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The Covid-19 pandemic has long since affected all national states, causing effects that are difficult to compare from country to country.

We continuously receive data on the state of the contagion in the various countries which are often provided in absolute values. Twenty thousand infected and one thousand deaths a day in Italy are certainly impressive figures, but would the same, or even double figures, be equally impressive if referred to the USA?

Evidently not. The United States have a population that is about 5 times that of Italy, therefore, without considering any particular difference, US data would be of similar gravity for much higher values.

We also know that the lethality of Covid-19 is a function of age and the pre-existence of certain pathologies in the infected, these variables can be different in different populations.

For example, considering the marked difference in coronavirus lethality for those below and above the age of 65, it must be considered that in Italy almost 23% of the population is over 65 years old while in the USA this percentage is 15.7%. Therefore, with the same number of infections, the number of  expected deaths in Italy is greater than that in the US,

The comparison of the effects of Covid-19 in different countries, and indeed in some cases even at the local level within the same country (think of the case of Florida which has much more elderlies than other US states ), is therefore not immediate and presents some difficulties that we wanted to address in the analysis describe below.

The purpose of this analysis, based on contagion and mortality data released daily by the World Health Organization, integrated with the real demographic data of the various countries, is to make, as far as possible, national data on coronavirus deaths comparable.

The number of deaths with coronavirus is, obviously, first and foremost a direct function of the number of infected people, then of the composition of those infected in terms of age and the incidence of certain previous pathologies among the infected. These data are not available with the necessary detail and, therefore, in order to carry out a comparative analysis, some simplifications must be made which, however, on closer inspection, and looking at the trends in the resulting graphs, do not seem to particularly affect accuracy nor the significance of the results.

In fact, it should be considered that, at least in countries with advanced and capillary national health systems and characterized by similarly statistical capabilities, the probability that serious Coronavirus cases will not be detected is quite remote and, therefore, serious cases not detected can be considered residual, as well as cases where the virus is not detected in a deceased individuals.

At the same time, the presence of previous pathologies is largely linked to age (collinearity) so the age variable largely incorporates the presence of previous causes that contribute to death in case of covid-19 infection. On the other hand, even in the presence of the same pathologies that may determine death if combined with Covid-19, such outcome is very rare if the infected person is young.

With the aim of making deaths with Coronavirus comparable in different countries, we therefore carried out a mixed analysis, partly descriptive (with regard to the emerged cases and the deaths actually recorded) and partly probabilistic or predictive, considering age the main discriminating data.

For the purposes of the analysis, the national populations were therefore divided into two age clusters: over 65 and under 65.

The first objective was to determine a probable composition of the emerged cases, or Confirmed Cases staying to WHO, in terms of age. To this end, we hypothesized that the probability of contracting or, better, to get in touch with, the virus is the same for the entire population, regardless of age and, therefore, the probability that an infected person is over 65 is equal to the percentage of over 65 in the country.

It is then necessary to determine the probability that a contagion will be detected and therefore that it appears within the Confirmed Cases. This probability, net of some distorting factors, such as the screening of cases’ close contacts, which often leads to the detection of other cases in individuals of an age that is not at risk, is intuitively linked to the severity of the disease which is also dependent on the age of the patient.

This said, considering a probability factor of emergence of the case, that we have called Criticality Rate (CR), specific to each age cluster (over and under 65), the likelihood that each single infection case emerges, and therefore the probability that it is counted among the confirmed cases, is equal to the probability that it belongs to its age cluster times the Criticality Rate of its reference cluster.

The default value of CR coefficients has been set to 0.85 for the over 65 and 0.10 for the under 65, that means that 85% of the over 65 cases (initially equal to the percentage of over 65 in the single country) emerge (normally due to the severity of symptoms) while this would happen only for 10% of the under 65s. Such values are already common with minor variations in many reference studies and, however, users can vary these coefficients to simulate different scenarios.

By normalizing the sum of both cluster’s probabilities of being detected as confirmed cases to 100%, it is possible to obtain the probability of the composition of confirmed cases in terms of age with an obvious leverage effect for cases over 65 if for these, as plausible, a CR significantly higher than for the under 65s is considered. The Criticality Rates for the two age clusters have been set equal for all countries due to globally similar testing dynamics.

Once the hypothetical distribution of confirmed cases in the two age clusters has been obtained for each country, it is possible to calculate, again at the national level, the expected number of deceases considering the same mortality rates, Fatality Rate (FR), specific to each cluster (FR Over 65 and FR Under 65) for all countries for the entire observed period.

Default Fatality Rates has been set equal to 0.23 for the over 65 and 0.02 for the under 65, as the real values ​​for Italy in the initial phase of the pandemic. The coefficients FR_Over65 and FR_Under65 are used to calculate, on a common basis (same mortality by age cluster), the number of deaths expected in each country, given the distribution of cases by age cluster hypothesized as above described.

Other possibly distorting variables of the analysis, such as the reliability of the tests (false positive rate and false negative rate), have considered equal for all states.

Once the expected deaths were obtained, based on the application of the FRs to the resulting quantities in the respective age clusters for each country, we calculated what we have defined Actual Death Index 2 (ADI2), as the ratio of actual deaths with Coronavirus and the expected deaths, while the Actual Death Index 1 does not take into account the Criticality Rate.

Beyond enabling an initial comparison of the most serious effect of the pandemic, the trend of the ADI indexes in the graphs obtained and the progressive convergence of their curves for the different states are, in our opinion, highly informative:

• of the evolving ability to react to the disease over time and to cope with it in terms of care;
• of the real impact of the containment measures (very different from each other) implemented by countries;
• of the actual relevance of the simplifying assumptions underlying the analysis.

Note that for any plausible value of the 2 indexes (or, better, of the 4 indices, one per each age cluster) CR and FR the curves of the Actual Death Index (ADI or ADI2) tend to converge, showing differences that are currently less than 20%, while in the initial phase of the pandemic these differences exceeded 100%.

The charts below refer to the ADI index (simplified) which takes into account the different demographics but not the CR coefficients, while the ones above refer to the ADI2 index which also considers the different probability of detection as a function of age.

The graphs on the left represent the trend of ADI indexes as a function of the penetration of the infection in each country’s population (as x axis is cases as % of total population), thus making ADI indexes comparable for equal stages of the pandemic, while the graphs on the right represent the trend of the two indexes over time or by date.

Obviusly, because it represents the ratio of actual deaths to expected deaths, the less the Actual Death Index is the better is the performance of the country .

According with the described model, an increase in the CR coefficient for the over 65 cluster has a leverage effect on the number of over 65s within confirmed cases compared to the mere percentage of over 65 in the national population, which reverberates in an increase of deaths expected due to a higher Fatality Rate for that cluster and, therefore, in a decrease in the Actual Index Rate (better performance) of all countries but, especially of those whose population is characterized by a higher percentage of over 65.

Charts are interactive users may vary the single CR and FR coefficients to check their impact on the resulting curves.

User can add or remove single countries from the analysis by clicking the country name from the list on the left holding the ctrl key pressed simultaneously.

You may also focus on a single country by picking it individually from the legend or on a group by doing the same holding the ctrl key.

Any comment, suggestion or request for clarification posted by using the box below will be highly appreciated.

14/12/2020