with comorbidity-speci c information to take this into account simultaneously in a sophisticated statistical analysis.

Conclusions
In conclusion, the age structure of cases, population differences regarding underlying comorbidities and risk factors, appropriate consideration of the time lag between reported infections and death, the capacity of the health system and potential underassessment of cases or deaths due to limited surveillance capacities are important to understand the differences between reported country-speci c CFR estimates. Our study has also shown that further improvement towards a better coordinated and uni ed public health data reporting system in Europe and worldwide is highly warranted to ght this and any other pandemic that may emerge in the future. Availability of data and materials The datasets generated and analyzed during the current study are available from the cited sources or the corresponding author on reasonable request.