### Review article

# Epidemiological Measures in the Context of the COVID-19 Pandemic

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__Background:__ The various epidemiological indicators used to communicate the impact of COVID-19 have different strengths and limitations.

__Methods:__ We conducted a selective literature review to identify the indicators used and to derive appropriate definitions. We calculated crude and age-adjusted indicators for selected countries.

__Results:__ The proportion of deaths (case fatality proportion [CFP]; number of deaths/total number of cases) is commonly used to estimate the severity of a disease. If the CFP is used for purposes of comparison, the existence of heterogeneity in the detection and registration of cases and deaths has to be taken into account. In the early phase of an epidemic, when case numbers rise rapidly, the CFP suffers from bias. For these reasons, variants have been proposed: the “confirmed CFP” (number of deaths/total number of confirmed cases), and the “delay-adjusted CFP,” which considers the delay between infection with the disease and death from the disease. The indicator mortality (number of deaths/total population) has at first sight the advantage of being based on a defined denominator, the total population. During the outbreak of a disease, however, the cumulative deaths rise while the total population remains stable. The phase of the epidemic therefore has to be considered when using this indicator. In this context, R_{0} and R(t) are important indicators. R_{0} estimates the maximum rate of spread of a disease in a population, while R(t) describes the dynamics of the epidemic at a given time. Age-adjusted analysis of the CFP shows that the differences between countries decrease but do not disappear completely. If the test strategies depend on age or symptom severity, however, the bias cannot be entirely eliminated.

__Conclusion:__ Various indicators of the impact of the COVID-19 epidemic at population level are used in daily communication. Considering the relevance of the pandemic and the importance of relevant communications, however, the strengths and the limitations of each parameter must be considered carefully.

COVID-19, the disease associated with SARS-CoV-2, has a major effect on the private and working lives of large numbers of people. COVID-19 was first reported in Wuhan (Hubei province, China), and 1 991 562 confirmed cases had been registered worldwide by 16 April 2020 (1). Different epidemiological indicators are used to characterize the impact of the infection and the disease on a population, the aim being to facilitate description of the situation and performance of international comparisons. In this article we present commonly used indicators and discuss their strengths and limitations.

Methods

We conducted a selective literature review to identify and define the indicators used. In order to compare the impact of SARS-CoV-2, crude and age-standardized indicators were computed for different countries. The Segi world population was adopted as standard population (2, 3). Table 1 provides definitions of a number of standard terms from infectious disease epidemiology that are used in this article.

**Table 1**

Indicators based on case numbers

One challenge encountered during the COVID-19 pandemic is first how to define a case and then how to correctly estimate the number of cases. Persons who come into contact with the virus are generally considered as “infected” if the virus replicates in their body and evokes a response (e.g., by the immune system). However, not every infected individual shows the same intensity of symptoms. Persons are considered symptomatic if they present with a typical clinical picture, oligosymptomatic if minimal symptoms are present, and asymptomatic if no symptoms appear although the person is infected (4). Furthermore, according to the World Health Organization (WHO) and to the European Centre for Disease Prevention and Control (ECDC) (5), a case of COVID-19 is defined as “confirmed” after laboratory confirmation, irrespective of clinical signs and symptoms.

If a seroepidemiological survey or repeated virological tests (e.g., by polymerase chain reaction [PCR]) of the whole population or a sample thereof are not feasible (for instance, because no serological test is available), there is considerable uncertainty about the total number of cases. Indeed, only a small proportion of the asymptomatic and oligosymptomatic cases can be identified, so the true population burden remains unknown.

In the case of COVID-19, the proportion of asymptomatic cases can be estimated on the basis of two study populations, both of them closed cohorts that were tested in their entirety. Nishiura et al. (6) analyzed 565 Japanese citizens evacuated from Wuhan on charter flights after the start of the outbreak in the city. The Japanese Institute of Infectious Diseases analyzed the 3711 passengers of the cruise ship “Diamond Princess” after COVID-19 broke out on board (7). In the first case 41.6% (95% confidence interval [16.7; 66.7%]) of the persons who tested positive were asymptomatic (6), while in the second case the figure was 51% (7). However, both studies are based on the data of persons with particular demographic, health-related (e.g. comorbidities), and socio-economic characteristics, so that the external validity (or generalizability) of the results is questionable. Furthermore, the statistical uncertainty of the estimates must be taken into account (see size of confidence interval).

Proportion of deaths among infected cases

The proportion of cases with mild or no symptoms in the population—in other words, the proportion not properly counted— has a considerable effect on indicators that use the total number of cases. The most commonly used such indicator is the case fatality proportion (CFP) (8), i.e., the proportion of infected cases that die due to the disease.

This indicator is often referred to as a ratio or a rate, although formally it is a proportion (9). The CFP can be used to estimate the severity of a disease, but only if the total number of cases can be estimated fairly reliably.

Heterogeneity in death registration affects the numerator of this indicator, and this can be an important factor when comparing different countries. If, for example, a given country tests all deceased persons post mortem for the presence of the virus and those tested positive are classified as COVID-19 deaths, this leads to overestimation of the true CFP unless the entire living population is tested for the virus at the same time. Moreover, differential misclassification of deaths due to COVID-19 may occur, e.g., if deaths without a positive test result for SARS-CoV-19 are classified in some countries as pneumonia or influenza, but in other countries not (10).

Similarly, heterogeneity in the guidelines for case detection can affect the denominator of the CFP. Therefore, the CFP should be only used to compare countries that make the same efforts and employ the same procedures.

One obvious way of making case definition consistent is to use only laboratory-confirmed cases for the denominator.

The “confirmed CFP” is then calculated as follows:

However, this indicator is also not always suitable for international comparisons if different testing strategies are being applied. In addition, both the CFP and the confirmed CFP are biased during an epidemic, because of the delay between the occurrence of a case and the potential death. If the daily case numbers increase exponentially at the beginning of an epidemic, the CFP is initially underestimated: The deaths at a given day are recruited from persons who become infected a number of days earlier. Comparison of the number of deaths with the number of cases on the same day is therefore inadequate. The size of this bias depends on the time between diagnosis and death: small if the lag time is short, but substantial if it is longer (as assumed for COVID-19) (11). Russell and colleagues therefore developed the delay-adjusted CFP (CFP_{del}) (12):

Lag times of 7–14 days have been described for COVID-19 (13). The delay with which cases are reported may also depend on the reporting systems, and this too needs to be taken into account when comparing different countries (14).

Another limitation of the comparison of CFPs across populations is that the age distribution of cases is not taken into account. There is evidence that the mean age of confirmed cases in Germany (47 years) and South Korea (44 years) is lower than in Italy (62 years), Spain (60 years), and Sweden (60 years) (Table 2). Given that the CFP for COVID-19 increases considerably with age (Table 3), higher CFPs are to be expected for Italy, Spain, and Sweden than for Germany and South Korea. To evaluate what part of the difference in CFPs can be explained by the age distribution of confirmed cases, we calculated an age-standardized version of the CFP. Table 2 shows crude (confirmed) CFPs in Germany, Italy, South Korea, Spain, and Sweden together with age-adjusted figures. The crude CFPs in Italy (12.6%), Sweden (10.6%), and Spain (8.1%) are much higher than in Germany (2.7%) and South Korea (2.2%). Adjustment for age reduces the differences among the countries but the adjusted CFP in Italy is still higher than that in Sweden, Spain, Germany, or South Korea (Table 4).

**Table 2**

**Table 3**

**Table 4**

The CFP_{del}, assuming a lag time of 7 days, is higher in Italy (CFP_{del} = 14.7%) than in Spain (10.1%) and much higher than in South Korea (2.2%) and Germany (3.3%) (Table 4). After age standardization of the CFP_{del}, the delay- and age-adjusted CFPs in South Korea (CFP_{del-std} = 0.8%) are compatible with those in Germany (CFP_{del} = 1.0%) (Table 4).

Indicators based on the total population

Mortality

Another indicator that can be calculated to compare the impact of an epidemic on the population in various regions is the mortality proportion (MP), i.e., the proportion of the general population in which death was due to a specific disease. This is not the same as the conventional mortality rate, which refers to a certain time span, e.g., a year, that cannot be calculated in this context.

Compared with CFP, MP has the advantage of relying on a known denominator, the total population. This is, however, also the principal disadvantage of this indicator during an epidemic: The denominator is stable over time, whereas the number of deaths increases exponentially in the early phases of an epidemic. Therefore, the MP depends strongly on the phase of the epidemic confronting the population at a given time. It is thus not an appropriate indicator for comparing different populations during the early phase of an epidemic, although it will be extremely helpful to assess the cumulative impact of the epidemic on a population once the epidemic is over.

In the early stages of an epidemic many indicators are reported without a denominator (i.e., as absolute numbers). While this seems odd at first glance, cases and deaths in this early phase are determined by the characteristics of the infectious agent, and not by the size of the population (Box 1).

**Box 1**

Indicators for the dynamics of the spread of an infection in a population

Central indicators of how an infection spreads in a population are (15):

- The base case reproduction number (R
_{0}) - The effective (or net case) reproduction number (R(t))

R_{0} represents the average number of persons to whom one infected person transmits the infection, during their infectious period, in a population with no immunity and no specific infection control measures. It is a theoretical indicator which can be assessed only when a newly occurring infection spreads for the first time in a given population. R(t) represents the average number of persons to whom an infected person transmits the infection during their infectious period—under the infection control measures in place and the proportion of immune persons in the population. R(t) changes over the course of the epidemic and may vary from region to region. R_{0} is assumed to be constant for an infection in a specific population (8). In the simple case, R(t) can be calculated by multiplying R_{0} by the proportion of susceptible persons in a population (the more immunes there are, the smaller R(t) will be). If we assume that the proportion of susceptible persons is 80% and that R_{0} is 2.5, then:

Both R_{0} and R(t) are directly dependent on the number of transmission-relevant contacts a person has per unit of time. Changes in contact behavior thus directly affect R(t). This aspect is crucial when comparing the spread of an infection in different countries. Mossong and colleagues compared the daily number of social contacts in different European countries and showed that the daily number of contacts in Italy (mean 19.8, standard deviation 12.3) is more than twice as high as in Germany (mean 8.0, standard deviation 6.3) (16). This affected especially contacts from children to persons over the age of 65 years. However, caution is advised when interpreting the results of this study, because the nature of data collection differed among the different countries.

R(t) is an important indicator during the spread of an infection in a population, as it takes into account the impact of control measures and the pace with which an infection is spreading (15). If R(t) >1, the number of new cases (measured, for example, as newly reported cases in one day) will increase further. This enlargement of the infected population will decrease the number of susceptible persons, eventually causing R(t) to drop below 1. When R(t) is <1, the infection will start to come to an end (8). This still happens if the contacts among individuals remain unchanged, because the risk of encounters between an infected and a susceptible individual is smaller. If the susceptible part of the population is small enough, the reduced risk of contact with the infection provides indirect protection for the remaining susceptible persons. This phenomenon is termed herd immunity. It requires a considerable proportion of immune individuals in the population, referred to as the herd immunity threshold (HIT). The HIT is specific for a given infection and is calculated as follows:

If the R_{0} for COVID-19 lies between 2.5 and 3.5, the HIT is between 60% and 71%. This is simplified logic, however, as no account is taken of changes in the general population. The situation does not remain stable after the HIT is achieved, because as time passes persons who are immune to the virus grow old and die, and newborns have no immunity. The proportion of immune individuals in the population falls progressively, eventually permitting a new wave of infection. This was observed, for instance, in the classic biennial measles epidemics (R_{0} = 15–18) before a vaccine was developed (17).

Understanding the dynamics of an epidemic is crucial for the implementation of effective strategies to limit the spread and the consequences of an infectious disease. The indicators discussed in this article are based on the observed cases of and deaths from a disease in a population, and cannot be used to project future developments. In order to predict the further dynamics of an infectious disease, mathematical models are typically used (Box 2).

**Box 2**

Discussion and conclusion

In this article we present indicators and epidemiological measures that are being commonly used in risk communication during the current COVID-19 pandemic. Models that can be used to predict the future course of the pandemic are only briefly outlined. We emphasize the necessity of considering the indicators together with the demographic structure of the population and of the affected cases. Apart from the differences in age structures, one must take account of the delays in reporting cases and deaths. Another aspect that has to be considered is the stage of the epidemic in which a country finds itself. This factor depends partly on the policies adopted in each country (and their sequence), for example border controls or efforts to isolate the initial clusters of the disease (18, 19). In addition, the correct identification of cases relies on the testing strategy and on the validity of the tests, especially in terms of their sensitivity and specificity (20).

The age-adjusted analysis of the CFP shows that while the differences among countries are smaller, they cannot be fully explained by different age structures. However, if the testing strategies depend on age or on severity of symptoms, the bias cannot be completely removed by age standardization.

The reasons for the observed differences in numbers of cases and deaths are multifactorial, and all comparisons should be conducted with great caution.

Acknowledgments

The authors wish to thank Dr. Annasara Carnahan and Dr. Emma Löf of the Public Health Agency of Sweden, Dr. Alexander Ullrich of the Disease Data Science Unit of the Robert Koch Institute, the Korean Centers for Disease Control and Prevention, and the Task Force COVID-19 of the Department of Infectious Diseases, Istituto Superiore di Sanità (Italy) for their support in data collection.

Conflict of interest statement

The authors declare that no conflict of interest exists.

Manuscript received 14 April 2020, revised version accepted 20 April 2020

Corresponding author

Dr. rer. physiol. Emilio Gianicolo

Institut für Medizinische Biometrie,

Epidemiologie und Informatik (IMBEI)

Universitätsmedizin Mainz

Obere Zahlbacher Str. 69

55101 Mainz, Germany

emilio.gianicolo@uni-mainz.de

Cite this as:

Gianicolo E, Riccetti N, Blettner M, Karch A:

Epidemiological measures in the context of the COVID-19 pandemic.

Dtsch Arztebl Int 2020; 117: 336–42.

DOI: 10.3238/arztebl.2020.0336

Situation Report – 87. 2020. www.who.int/docs/default-source/coronaviruse/situation-reports/20200416-sitrep-87-covid-19.pdf?sfvrsn=9523115a_2 (last accessed on 20 April 2020).

Institute for Clinical Physiology, National Research Center, Lecce, Italy:

Dr. rer. physiol. Emilio Gianicolo

Institute for Epidemiology and Social Medicine, University of Münster:

Prof. Dr. med. André Karch, MSc

**Box 1**

**Box 2**

**Key messages**

**Table 1**

**Table 2**

**Table 3**

**Table 4**

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