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All‐cause versus cause‐specific excess deaths for estimating influenza‐associated mortality in Denmark, Spain, and the United States

Abstract Background Seasonal influenza‐associated excess mortality estimates can be timely and provide useful information on the severity of an epidemic. This methodology can be leveraged during an emergency response or pandemic. Method For Denmark, Spain, and the United States, we estimated age‐stratified excess mortality for (i) all‐cause, (ii) respiratory and circulatory, (iii) circulatory, (iv) respiratory, and (v) pneumonia, and influenza causes of death for the 2015/2016 and 2016/2017 influenza seasons. We quantified differences between the countries and seasonal excess mortality estimates and the death categories. We used a time‐series linear regression model accounting for time and seasonal trends using mortality data from 2010 through 2017. Results The respective periods of weekly excess mortality for all‐cause and cause‐specific deaths were similar in their chronological patterns. Seasonal all‐cause excess mortality rates for the 2015/2016 and 2016/2017 influenza seasons were 4.7 (3.3–6.1) and 14.3 (13.0–15.6) per 100,000 population, for the United States; 20.3 (15.8–25.0) and 24.0 (19.3–28.7) per 100,000 population for Denmark; and 22.9 (18.9–26.9) and 52.9 (49.1–56.8) per 100,000 population for Spain. Seasonal respiratory and circulatory excess mortality estimates were two to three times lower than the all‐cause estimates. Discussion We observed fewer influenza‐associated deaths when we examined cause‐specific death categories compared with all‐cause deaths and observed the same trends in peaks in deaths with all death causes. Because all‐cause deaths are more available, these models can be used to monitor virus activity in near real time. This approach may contribute to the development of timely mortality monitoring systems during public health emergencies.


| INTRODUCTION
Globally, influenza has been estimated to be associated with up to 646,000 respiratory deaths annually with significant seasonal variation. 1 Furthermore, influenza pandemics can result in much greater mortality than observed. The 1918 influenza pandemic resulted in approximately 50 million deaths and reduced the life-expectancy in the United States by 12 years. 2 However, the risks posed by new strains of respiratory viruses have never been more salient. 3 The ongoing COVID-19 pandemic highlights a need for robust and timely mortality estimates for assessing risks and prioritizing public health interventions during seasonal influenza epidemics and during novel virus pandemics.
There are many different methods used for estimating the influenza-associated mortality. 1,[4][5][6][7] One important distinguishing factor is the use all-cause mortality compared with selected causespecific mortality data. All-cause mortality data are, by definition, multicausal, and it is only possible to associate excess mortality to a specific underlying cause (e.g., influenza) by assessing the correlation over time with specific indicators of that specific cause. Because of this multicausality, all-cause excess mortality may overestimate the true number of deaths associated with one cause. 8 However, during winter seasons in temperate zones, increases in all-cause mortality are often observed, and the circulation of influenza has been historically shown to be the main seasonal driver of this excess mortality, although other factors (such as extreme temperatures and other respiratory viruses) may contribute as well. [8][9][10] Furthermore, all-cause mortality data are readily available in many countries with a short delay and can be used for weekly monitoring to inform timely risk assessments of a wide range of threats. 11 Cause-specific mortality data, on the other hand, can be more disease-specific and may provide estimates that are more accurate.
However, the categories commonly used for estimating the influenzaassociated mortality (such as respiratory diseases) are also multicausal and contain many causes unrelated to events of interest for monitoring of influenza-associated mortality. 1 Due to the higher specificity, models based on cause-specific data (e.g., respiratory diseases) tend to lose sensitivity and may underestimate the total number of deaths associated with influenza. 1,8,[12][13][14] Furthermore, processes to clean, code underlying and contributing death causes, and to validate the data are currently causing up to 2 years of delays in most countries and potentially even longer delays during pandemics. For these reasons, cause-specific mortality data may be less suitable and less timely for real-time monitoring purposes.
The true influenza mortality burden is likely to be between these two outcome data sources used in estimation. Therefore, causespecific mortality data are valuable for validating excess mortality estimates derived from all-cause mortality data. However, few direct comparisons between the estimates obtained using these two data sources have been made.
Emerging threats like the COVID-19 pandemic highlight the utility of monitoring all-cause mortality in real time. By the time global guidance for coding deaths due to COVID-19 was released on April 16, 2020, 131,034 global deaths were already reported. 3,15 However, it has become apparent through estimates of all-cause excess mortality that the reporting is likely an underestimate. 11,16 Since 2009, the European network for monitoring of excess mortality for public health action, EuroMOMO, has monitored weekly all-cause mortality in up to 24 participating European countries and provided pooled estimates of excess mortality (observed deaths minus baseline deaths), using the EuroMOMO model. 11,[17][18][19] We examined the differences between using all-cause and select cause-specific mortality data for estimating mortality related to influenza. We did this by applying the EuroMOMO model to (i) all-cause, (ii) pneumonia and influenza (P&I), (iii) respiratory and circulatory, (iv) respiratory, and (v) circulatory mortality data. We compared the weekly and seasonal cumulative excess mortality estimates using data from Denmark, Spain, and the United States for the 2015/2016 and 2016/2017 seasons and compared these estimates with official estimates from the national public health authorities in these countries.

| Mortality data
To estimate the weekly mortality attributable to influenza, we used mortality data by age group (0-64, 65-74, and ≥75 years) from the 2010/2011 through the 2016/2017 season. Deaths were categorized using the International Classification of Diseases, 10th Revision (ICD-10) codes. We focused on underlying causes of death categorized as all-cause (A00-Y99), diseases of the circulatory system (I00-I99), diseases of the respiratory system (J00-J99), influenza (J9-J11), and pneumonia (J12-J18). For each mortality record, the primary underlying cause was listed, defined as "the disease or injury which initiated the train of morbid events leading directly to death, or the circumstances of the accident or violence which produced the fatal injury" as specified by  For Denmark, the mortality data were obtained as individual notifications with the underlying cause of death, dates of deaths, and dates of birth from the Danish Civil Registry. For the United States, the mortality data were obtained as weekly aggregated age groupspecific data from the National Center for Health Statistics (NCHS).
For Spain, the mortality data were obtained as weekly aggregated age group-specific data from computerized civil registers covering 92% of the total Spanish population through the Centro Nacional de Epidemiología, Instituto de Salud Carlos III (CNE-ISCIII).

| Mortality rates-Population data
For Denmark and Spain, the population data were downloaded from Eurostat in Week 5/2020. 21 For the United States, the population data were obtained from the United States Census Bureau. 22 Based on the estimated number of deaths, mortality rates were calculated using national population data as of January 1 every year and linearly interpolated through the year. We interpolated population data provided by each country on December 31 of each study year to obtain weekly population counts using the following formula: where y = population at a given week (e.g., Week 422,014), X = given time (e.g., Wednesday, Week 422,014), y 2 = known population at time after x (e.g., Week 532,017), y 1 = known population at time before time x (e.g., Week 12,013).

| Weekly all-cause and cause-specific excess mortality-Spain
Within the possible influenza season, there were distinct periods with excess mortality for all-cause and cause-specific mortality ( Figure 1). The periods with excess mortality for circulatory mortality were similar to all-cause mortality with respect to when the excess mortality started, the timing of peaks, and the length of the period. The periods with excess mortality for P&I and respiratory mortality tended to start later than all-cause and circulatory mortality, but the peaks were synchronous. There was significantly more excess mortality in the 2016/2017 season than in the 2015/2016 season.

| Weekly all-cause and cause-specific excess mortality-Denmark
Within the possible influenza season, we observed periods with excess mortality across all-cause and cause-specific mortality ( Figure 1). However, it was more difficult to determine the periods of excess mortality due to the smaller population size. In particular, we observed distinct periods of excess mortality in respiratory and allcause mortality. Compared with all-cause excess mortality, the respiratory and P&I excess mortality started later and were shorter in length but similar in the timing of peaks.

| DISCUSSION
We found that the periods of weekly excess mortality for all-cause and the respective cause-specific causes of death were generally similar with respect to when the excess periods started, their length, and their timing of peaks, especially for the United States and Spain.
T A B L E 2 Ratio between cumulated pneumonia and influenza excess mortality and cumulated respiratory, circulatory, respiratory and circulatory, and all-cause excess mortality during the winter season (Week 40 to Week 20) Note: The ratios are based on the corresponding excess mortality estimates in Table 1.
Furthermore, we found that these periods were within the period where the influenza season typically occurs (Week 40 to Week 20 of the following year).
The ratios between cumulative seasonal all-cause excess mortality and excess mortality of the cause-specific causes of death (except for P&I) remained constant for Denmark across the two seasons.
However, for the United States, a constant ratio was only observed for P&I mortality, whereas for Spain, the constant ratio was only observed for circulatory excess mortality. These ratios did not remain constant when stratified by age groups. Overall, this suggests that excess mortality estimates based on all-cause may be used to infer excess mortality estimates for some of the cause-specific categories only, but these inferences may only work within a country as the ratios vary substantially between nations.
Our seasonal all-cause excess mortality estimates for the under-detection of influenza. This is done by using a death to hospitalization ratio that represents the expected number of influenza deaths relative to the number of influenza-associated hospitalizations. 7,30 In principle, using laboratory-confirmed influenza-associated hospitalizations adjusted for the proportion of individuals who may not be tested for influenza may be an accurate way of approximating the true underlying mortality burden of influenza. In contrast, estimates based on all-cause excess mortality are expected to be an overestimate or, perhaps, an upper bound of the true underlying mortality burden. 8 Given this, it is surprising that our all-cause excess mortality estimates were not considerably higher than the CDC estimates. One potential explanation for this might have been that we did not truncate negative excess values, such that any week where the predicted number of excess deaths was lower than the expected number of deaths those deaths were subtracted from total excess deaths. However, as shown in Figure 1 It is unclear whether there is a constant proportionality between the P&I deaths and other cause-specific or all-cause excess mortality estimates. In all three countries, proportionality differed by season.
The differences were smallest in the United States, perhaps owing to the larger population, which may provide more year-to-year stability.
For example, for every one excess death due to P&I there were 9-10 times more all-cause excess deaths, 10 On the other hand, the proportionality between the seasonally cumulated all-cause excess mortality and the select cause-specific excess mortality estimates (such as P&I and respiratory) does not seem to be reliably constant across seasons within all three countries. Additionally, all-cause excess mortality estimates come with the risk of losing specificity and consequently overestimating the influenza mortality burden. This was indicated by the fact that our estimates for Denmark and Spain were between 1.5 and 3.5 times higher than the estimates produced by the FluMOMO model, which includes indicators of influenza-activity and temperature, whereas our respiratory and circulatory excess mortality estimates approximated the FluMOMO estimates. 6,31,32 Moreover, some cause-specific mortality data are increasingly available more quickly in some countries; for example, CDC has access to P&I mortality data on a weekly basis, and additional advances in the timeliness of data availability are likely to be gained from the ongoing pandemic. 4 However, it is important to note that these real-time cause-specific data may not be clean and the death counts are continuously updated as deaths are reported.
In conclusion, using a simple model of all-cause excess mortality is a valuable tool for timely risk assessment of seasonal influenza and emerging threats such as the COVID-19 pandemic, as the data are readily available in many countries, and the approach is not sensitive to coding practices in cause-of-death-registers and collection of other indicators. To obtain precise estimates of excess mortality related to influenza, all-cause mortality data should be supplemented with cause-specific data and indicators of influenza transmission.

ACKNOWLEDGMENTS
This study was conducted as part of Sebastian Schmidt's research fellowship, which was financially supported by the Novo Nordic Founda-

DISCLAIMER
The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the Centers for Disease Control and Prevention.

PEER REVIEW
The peer review history for this article is available at https://publons. com/publon/10.1111/irv.12966.

DATA AVAILABILITY STATEMENT
The data utilized in this manuscript are not publicly available given the identifiable nature of some of the components of these data.