Ebola — growth rate of outbreak correlates with poverty

The plot at the end of the previous post has suggested a link between nominal Gross Domestic Product (nominal GDP) and the growth rate of the Ebola outbreak during the exponential stage. I had used the nominal GDP as a proxy for poverty. Thus, the argument was: the poorer the population, the faster the spread of Ebola. Caitlin Rivers had commented that it would be interesting to see such an analysis at the level of counties.

Caitlin and colleagues provide Ebola data at the county or district level. Hence, we need only to find the corresponding socio-economic data at the same level. In fact, The World Bank and the government of Sierra Leone have compiled a report (“A poverty profile for Sierra Leone”, PDF). They derive a handy aggregated poverty measure:

… welfare is measured by aggregate household consumption over the last twelve months. The aggregate incorporates food consumption, non-food consumption, housing, and benefit derived from durable goods. (p.27)

The report presents in Table A2 on p. 36 the number of poor people in each district based on the above poverty measure. I divide this number by the total number of inhabitants of each district to obtain the fraction of poor people as a measure of the poverty of the respective district.

Now let us bring the two sets of data together. First a look at Ebola at the level of districts (Figure 1).

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Figure 1: Accumulated confirmed Ebola cases in the districts of Sierra Leone in August to October 2014. The vertical axis is scaled logarithmically.

Since we are interested in the growth rate during the exponential stage of the outbreak, we have to exclude four districts: Kailahun and Kenema are the two districts with the greatest numbers of confirmed cases, but, obviously, the growth there is no longer exponential but the number has levelled off (top two curves in Figure 1). At the other end of the spectrum are districts Bonthe and Koinadugu, both having (almost) no confirmed cases and thus no exponential growth (bottom two curves). All the other districts show a marked, and approximately exponential growth in September, perhaps with the exception of district Kambia where the first cases occur only in mid-September and the number stays relatively small; hence, I also exclude Kambia.

For the remaining districts I fit exponentials to the points and determine the growth rates. When I first plotted these growth rates against the district poverties, I saw a clear positive trend, but also a remarkable outlier (Figure 2): the Western Area Urban, with the capital Freetown.

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Figure 2: Growth rate of Ebola outbreak in Sierra Leone by district, as a function of district poverty.

In Sierra Leone, Freetown is unique in several respects. For instance, the fraction of poor people is by far the smallest of all districts, while the population density is by far the largest of all districts (Figure 3).

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Figure 3: Population density and poverty in the districts of Sierra Leone. The Western Area Urban (upper left) with the capital Freetown is an outlier in both respects.

Figure 2 suggests a relatively fast spread of Ebola in the Western Area Urban despite the relatively low poverty. This seems to contradict our hypothesis of “greater poverty means faster spread of Ebola”. But it is also obvious that the Western Area Urban with the dominating capital Freetown has an exceedingly high population density, which of course supports the spread of infections. Including this high-population density point in our analysis will partially mask the effect of poverty. Hence, I drop this point, too. This brings us then to our final analysis (Figure 4).

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Figure 4: Ebola growth rate correlates with poverty in the districts of Sierra Leone. Red line is least-squares-fit to the points.

Ebola growth rate and poverty are linearly correlated with an adjusted R^2=0.43. The correlation is significantly different from zero with p=0.047. Although we have not proven a causal connection of poverty and Ebola growth rate, this result is compatible with Ebola feeding on poverty.

Ebola — first signs of a new stage?

In previous posts I had noted that the growth of the current outbreak of Ebola in West Africa had entered an exponential growth phase. Since then there were no new Ebola Disease Outbreak News for West Africa from WHO, but Caitlin Rivers and colleagues kindly provide a rather comprehensive data collection.

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Figure 1: Ebola cases over time during current outbreak in several West African countries. Note that the vertical axis is scaled logarithmically.

The bad news is that the outbreak is still growing, and for Guinea and Sierra Leone we still have exponential growth. But there is also some potentially good news: First, two of the affected countries, Nigeria and Senegal, have reported no new cases for some time now and thus may have managed to contain the outbreak in their areas (see e.g. lower right of Figure 1). Second, in Liberia, the worst affected country, it looks as if the growth rate is slowing down, i.e. we have no longer an exponential growth there. In the logarithmic plot (lower left of Figure 1), this shows up as a development from a straight line in August to a slight curvature in September. Third, in Guinea and Sierra Leone, the gap between infections and deaths increases. This could be due to more effective medical help or to the virus becoming less pathogenic.

Big caveat: It is unclear how reliable the data is. The countries from which the data originate are in a very difficult situation and may not be able to register all Ebola cases and deaths. Thus, the development in Liberia (lower left of Figure 1) may reflect not the course of the epidemic but the collapse of the medical infrastructure.

In an earlier post I have referred to “extreme poverty” as one of the roots of Ebola. In fact, it is possible to find evidence for this, or at least a correlation between poverty and Ebola. Figure 2 shows a map of the world with countries coloured according to Gross Domestic Product (GDP) per capita. In West Africa, there is a cluster of five low-GDP countries (yellow, nominal GDP per capita between 400 US$ and 800 US$). These are also those countries where Ebola could not be contained. The only exception is the small Guinea Bissau, a country with a low GDP where so far no cases have been reported. Senegal and Nigeria, the two countries that have contained the outbreak, have higher GDPs (Senegal 1072 US$, Nigeria 1692 US$).

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Figure 2: Nominal Gross Domestic Product (nominal GDP) per capita in the countries of the world – the brighter the colour, the lower the GDP. The red circle marks the region of the West African Ebola outbreak. The countries worst affected have a particularly low nominal GDP (yellow). Map from Wikipedia.

A related quantitative question is whether the size of the exponential growth rate depends on the degree of poverty. The bottom panel in Figure 3 shows that there is something like a correlation of nominal GDP per capita (based on IMF data taken from Wikipedia) and the growth rate during the exponential phase of the outbreak in each country. Liberia, the country with the highest Ebola growth rate, is also the poorest country, if we accept the nominal GDP per capita as indicator of poverty. GDPs per capita of Sierra Leone and Guinea are higher than those of Liberia, and the growth rates lower than that in Liberia. Senegal and Nigeria are better off with respect to both GDP and Ebola.

Other quantities such as the population density of the Human Development Index (HDI) do not show no clear correlation (top and centre of Figure 3).

Of course, we have only five points here, and therefore these (non-)correlations have to be taken with a huge grain of salt.

Figure 3: Dependency of Ebola growth rate (vertical axes) on various indexes (horizontal axes). The Ebola growth rate is the growth rate during the exponential expansion phase of the epidemic in the respective country. Top panel: Dependency of growth rate on inequality-adjusted Human Development Index (HDI), 2013, as taken from Wikipedia. Centre panel: Dependency of growth rate on population density in 1/km^2  (taken from Wikipedia page of the respective country). Bottom panel: Dependency of growth rate on nominal GDP per capita.

 

Dogs do it, too, while they pee and poo

A dog in the earth’s magnetic field.

Hurray! The 2014 Ig Nobel Prize in Biology goes to a group of researchers led by Hynek Burda from the Department of General Zoology of my faculty, and including colleagues from the Czech Republic. The performance of team members Sabine Begall and Pascal Malkemper at the awards ceremony was breathtaking, literally (you know what I mean if you watch the life webcast after about 52 min). But now a bit about the science. After having found previously preferential alignment with the earth’s magnetic field in grazing cattle, deer, and foxes, they have now studied dogs (see publication). Specifically, they collected thousands of observations of dogs defecating, urinating, and marking their territories, and then correlated the orientation of the dogs with the magnetic field. A statistical analysis showed that dogs indeed also preferentially align with the magnetic field in these situations — if the magnetic weather is calm. So, if you have lost your compass while hiking, watch man’s best friend in the morning, and you regain your orientation. Of course, only if the magnetic weather is calm.

What is significant? The Global Mean Rank Test may bring the answer

Comparison of the Global Mean Rank test with the established tests SAM and LIMMA. The Global Mean Rank test has consistently a low False Discovery Rate (FDR) and a high True Positive Rate (TPR). The performance of the Mean Rank Test is high and relatively robust against different types of data processing.

In the public perception, statistics is at best boring if not dubious. However, many modern scientific methods generate huge amounts of data. To find important information in these data, new statistical methods are needed. For instance, such methods can tell us which genes or proteins are important for a certain disease amongst the many thousands that form just background noise? The Global Mean Rank Test (“MeanRank” for short) is a statistical test that has been developed for such purposes. It is based on a very simple idea: If an element (e.g. a protein, a gene, etc.) turns up very prominently in several comparable experiments which study a certain phenomenon (e.g. a disease), it is probably “significant” for this phenomenon. The authors have implemented this idea in an efficient way, and they could show that MeanRank performs well with real world problems.

PLOS ONE: Identification of Significant Features by the Global Mean Rank Test.