Is the Case Fatality Rate (CFR) an Appropriate Method of Analysis for Urban Studies?
The present document sums up the data on the coronavirus outbreak we have been collecting latetly from the website Worldometer. The figures cover all the cases in Europe and are divided into two groups. One of them indicates the number of deaths. The other discloses the digits of people infected in the region. Both influenced by the massive effect of the virus outbreak in urban context. However, what is the difference between the present publication and the source we consulted? We basically build our observations “photographing” the data in aleatory periods. By briefly stating, the total of fatal cases and the aggregate of people diagnosed with the infection will be shown in different weeks. The reason for that is related to our curiosity in testing if the numbers unravelled by our analysis herein will corroborate the predictions or estimations of official institutes.
Nevertheless, our study is much more than the behaviour examination of the coronavirus outbreak from country to country in linear projections. Why? One of the reasons refers to those public policies being decided and taken into account by authorities, i.e., in municipal, provincial and national levels in different periods. We want to check if the coordination or de-coordination of the same official measures against coronavirus may result in more effective results in a place and not in other ones either in domestic or international level. Another intriguing aspect is about the tendencies of infections and fatal cases. Is it possible for a non-sequential set of data to behave similarly to those collections with a rigorous periodicity.
Our main objective with the present debate is an attempt for ulterior analyses linking urban and environmental issues to pandemic diseases. However, it is very important to mention two non-evident issues. The first one is about demography in urban centres since we understand cities as vectors of disease outbreaks caused by human agglomeration and street conditions (Barbu, Hong, Manne, Small, Quintanilla Calderón, et al., 2013). In short, it is not about how big a country is per se in terms of population, but how public policies are designed for different urban realities. The second one is more complex and has to do with the way we produce knowledge on diseases in connection with local governance. In order to address adequately this second matter, we call the attention to the importance of studying diseases and their outbreaks taking into consideration city aspects. For example, metropolises tend to fail in accomplishing the World Health Organization’s checklist for healthy cities (WHO) since their government mechanisms do not usually meet “basic needs (food, water, shelter, income, safety and work) for all the city’s people” among other elements. In that case, conurbation is the independent variable that increases the possibility of diseases outbreak and lockdown is the dependent variable. The Deparment of Economic and Social Affairs (United Nations) states that “Today, 55% of the world’s population lives in urban areas, a proportion that is expected to increase to 68% by 2050.”.
In order to make a start based on descriptive statistics, we carried out a regression for each pair of data, that is to say, four different correlations taking into account the total cases of infected people and the total of fatal cases in four distinct moments (\(P1\), \(P2\), \(P3\) and \(P4\)).
Pearson's product-moment correlation
data: corona$totalmars2 and corona$deathmars2
t = 20.068, df = 32, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.9255875 0.9812714
sample estimates:
cor
0.9624915
Pearson's product-moment correlation
data: corona$totalmars3 and corona$deathmars3
t = 16.065, df = 32, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.8884609 0.9715162
sample estimates:
cor
0.9432346
Pearson's product-moment correlation
data: corona$totalapril1 and corona$deathapril1
t = 21.429, df = 32, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.9341455 0.9834803
sample estimates:
cor
0.9668783
Pearson's product-moment correlation
data: corona$totalapril4 and corona$deathapril4
t = 17.76, df = 32, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.9068738 0.9763897
sample estimates:
cor
0.9528313
The function lm{stats} in R calculated the following regressions for the respective extracts. There is also a single stratum analysis of variance for each \(P\) and analysis of covariance (although AOV may indicate a more convenient interface for these).
The following boxplots represent the 34 countries in Europe (see the interactive complete list at the end of the present document) and their main urban territories in four different periods as well. The first boxplot on the left refers to the second week of March, then the second from left to right the third week of March, the other two boxplots for the first and fourth week of April. Total indicates the total of people infected in Europe for the referred period and the same for the fatal cases.
The following equation brings forward a method for the calculation of proportions known as Case Fatality Rate (Ritchie, & Roser, 2020). In our case, the sum of the fatal cases for each country is divided by the totals. From the second to the third weeks of March 2020, the percentage of people infected with fatal results rose up from 3.9% to 5.19%. From the first week of April to the fourth, the proportion calculated was 9.69% and then 7.2%. Considering F the number of fatal cases and N the quantity of cases, we have the following equation:
\[{CFR} = \left({\frac{\sum_{j=0}^F j}{\sum_{j=0}^N j}}\right) * 100\]
The plot below indicates the distribution of probabilities in different colours. CFR1 stands for the Case Fatality Rate (CFR, in %) during the second week of March. CFR2 represents the same relation for the third week of March. CFR3 for the first week of April and CFR4 for the fourth week of April.
[1] 3.90859
[1] 5.194782
[1] 7.664433
[1] 9.695049
If we observe the dynamics of the colors in following graph, we can see that the Case Fatality Rate (CFR, in %) for each country with the majority of the cases occurring in more populated capitals mainly those urban contexts defined as metropolises too. The contrast between the CFR and the linear progression of the COVID-19 outbreak is really intriguing. The European cities belonging to different geographic spaces, for example, Nordic and Southern urban areas have had different proportions since lower proportions are more common in non-complex metropolitan areas or cities without the conurbation phenomenon. Therefore, the CFR points out higher proportions of spread for metropolitan areas.
That is why we strongly recommend to take into account urban demographical, spatial and social aspects as variables for the COVID-19 and other sorts of disease spreading rapidly in metropolitan contexts. Although the CFR is a very appropriate form of measurement to avoid biased assessment of data behavior, the equation cannot offer a more accurate prediction of the outbreak since it is not possible to see under which probability the averages are subject to.
Since the Case Fatality Rate (CFR, in %) does not capture probability in average calculation for the European case during the weeks under analysis, we have built up the following normal distributions for the COVID-19 dynamics considering the impact of the outbreak overwhelmingly happening in dense, huge and complex urban metropolises Nevertheless, observing the normal distributions and the Rs from the values unravelled in the previous section, we may affirm that the probability of people being infected in Europe is gradually decreasing if we consider the data from the second week of March on till the present moment. That phenomenon refers to the effect that has been called “flattening the curve”. In a nutshell, the public policies and actions during the confinement is working for Europe as a whole.
All data cover 34 countries in Europe and their main urban areas, i.e., metropolises and main cities. The following maps give us a visual feedback about how the coronavirus has spread in the region. The data indicate also the outburst of the Covid-19 mainly takes place with a more devastating impact in the metroplitan or conurbated areas/regions and, therefore, representing the capitals but not the demographic factors in national levels. It is interesting to notice with the subsequent cartographies how the coronavirus behaves from the southern part of Europe to the central and north territories of the continent. Even the confinement policies varying from country to country, the CFR does not show a geometric progression which would generate a chaotic urban scenario. The control of the Covid-19 depends on political, social, informational and technological responses considering the complexities of local, national and international actions expected to be taken by public administrations as well. In other words, it is definetely a topic for urban governance in regional and global scale.
Barbu CM, Hong A, Manne JM, Small DS, Quintanilla Calderón JE, et al. (2013) The Effects of City Streets on an Urban Disease Vector. PLOS Computational Biology 9(1), 01-09.
Ritchie, H., & Roser, M. (2020). What do we know about the risk of dying from COVID-19? Our World in Data. Retrieved from https://ourworldindata.org/covid-mortality-risk
World Health Organization (2018). Healthy City Checklist. Retrieved from http://www.euro.who.int/en/health-topics/environment-and-health/urban-health/who-european-healthy-cities-network/what-is-a-healthy-city/healthy-city-checklist
Worldometer (2020). Coronavirus. Retrieved from https://www.worldometers.info/coronavirus/