# On the informativeness of statistical mortality indicators during the COVID-19 outbreak

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(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)

There are generally accepted in statistical practice the indicators (coefficients) of mortality, calculated by the following formulas:
1. I (WHO) = D / TC
2. I (CC) = D / (D + R)
where
I — index (mortality rate)
WHO — World Health Organization
D — Death
TC — Total Cases (total number of infected)
CC — Closed Cases (closed cases: recovered + dead)
R — Recovered (recovered)

During the outbreaks the above stated indicators are calculated daily.

The correct use of these indicators requires an understanding of what information they carry. Logical analysis of the outbreak spread process structure allows us to distinguish two main qualitatively different components (subsystems) in it: (1) spread of infection and (2) provision of medical care to the infected (patients). The input of the first subprocess is population of the region. The output forms a flow of infected people, which enters the second subsystem and is an input for it from system positions. The output of the second subsystem is recovered and dead.

The number of infected people depends on various mechanisms of the virus transmission from person to person, as well as on measures taken by the state and the population to limit the spread of the virus. At this stage, it is necessary to distinguish between latent (hidden) and detected infected. The relationship between them depends, inter alia, on measures to diagnose the population. Official statistics operate on the number of infected.

Considering these ideas, the semantic content of indicator I(WHO) becomes clear. The value of this indicator depends on the number of infected people (output of the first subsystem) and the number of deaths (one of the two outputs of the second subsystem). It follows that, in order to “lower” the mortality rate, it is “enough” to speed up the process of detecting the number of infected people. This is obvious nonsense. The reason for this has systemic nature. The mentioned indicator links the result of the activity of one subsystem with only one of two results of the second subsystem, which operates according to its own laws. This leads to significant underestimation of the mortality rate at the initial stages of the development of epidemics, in which an increase in the number of detected infections predominates. That is why WHO has to adjust up the mortality rate of coronavirus COVID-19 daily.

Indicator I(CC) is internally consistent and characterizes the effectiveness of medical care for patients (the effectiveness of the second subsystem), showing the proportion of failures in providing care for patients (deaths) in total number of closed cases. However, this indicator is not without certain drawbacks also as an indicator of mortality at initial stages of the outbreak. The main one is that the speed of the number of deaths at the first stages exceeds the speed of the number of recovered. That is to say, the characteristic time of transition from the state of the identified infected to the state of recovered and deceased is different. Therefore, with a daily comparison of the recovered and the dead, essentially different entities are compared. As a result, the mortality rate I (CC) at the initial stages of the outbreak is often higher than at the final stages. This is most clearly evidenced by the dynamics of the indicator values ​​as exemplified by the COVID-19 outbreak (see examples below). The second of these examples, due to an abrupt and unpredictable change in values, directly indicates the impossibility of constructive application of indicator I (CC) at the initial stages of the outbreak.

Nevertheless, there is a way out.

(To be continued)