Introduction

Mortality crises are much less frequent in countries that have completed the so-called epidemiologic transition (Omran, 2005). This term describes the passage from a dominance of infectious and malnutrition-related diseases to a dominance of degenerative and “man-made” diseases. Before such transition occurred, mortality shocks used to hit population once or twice over a generation (Livi Bacci, 2001). In modern Western societies, mortality crises driven by infectious diseases occur more rarely, whereas the major causes of deaths are increasingly related to neoplasms and cardiovascular diseases. Although the increase in these diseases constitutes a serious public health issue, they hardly represent a real mortality shock. Nevertheless, in addition to crises that occur in countries that have not completed the epidemiologic transition, even in more advanced countries, some crises—albeit lighter and shorter—occur. Therefore, measuring the magnitude of these crises is still paramount in a public health perspective. This has been particularly evident during the COVID-19 pandemic that started in 2020, but the necessity to monitor mortality levels is also brought about by other emergencies, such as the 2003 heatwave in Europe (Robine et al., 2008) or the influenza outbreak that occurred in several European countries in 2014–2015.

Although it might seem straightforward to provide a measure of the effect of a crisis on population mortality levels, several issues hamper the most common methods. In this article, three main approaches are considered: the count of cause-specific deaths, excess mortality, and the decrease in life expectancy (or any other index derived from a life table). However, before describing these approaches, data availability and quality are discussed because these are crucial aspects of mortality monitoring—not just for less developed countries—that should be taken into account.

Data Availability and Quality

Mortality crises are often limited in time and space. The 2003 heatwave in Europe occurred during the summer, and influenza peaked in winter. The effect of the first wave of COVID-19 in Italy was limited to some provinces in the north of the country, as shown in Figure 1.

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Figure 1. Life expectancy decline in Italian provinces. Comparison between January 1 and 30 September 30, 2018 and 2020.

Source: Own elaborations from data released by the Italian National Institute of Statistics.

Thus, a proper monitoring of mortality calls for a finer detail of data than what is usually provided (country-specific and yearly data). The COVID-19 outbreak made this need more evident, and several new databases have been made available by scholars, institutes, and research groups. The Human Mortality Database (HMD), for example, issues Short-Term Mortality Fluctuations (STMF) data with deaths for all causes on a weekly basis (Jdanov et al., 2021). Karlinsky and Kobak (2021) extended the country coverage of STMF, combining data from HMD with those from other institutes (e.g., Eurostat, the United Nations, and national institutes of statistics). A team of researchers created a database of COVID-19 deaths for several countries, in many cases also at the regional level (Riffe et al., 2021). Some of these databases are listed in Table 1.

Unfortunately, the quality of mortality data is reduced when the detail is finer. For instance, delayed reporting significantly affects daily or weekly data but not yearly data. Figure 2 shows the number of COVID-19 deaths in Sweden for a specific time period that were later reported as dropped on two different dates. Such a difference is striking given that Sweden is considered one of the countries with the highest quality mortality data. Data on causes of death are also affected by quality issues, mainly due to lack of standardized instructions on how to compile death reports, leading many certifiers to use the so-called garbage codes (e.g., “old age”) that are not useful from a public heath perspective (Mikkelsen et al., 2020). Conversely, mortality data for small areas are not affected by specific quality issues, but estimating vital rates is challenging due to small sample size; hence, in these cases, scholars are inclined to use statistical models that envisage a borrowing of information for those areas with smaller size (see Gonzaga & Schmertmann, 2016).

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Figure 2. Daily COVID-19 deaths in Sweden, October 20–29, 2020, as reported on October 30 and November 12, 2020.

Source: Edouard Mathieu, Our World in Data.

Such issues are, of course, even more severe in countries in which coverage of vital events registers is far from 100%. Mathers et al. (2005) found that in 2003, only 64 out of 192 countries had a complete coverage of death registration—mainly European, American, and Western Pacific countries, whereas almost all African countries had less than 100% coverage. Moreover, only 23 countries have been classified in a “high-quality” category as it concerns the causes of death information.¹

Thus, the question of data quality should not be ignored in the perspective of quantifying mortality crises because there are still many open issues not limited to least developed countries, but also involving developed ones.

Cause-Specific Deaths

One way to quantify the impact of mortality crises is to count deaths due to causes that are related to the public health issue under analysis. For example, the impact of seasonal influenza can be quantified by counting the number of deaths due to influenza and pneumonia. Alternatively, rates or other functions of the number of deaths by a specific cause can be used (e.g., the infection fatality rate or the case fatality rate are used when a mortality crisis is due to an epidemic).

Figure 3 shows the trend of influenza and pneumonia deaths in the United States from 2016 to 2021. Also COVID-19 deaths are shown, so they can be compared with influenza deaths in the previous years. It can be noted that also in 2017, there was a significant increase in influenza-related deaths.

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Figure 3. Number (and percentage) of deaths due to pneumonia, influenza, and COVID-19 (PIC) in the United States, 2016–2021.

Source: Centers for Disease Control and Prevention.

This approach is seemingly simple to implement; however, there are several issues challenging its validity, especially in a comparative perspective. A first challenge is posed by the changing age structures, which can significantly affect this measure. Dowd et al. (2020), for instance, highlight the role of age structure in reducing or amplifying differences across countries in COVID-19 deaths and case fatality rate. This issue also applies to comparisons of the same country in two different periods: Figure 4 shows the number of deaths by some selected causes in France (2000 and 2013). The comparison between the two plots might suggest that something has changed in France between 2000 and 2013, particularly for the age range of 55–60 years, for which the number of deaths by neoplasm is much higher in 2013 than in 2000. However, it also appears that for the same ages, deaths due to other causes significantly increased as well. This can be explained by a larger number of exposed population, as those aged 55–60 years in 2000 were born during World War II when fertility has decreased significantly, leading to a lower size cohort. The same reasoning applies to those aged 80–85 years. Thus, standardization by age structure is necessary. Dudel et al. (2020) show that the age component explained 70% of the differences in case fatality rates across countries. This issue can be resolved by standardization, but this means that data should be broken down by age, and in some cases this might lead to sparse data, with negative consequences regarding reliability.

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Figure 4. Number of deaths in France (2000 and 2013) by some selected causes of death.

Source: Own elaborations of Human Causes-of-Death Database.

A more challenging issue of using cause-specific deaths to measure the extent of a mortality crisis is related to problems of classification. Despite efforts to standardize the nosological coding of causes of deaths, many issues remain (Winkler et al., 2010), depending on differences in training and in the interpretation of the International Classification of Diseases (ICD) guidelines by coders. As a result, considerable differences in cause-specific mortality rates can be found across countries. For example, Timonin et al. (2021) find that differences between Russia and Norway in myocardial infarction mortality rates are driven by different interpretations of international classification criteria by specialists in the two countries.

Such issues also involve within-country and time comparisons. Figure 5 shows the outcomes of three different classification issues by plotting some causes of death (i.e., the number of deaths by a specific cause divided by plotting the deaths composition by some causes). In the first panel, it can be seen that during 2011 in Japan, there were both an increase in the number of deaths by external causes and a decrease in neoplasm-related deaths. It is highly unlikely for cancer mortality to decrease this significantly for only 1 year, and the increase in external causes of death (just for 1 year) might lead one to conclude there has been a severe coding issue, possibly related to the high suicide rate among cancer patients in Japan (Akechi et al., 2004). The central panel in Figure 5 shows a sudden decrease in circulatory-related causes of death and an increase in endocrine system diseases. This is the result of a change in how diabetes with circulatory complications is classified; the change occurred in the most recent update of the ICD coding system. The right panel in Figure 5 shows that in Belgium, deaths by diseases with symptoms not elsewhere classified increase and decrease suddenly in some years. This is due to a varying classification protocol of deaths of Belgian citizens that occurred abroad, which in some years are classified using the codes assigned in the nation in which the death occurred and in other years are assigned to “not elsewhere classified” causes. Thus, even in countries with high-quality coverage of mortality data, cause-specific information is not free from drawbacks. Such classification problems also arose during the COVID-19 pandemic: A specific ICD code was created as the number of deaths due to the virus increased, but the way deaths were classified varied significantly from one country to another. Whereas in Russia, the case definition for a COVID-19 death, for example, relied only on results from autopsy, Spain’s definition required a positive polymerase chain reaction or antibody test for COVID-19, with only hospital deaths included. Belgium, conversely, included all suspected cases as COVID-19 deaths, which resulted in the country being ranked first in terms of COVID-19 mortality (Beaney et al., 2020). More generally, Garcia et al. (2021) have shown that different registration systems that are used by several countries are not comparable in terms of quantification of COVID-19 mortality.

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Figure 5. Composition of some causes of deaths in three selected countries, ages 25–64 years.

Source: WHO Mortality Database.

Moreover, there might be circumstances in which the mortality crisis is not limited to a set of causes of death. For example, the mortality increase due to a particular severe heatwave, such as that which occurred in 2003 in several European countries, is not associated with a specific cause.

Finally, note that for most countries, data on causes of death are not available, and this approach cannot be used. In this case, the burden of a specific cause cannot be easily assessed (Whittaker et al., 2021).

Excess Mortality

Due to the previously discussed limitations of cause-specific mortality, an alternative measure of the impact of mortality crises is often considered—that is, excess mortality (or excess death).

Basically, this measures is defined by the difference between the observed number of deaths (for all causes) and a baseline which should be interpreted as the expected number of deaths that would have been observed without the public health issue that caused the mortality crisis. This approach is appealing because cause-specific data are not necessary, and all-cause mortality data are made available much earlier and with a higher quality. In this way, issues related to reporting case-specific deaths are overcome under the assumption that the other causes of mortality remain steady over time. Even in this case, the impact of age structure can bias the cross-country differences, and a standardization is needed. Moreover, the definition of the baseline (i.e., the expected number of deaths) is far from trivial, and it involves choices that can significantly affect the estimates. A naive solution is to define the baseline by the weekly average of past years, as proposed, for example, by the visualization tool of STMF data (Jdanov et al., 2021). However, this solution has the following shortcomings: (a) Countries can have very different mortality time trends, and the simple 5- or 10-year averages disregard this (Schöley, 2021); and (b) mortality is seasonal, and taking into account such seasonality might be important to quantify the weekly or monthly excess of deaths. Several authors have noted that the specific-average method is too simplistic and often leads to an underestimate of excess mortality (Basellini et al., 2021; Karlinsky & Kobak, 2021; Németh et al., 2021; Schöley, 2021). Considering the averages of age-specific rates or standardized rates rather than death counts might be a solution to take into account the age structure, but the issues of time trends and seasonality remain. A more refined solution has been offered by Serfling (1963), who proposed a regression model to fit the trend of observed number of deaths, also taking into account seasonality. The fitted model is used to predict the baseline, which in turn is then used to estimate the excess mortality. Since the original work, some variants of the Serfling model have been proposed; for example, some introduce the temperature as a covariate, whereas others consider different specifications of the regression model (for a complete review of different variants, see Schöley, 2021). EuroMOMO, a project that monitors excess mortality in European countries due to influenza epidemics, employs a version of the Serfling model in which deaths are modeled via a Poisson model with overdispersion with both a trend and a seasonal component. However, although this overcomes some of the issues outlined previously, the estimate of the baseline remains sensitive to some choices, as described by Schöley (2021) and Nepomuceno et al. (2022). One choice concerns the time period used to fit the model: A time period of 5 years is commonly used, but its validity depends on whether this period includes some other epidemic years. For example, in 2015, many European countries experienced a severe influenza outbreak, resulting in a significantly higher level of mortality (Fedeli et al., 2017); thus, including such exceptional years when defining the baseline makes a difference. Nepomuceno et al. (2022) find that the difference between the excess mortality in 2020 attributable to COVID-19 estimated using the years 2015–2019 as a reference period and that obtained using other periods (2011–2019 or 2017–2019) was more than 50 deaths per 100,000. Schöley (2021) compared different models, considering weekly averages, the Serfling model (with or without population exposures), general additive models with or without temperature anomalies, and a latent Gaussian model with or without temperature anomalies. Schöley found not only that the excess mortality estimate changed but also that the ranking of countries in terms of P score (a normalized score of excess mortality, which takes into account the different population size) changed as well (Figure 6).

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Figure 6. Excess mortality ranking of countries, estimated with several models.

Source: Schöley (2021).

Therefore, estimating excess mortality is far from straightforward, and several choices (especially regarding the time frame and statistical model used to estimate the baseline) have to be made based on the contingent situation. For instance, the choice of time frame used to estimate the baseline depends on the past trend of mortality and the existence of past mortality shocks such as that observed in 2015 in several European countries. Similarly, the model choice depends on past mortality trend in the time frame considered; some models tend to amplify the past trend in the predicted baseline, whereas others tend to disregard it.

Assessing excess mortality is easier than quantifying the cause-specific number of deaths; however, if coverage of mortality data is not complete, underregistration of deaths might be an issue. During the COVID-19 pandemic, quantification of excess mortality has not been possible (Aburto, 2021). This might lead scholars to use alternative data sources, such as burial patterns or postmortem surveys (Whittaker et al., 2021), or adjustment methods to take into account underregistration issues (e.g., see Dorrington et al., 2021).

Life Tables Indices

Life tables are used to measure mortality levels of a given country and compare them with those of other countries. Comparisons are usually made using a summary index of life tables. Life expectancy at birth is by far the most commonly used measure; however, other measures are also used, such as modal age at death (less sensitive to infant mortality with respect to life expectancy) or life span disparity, a measure of inequality (for a detailed description of these and others measures of mortality, see Canudas-Romo et al., 2018). The main advantage of using life table–based metrics is that they are naturally already standardized with respect to age structure; thus, comparisons are easier. Another advantage is that life table data are available for a significant period of time; thus, the effect of a mortality shock on these kinds of measures can be compared with respect to historical trends.

The HMD, for example, contains life tables for Sweden that date back to 1751, so the decrease in life expectancy that occurred during the COVID-19 pandemic can be compared with life expectancy changes during the past 270 years. One drawback of life table–based measures is that there is a high risk of misinterpretation because they are period measures (i.e., they reflect the mortality of a given year, experienced by several cohorts); the way they are represented might lead to them being considered cohort measures (i.e., they reflect the mortality of a cohort mortality, experienced during several years). Indeed, life tables mimic the survival of a hypothetical cohort, as if cohort members were exposed to the same mortality level (i.e., mortality of a given year) until extinction, but cannot be used as a measure of actual cohort survival (Goldstein & Lee, 2020).

During the COVID-19 crisis, several scholars measured its impact in terms of life expectancy losses. This has been done for single countries (Aburto, Kashyap, et al., 2021; Andrasfay & Goldman, 2021; Trias-Llimos et al., 2020) and for multiple countries (Aburto, Schöley, et al., 2021).

Aburto, Schöley, et al. (2021), in particular, estimated the life expectancy (at ages 0 and 65 years) loss for all countries included in the STMF database; results are shown in Figure 7. In the figure, the loss in 2020 is also paired with the average yearly change in the past 5 years, so it can be easily seen that the 2-year decrease in male life expectancy in the United States in 2020 is much larger than the average variation in the past 5 years. It can also be seen that this decline is much larger than that of any yearly variation dating back to 1933. Similarly, the decrease in 2020 in Italy is unprecedented since the end of World War II.

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Figure 7. Life expectancy loss in 2020 at ages 0 and 65 years for several countries.

Source: Aburto, Schöley, et al. (2021).

A possible drawback of using the decrease in life expectancy is that normally life tables are constructed based on yearly data, but mortality crises can be limited to few weeks or months of the year, as is case for influenza-driven crises or particularly severe heatwaves. This issue can be overcome by calculating the weekly (or monthly) life expectancy, which is basically the life expectancy derived from weekly death rates. Trias-Llimos et al. (2020) used this method to show the effect of the COVID-19 pandemic in Spanish regions. Another possible pitfall of this measure is that the decline in life expectancy at birth (or any other measure derived from life tables) might also depend on the phenomenon of mortality displacement, also referred to as the harvesting effect or the dry tinder effect. The latter term refers to the case in which a population enters a mortality crisis period with a large number of frail individuals, leading to a higher mortality rate compared to those of other populations. Herby (2020) suggests that Sweden might have entered the COVID-19 pandemic period with an exceptionally large amount of “dry tinder,” and this might explain why mortality in 2020 was much higher in Sweden than in neighboring countries. Note that Rizzi et al. (2022) showed that such effect only accounts for a modest fraction of excess mortality in Sweden. However, this effect is not considered when the decline in life expectancy is estimated; similarly, the mortality trend is also not taken into account.

Also note that life expectancy at birth, different from other measures, takes into account not only the number of deaths but also the age at which deaths occur, and this can be relevant in a comparative perspective. Figure 8 shows the excess mortality for the population aged 15–64 years in countries that experienced a significant decline in life expectancy. As can be seen, whereas Italy, the United Kingdom, and the United States experienced a much higher number of weekly deaths than in previous years, especially in March and April, countries such as Belgium, France, and Sweden do not show such a large excess—a increase in mortality in March and April is visible, but it is much less pronounced than that of the other three countries. Thus, although Belgium is one of the countries with the highest excess mortality and the United Kingdom is much lower in this ranking (see Figure 6), when the decreased life expectancy is considered, Belgium and the United Kingdom are more or less at the same level (see Figure 7). This can be explained by a higher mortality at younger ages in the United Kingdom, whereas in Belgium the excess mortality was mainly concentrated at older ages (65+ years).

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Figure 8. Weekly number of death at ages 15–64 years in selected number of countries—comparison between 2020 and previous years.

Source: Own elaborations from the Short-Term Mortality Fluctuations database.

A specific issue of using decreased life expectancy is that the reference level may vary across countries: In 2019, life expectancy in Sweden was 83.05 years, whereas in the United States it was 79.16 years. The decreases shown in Figure 7 for these two countries are therefore calculated using a quite different reference value, so comparison is difficult. The same issue applies to the related method used by Pifarré i Arolas et al. (2021), who consider the number of years of life lost (YLL): COVID-19 age-specific deaths are multiplied by the distance (in terms of life-years) age of occurrence and life expectancy. This means that a death occurred at an age between 80 and 83 years does not account for YLL in the United States but does so in Sweden.

Comparing the Measures

The three measures of mortality crises all have advantages and limitations, so it may be tempting to compare them to determine if they convey the same information. However, comparisons are difficult for several reasons. Life expectancy and other indices derived from life tables cannot be compared with cause-specific deaths nor with excess mortality because life tables refer to a hypothetical cohort of 10^k individuals; thus, the size of the exposed synthetic population is different from that of the actual population. Moreover, the age structure is different: That of the hypothetical cohort is, in essence, standardized, thus allowing comparisons with life tables of other countries, but the age structure of a real population is inevitably different. Finally, summary measures derived from life tables, such as life expectancy at birth, also take into account the age at which deaths occur, and deaths at younger ages have a higher weight than deaths at older ones, whereas both excess mortality and cause-specific mortality do not make any distinction—all deaths are equally weighted. As shown in Figure 8, it might be the case that the age patterns of increased mortality differ between countries. A comparison between cause-specific deaths and excess death does not suffer from these issues, but other problems arise: In some cases, the mortality crisis can affect other causes of death indirectly, and whereas excess mortality takes into account these indirect effects, cause-specific mortality does not. During the COVID-19 pandemic, this appeared clearly: The excess mortality registered during the peak of the virus spread was, in several cases, much larger than the number of COVID-19 deaths. This can be attributed to difficulties, especially during the first stage of the pandemic, in correctly identifying all COVID-19 deaths, but it is also partly due to other indirect effects, such as an increasing inability to treat ordinary cases by hospitals and emergency rooms that were overwhelmed by COVID-19 patients. At the same time, the nonpharmaceutical measures that several countries implemented also had an effect on other causes of death. Calderon et al. (2021) found that the number of external causes of death declined during the lockdown measures in Peru. Similarly, cases of influenza and other respiratory diseases declined in 2020 in several countries due to mandatory masking orders (Sullivan et al., 2020). This is why Sanmarchi et al. (2021) found that some countries, such as Denmark and New Zealand, had an excess mortality lower than the number of COVID-19 deaths.

Comparison between cause-specific mortality and life table measures is also complex. One issue is that measures such as life expectancy at birth take into account not only the number of deaths but also the age at which deaths occur. In addition, life expectancy is an age-standardized measure and cause-specific mortality can be standardized as well, but not in the same way because life expectancy is not a proper age-standardized measure; rather, it is a weighted average of age-specific death rates, where weights are internally derived from actual rates (Modig et al., 2020). The same issues apply to comparisons between excess mortality and life expectancy.

However, although comparisons between these three measures appear difficult, it is possible to combine some of their feature. For example, the decrease in life expectancy can be calculated taking into account the trend of mortality. Counterfactual death rates can be predicted using the most appropriate model in the same way as is done to estimate the excess mortality. Then rates can be used to estimate a “counterfactual” life expectancy that can be compared with the observed one. Cause-specific mortality and life expectancy can also be combined by using a “cause-deleted” life table, which in turn can be derived from a “multiple decrement” life table (Preston et al., 2001). Basically, cause-specific rates are used to calculate a multiple decrement life table, which takes advantage of life table internal age standardization. Similarly, a cause-deleted table can be constructed (see Preston et al., 2001, Box 4.1), where it is hypothesized that deaths for a specific cause are removed. Table 2 shows an example in which life expectancy of Ukraine in 1995 is compared with life expectancy that would have been observed without heart disease-related deaths.

It should be kept in mind that multiple decrement life tables are based on the independence assumption (no overlap or synergies between causes). However, as Preston et al. (2001) explain, this does not significantly affect results; rather, the process of independent assignment of causes is the main issue here—an issue that analysts cannot avoid.

Heuveline (2021) has proposed a more elaborate measure—the Mean Unfulfilled Lifespan (MUL). This measure also combines life tables with cause-specific mortality and calculates the difference between the average age at death and the expected average age at death in the absence of a specific cause of death. The advantage of MUL with respect to the difference in life expectancies is that it is calculated based on an actual cohort of individuals, not a synthetic one.

Conclusion

The measurement of mortality shocks is important for all countries, from the least developed to the most developed. However, such measures are not straightforward, and three different approaches (cause-specific mortality, excess mortality, and life table–based indices) are employed, all with specific strengths and weaknesses. The choice of the most appropriate measure depends on data quality, mortality trends before a shock, and differences in age structure.

For example, if there are issues with classifying the causes of death associated with a mortality crisis, the method of cause-specific mortality should not be used. In some cases, it is difficult to identify the causes associated with the crisis (e.g., when the shock is caused by a heatwave). Excess mortality can be used in these cases, but care should be given to the way the baseline (i.e., the expected number of deaths if the crisis had not occurred) is estimated. If the trend of mortality varies significantly across countries, choosing a good baseline might be difficult: On the one hand, the same baseline for each country must be used for a fair comparison; on the other hand, this baseline may be applicable for one country but not for others. The choice of a baseline is much less an issue when the mortality trends of the countries are similar. Life table measures are an alternative, with the advantage that they are age standardized, but it should be kept in mind that such measures refer to a so-called synthetic cohort and not a real population, so they can be easily misinterpreted. Moreover, it is questionable to compare countries with different life expectancies before a mortality shock because the weight given to additional deaths is affected by such differences. In summary, there is no unique formula for quantifying a mortality shock, and before choosing a particular approach, a careful evaluation of the data and mortality shock characteristics should be performed.