Coronavirus, Covid-19: population density vs mortality

Coronavirus Covid-19: The fallacy of some simple arguments as to why countries differ

There is a lot of discussion about mortality rates, population factors, population density and health systems around in this coronavirus, Covid-19 pandemic. Doubtlessly some are contributing factors but are they on they exclusively so? Their is a certain fallacy of some simple arguments why countries differ in this pandemic. That they differ is obviously not under question but why they differ is a very complex matter, on which doubtlessly many billions will be spent over the coming decades going to the best connected academics in each country.

Please see this paper for detailed analysis on mobility and influenza.

The complex answer is though not what we are after here. We want to have a look at, why simple explanations are often fallacious.

For example explanations like:

“Germany is doing well, besides their high case load,  because xyz.”

Most people think two dimensional. This effects that. But in reality many variablesaffect an outcome unless the signal is very strong.

For example: Pregnant or not pregnant will usually have one cause.

The coronavirus, Covid-19 pandemic will vary about many countries, due to their health systems, population densities, age pyramid, housing situation, preexisting healthy eating habits  and cultural norms and possible many more variables (factors or features).

Let’s have a look at some simple explanations:

Population size adjusted Cases vs Deaths

https://www.worldometers.info/ has a column Cases per Million population and Deaths per Million Population.

Covid-19: cases vs deaths
Covid-19  Coronavirus:Population size adjusted cases vs deaths on the 12 04 2020 with 99% confidence bar and gam  smoother

As we can see there is a relationship but it is not as strong as one would suspect.

Population size adjusted Tests vs Cases

 Covid-19, Coronavirus population size adjusted tests per million vs cases per million population. Data from the 12 04 2020
Covid-19, Coronavirus population size adjusted tests per million vs cases per million population. Data from the 12 04 2020 with 99% confidence bar and gam  smoother

There might be a relationship,  but as we know testing early is key so testing later in an epidemic will take a lot more tests than early in an outbreak.  Testing early would introduce an extra dimension not readily displayable in a 2 D graph.

Population size adjusted Tests vs Deaths

 

Covid-19, Coronavirus population size adjusted tests per million vs deaths per million population. Data from the 12 04 2020
Covid-19, Coronavirus population size adjusted tests per million vs deaths per million population. Data from the 12 04 2020 with with 99% confidence bar and gam  smoother

Here we see the gam smoother is trying to fit something again but it is not a very clear relationship.

From now on I used only European countries as I wanted ICU (Intensive Care Units) per 100.000 population in the analysis and data for all countries listed in the John Hopkins University Github is not available.

Population Density of countries vs population size adjusted Cases

Covid-19, Coronavirus population size adjusted cases per million vs population density. Data from the 12 04 2020
Covid-19, Coronavirus population size adjusted cases per million vs population density. Data from the 12 04 2020 with 99% confidence bar and gam  smoother. Population density from Google and Wikipedia

Also here there are no clear results visible. Population density does not tell you anything clear on how many cases a country will have in this coronavirus, Covid-19 pandemic.

Population Density of countries vs population size adjusted Deaths

Covid-19, Coronavirus population density vs population size adjusted deaths per million vs . Data from the 12 04 2020
Covid-19, Coronavirus population density vs population size adjusted deaths per million vs . Data from the 12 04 2020 with 99% confidence bar and gam  smoother.

There is a slight relationship here but nothing too obvious and we can certainly not rely on it to be the one and only explanation.

Number of ICU beds per 100000 vs population size adjusted deaths (deaths per 1000000)

Now here is a nice graph that looks pretty convincing why Germany is top in low mortality.

icu beds per 100000 population
Intensive Care Units beds per 100000 population
Coronavirus Covid-19 Number of intensive care units per 100000 people vs deaths per million
Coronavirus Covid-19 Number of intensive care units per 100000 people vs deaths per million with 99% confidence bar and gam  smoother

As we can see there is in Europe actually no obvious connection whatsoever.  Belgium for example that has also relatively many ICU units is not doing very well on the number of deaths per population. One could have adjusted the deaths per 1 million to deaths per 100000 but that’s just multiplying them by 10. This has been done but made no difference.

There is apparently NO clear relationship over the countries listed here between the number of ICU beds and the population size adjusted deaths. This can obviously have many reasons from badly trained, or non existent staff, useless equipment, centralised hospitals inaccessible to many in the country side and so on.

Number of ICU beds per 100000 vs mortality

Coronavirus Covid-19 Number of intensive care units per 100000 people vs mortality
Coronavirus Covid-19 Number of intensive care units per 100000 people vs mortality with 99% confidence bar and gam  smoother

Interestingly in Europe there is no obvious link between number of ICU units and mortality.

Population Density of countries vs mortality

 

Coronavirus, Covid-19: population density vs mortality
Coronavirus, Covid-19: population density vs mortality with 99% confidence bar and gam  smoother

Here we are finally getting somewhere. There is actually an effect in European countries densities (how many people live per square km) on mortality in these countries.  Generally one would have assumed that cases would be linked more clearly to a dense population. We are also not talking the number of victims to this virus but mortality.

Like everything in statistics, correlation is not causation. This relationship might be driven by the outliers Belgium and the Netherlands.

Fitting a Gamma GLM brought some results:

Call:
glm(formula = mortality ~ density, family = Gamma(link = "inverse"),
data = hbdf)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.8595 -0.6245 -0.3098 0.2218 1.1039
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 29.15803 4.79049 6.087 1.68e-06 ***
density -0.04690 0.01509 -3.108 0.00441 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for Gamma family taken to be 0.5793202)
Null deviance: 21.303 on 28 degrees of freedom
Residual deviance: 17.592 on 27 degrees of freedom
AIC: -120.38
Number of Fisher Scoring iterations: 6

There are many models but the histogram of mortality and log mortality look look difficult to fit easily to a distribution. Maybe with more work we could eventually get to something if one really desires to show some leet statistics.

mortallity histogram
mortality histogram
log mortality histogram
log mortality histogram
Model fit Residuals vs Fitted, Normal QQ, Scale, Location and Residuals vs Leverage glm( mortality ~ density, hbdf, family = Gamma(link = "inverse"))
Model fit Residuals vs Fitted, Normal QQ, Scale, Location and Residuals vs Leverage glm( mortality ~ density, hbdf, family = Gamma(link = “inverse”))

As we can see from the Residual vs Leverage Plot the Netherlands are quite influential in above model. But the analytics plots show that the model is not really a good fit. We have not enough data for the model to be really any use.

So also here there is not that much to write home about on these single influencing factors, variables or features.

What is important though is:

“In conclusion, the global dynamics of influenza viruses are best explained by combining human mobility data with the spatial information inherent in sampled viral genomes.”

Unifying Viral Genetics and Human Transportation Data to Predict the Global Transmission Dynamics of Human Influenza H3N2

What is important are interactions between people, so population density and mobility will play a role (hence we are asked to isolate), but we need to see that there are also local mobility and local density. Look at Greenland, it has a population density of 0.028/sq km but most people will live in some settlements and not in the freezing cold. In Canada most population is concentrated in the south. So local effects need to be taken into consideration.

Conclusion

Besides the uncertainty that we do not really know if death and case numbers that individual countries give us are correct we can conclude:

Looking at these simple relationships we can see there are no simple answers and if one notices someone, usually very very confident, to push one simple explanation in a politically motivated debate, one should take a step back and evaluate if this person speaks at least with some knowledge or only with confidence without knowledge.