This is a part of a series of posts analysing the data being published about the spread of COVID-19. The focus is on the cumulative number of deaths reported. If you find such data upsetting, please do not view this post.
This post examines the COVID-19 data by focusing on different approaches to monitoring counts and comparing countries. The focus is on reported deaths rather than confirmed cases because the latter is dependent on how much testing is being performed, which appears to be varying substantially between countries based on news reports. This is a sensitive source of data. Please do not read on if you find such statistics upsetting. The purpose is to show just how challenging it can be to interpret data about a real-world phenomenon, and how making an adjustment to the scale for comparing countries can produce a different visualisation.
For details about the data sources and preparation, and to view the most recent data updates, view COVID-19: Daily Updates. The plots presented are based on data as of 29 March 2020.
Changing the start point for comparing countries
The following charts examine how comparisons between countries change if you change the starting point used to align them.
In the related post COVID-19: 28 Days Later, countries were initially compared per continent from the date of the first reported death attributed to COVID-19 for each country. Within Europe (and world-wide), France stood out for having a longer period of low counts before experiencing a similar rise to other countries.
The following charts compare countries with more than 200 reported deaths so far when day 1 is a) the first death attributed to COVID-19 was reported, b) at least 10 deaths were reported, c) at least 100 deaths were reported, and d) at least 1000 deaths were reported, for each country. The count is the cumulative total reported each day.
a) day 1 is when first death attributed to COVID-19 is reported
b) day 1 is when at least 10 deaths are reported
c) day 1 is when at least 100 deaths are reported
d) day 1 is when at least 1,000 deaths are reported
As the start point increases, two broad curves emerge: one for Iran and China, and one for everyone else. The separation into two types of curve is visible when plotting from the day when at least 100 deaths have been reported and is even more apparent when the first day is for when at least 1,000 deaths have been reported. It suggests that many countries may not have identified the first death caused by COVID-19 and/or that the curve will not become evident until two weeks after at least 100 deaths have been reported and one week after 1,000 deaths have been reported.
Scaling the count
The above charts plot actual counts. However, the number of people that can be infected by COVID-19 within a country will depend on the size of the population and the distribution of the population across the land area. An alternative approach is to scale counts to accommodate for differences in population size.
The following table shows some basic statistics per country that may affect the spread of the virus.
The data source for population data is Worldometer: http://worldometers.info/world-population/population-by-country/ accessed 27 March 2020. ‘pop_density’ is the average population per km2 of land area; ‘urban_pop’ is the amount of the population living in urban areas; ‘median_age’ is the median age of the population in years; day is the number of days since the number of deaths recorded exceeded 100; deaths = number of deaths recorded as of 23:59 on 28 March 2020 or up to 56 days after the number of deaths exceeded 100.
The following chart shows the number of deaths attributed to COVID-19 per hundred thousand of the population for each country. This is using the same starting point as chart c) above: day 1 is when at least 100 deaths have been reported.
e) Scaling counts by population size (per hundred thousand people)
Incorporating population size gives an indication of scale. Italy has, up to 29 March 2020, experienced nearly 17 deaths per 100,000 people whilst the USA has experienced less than 1 death per 100,000 people. The USA curve looks more like Iran than Italy when scaling by population size. Belgium, Switzerland and the Netherlands are all experiencing earlier rises on this scale. France is on Italy’s trajectory as is the UK albeit just behind in terms of the number of days since more than 100 deaths were first recorded.
However, scaling by population can also mislead. A country with a smaller but denser population would likely experience more rapid and higher rates than a large country during the early stages of a virus spread by social contact. However, a large country could have areas – cities – where the population is just as, if not more, dense than smaller countries and of a similar size but the effect will be diluted when comparing countries. An alternative measure would be to use population density – divided the population by the land area for the country.
f) scaling counts by population density (population/km2)
The following chart shows counts divided by population density, where population density is the population divided by land area for each country to calculate the average number of people per km2. When scaling by two factors, the results become harder to interpret.
Whereas scaling by population size penalises smaller countries, scaling by land area penalises larger countries that have substantial areas that are uninhabited or scarcely populated and are experiencing localised clusters of COVID-19 infections. In this instance, the USA now looks more like Spain and Iran looks more like Italy. Both the USA and Iran have low population densities when averaging the population across the entire land area of the country.
So does scaling the count provide more information than using actual counts? When studying a real-world phenomenon that is not evenly distributed over space and/or time, scaling can have limited value unless the scaling method also reflects the distribution of the phenomenon. In this case, we are looking at the rates for an entire country when infections appear to be clustered locally within the country, predominantly in urban areas that would have a higher population density than the average across the country. We need data that can incorporate that variation in the scaling method.
An alternative approach is to try and identify whether or not countries can be categorised based on shared attributes. When comparing countries from when each first reported more than 1,000 deaths, two distinct curves are visible. Can those differences be explained by differences in the attributes for each country and/or approaches taken to contain the spread of the virus?
Comparing country attributes
Assuming that reporting is accurate (and there is no way to verify it), one way to investigate the differences in the curves is to compare the countries based on different attributes and see if there are patterns that may help explain the different curves. The following charts are based on the values in the table presented earlier.
g) comparing attributes: land area and population
The chart below shows the distribution of countries when comparing land area and population size.
It is immediately evident that the USA and China are very different to the other countries in terms of both population size and land area, and even Iran sticks out compared with the cluster of Western European countries.
The chart below plots the same data points but excludes China and the USA.
The Netherlands, Belgium and Switzerland all have much smaller populations and land areas. This could perhaps explain why their curves appear to be more rapidly rising when scaling counts by population size. However, whilst the Netherlands and Belgium have much higher population densities than the other European countries, Switzerland is lower than both Germany and the United Kingdom, so we can’t be certain. The landarea_km2 value is the total land area for each country. A better measure might be the total inhabited land area for each country. Switzerland includes a substantial mountain range that could mean urban population density is closer to Belgium and the Netherlands.
h) comparing attributes: urban population and median age
We do have the statistics for how much of the population is urbanised, and the median age of the population. Both are factors that may influence the spread and impact of the virus. The chart below shows the countries plotted on these two factors.
On this plot, China and Iran appear to be outliers. Germany appears to be on the same line as Italy, Spain, the Netherlands and Belgium yet is not experiencing the same impact of the COVID-19 virus so far.
The reason for including these scatters is to show that, even with some simple attributes, it becomes possible to see differences between countries but also that it is important to consider the underlying data. Land area is perhaps not effective for calculating an average population density. We need a measure of the land area that is inhabited per country. And even then, perhaps need a separate measure for urban and rural density. However, sticking with the data we have, China is an outlier when plotting against attributes and rates of Western European countries, as well as when plotting actual counts. It is unlikely to provide a reliable indication for how other countries will progress. And that is before considering and comparing containment strategies, when they were implemented and the different approaches taken within different countries. And the plots are all based on an assumption that the data being reported is accurate. It gives an indication of just how difficult it is to build a model that is reliable and representative of a real-world phenomenon.
In terms of comparing the impact of COVID-19 between countries, it appears to be more reliable to start the count from when at least 100 deaths have been recorded to give an indication of how countries compare. Looking at the charts comparing from 1, 10, 100 and 1,000 deaths attributed to COVID-19, it appears that some countries have failed to identify the first death caused by COVID-19. This is important to consider for other countries currently reporting no or low counts. An early assumption of achieving control over the virus could lead to a premature relaxing of containment policies with terrible, and avoidable, consequences.
The different curves produced when using different scaling measures emphasise the importance of carefully viewing any visualisation before drawing conclusions. Pay close attention to the labelling and values on the axes to understand what is being plotted. Scaling may be more appropriate when evaluating how different countries are likely to experience a spread of the virus, and it may be possible to build a model to study developments per country in more detail given more data about attributes that can affect the spread. But for a simple visual to monitor and compare countries as the pandemic unfolds, actual counts are sufficient.
Banner image at top of post by mattthewafflecat from Pixabay
I really appreciate your sharing this information with us, Sharon. I also appreciate the apolitical manner in which you present the data and the information gleaned from the data.
I hope you are staying well.
Thanks Dan, I always appreciate your comments. This is a difficult subject to write about, given the data represents lives taken prematurely. I wanted to produce something simple to compare against media messages being reported over here that are often confusing or difficult to interpret.
Hope you and your family are all safe and well.
Post updated 31 March to include plot and notes for scaling by population density
Note: WordPress did something funny – apologies if this comment appears twice.
Thanks very much for the analysis Sharon. Three thoughts for now:
1. Looking at graph (d), day 1 is when at least 1,000 deaths are reported, you do indeed see two different curves, China/Iran and the rest. It is of course possible that Spain and Italy will plateau in the same way as China when they get up to 50 days, but at a much higher figure. That should not surprise us. If you start off badly and you have exponential growth in the early stages (driven by infections around Ro^t and a reasonably stable ratio of deaths to infections), you are going to get to a very bad place. Could one reason why the pattern becomes clearer when you start at 1,000 deaths be that by that stage the rate is being driven by a stable Ro and a stable ratio of deaths to infections, and is immune to random fluctuations which might have been more significant in the early stages?
2. You cover population density and urbanization. Would it also be worth combining these into, for example, a Gini coefficient for each country that plots cumulative total of population against cumulative number of square kilometres, starting with the least densely populated square kilometres? This might be a step towards the measures of urban and rural density that you mention. I have no ideal whether the data would be available, and there are probably better measures of clustering of people, but this might be a start.
3. Once this is all over, people are going to ask whether Korea or Taiwan or the UK or Italy or Sweden or someone else had the best approach, for future reference. What is best will probably depend on country-specific factors such as those you highlight, and perhaps some others. I have read that Sweden may get away with its relaxed approach because there are few multi-generational families and Swedes keep physical distance anyway. But it will also be helpful to know which general factors make a difference regardless of such cultural differences. I predict a bright future for your graphs.
Thank you so much for such a comprehensive review! Yes I think you are right. It’s taking up to reporting of 1,000 deaths to get to a stable report of the reproduction rate. Just yesterday the UK gov acknowledged they had misreported during the initial stage. I hadn’t thought of using a measure along the lines of the Gini coefficient. That’s a brilliant idea and I’ll definitely look into it. And yes, I think identifying similar and different attributes for geodemographics, and cultural and social norms as well as the approach taken during the early stages could produce insights for tackling future breakouts.
Thanks again!, I’ll ping you when I have an update on a coefficient-based approach.